E U R O P E A N OR G A N I Z A T I O N F O R NU C L E A R RE S E A R C H
CERN/AT/95-44 (ET)
CONCEPTUAL DESIGN OF A FAST NEUTRON OPERATED
HIGH POWER ENERGY AMPLIFIER
C. Rubbia, J.A. Rubio, S. Buono1), F. Carminati, N. Fiétier2), J. Galvez, C. Gelès,
Y. Kadi, R. Klapisch, P. Mandrillon2), J.P. Revol and Ch. Roche
Abstract
The basic concept and the main practical considerations of an Energy Amplifier (EA) have been
exhaustively described in Ref. [1]. Here the realisation of the EA is further explored and schemes are
described which offer a high gain, a large maximum power density and an extended burn-up, well in
excess of 100 GW × day/t corresponding to about five years at full power operation with no
intervention on the fuel core. Most of these benefits stem from the use of fast neutrons, as already
proposed in Ref. [2].
The EA operates indefinitely in a closed cycle, namely the discharge of a fuel load, with the
exception of fission fragments, is re-injected in the sub-critical unit with the addition of natural
Thorium to compensate for the burnt fuel. After many cycles an equilibrium is reached, in which the
Actinide concentrations are the balance between burning and “incineration”. The fuel is used much
more efficiently, namely the power obtained from 780 kg of Thorium is roughly the same as the one
from 200 tons of native Uranium and a PWR (33 GW × day/t of burn-up). The probability of a
criticality accident is suppressed since the device operates at all times far away from it. Spontaneous
convective cooling by the surrounding air makes a “melt-down” leak impossible.
An EA module consists of a 1500 MWth unit with its dedicated 1.0 GeV proton accelerator of
12.5 mA. A compact, highly reliable and modular Cyclotron has been designed. A plant may be made
of several such modules. For instance a cluster of three such modular units will produce about
2,000 MWe of primary electrical power. A relevant feature of our design is that it is based on natural
convection to remove the heat generated inside the core. The EA is a large, passive device in which a
proton beam is dumped and the heat generated by nuclear cascades is extracted, without other major
elements of variability. The delivered power is controlled exclusively by the current of the accelerator.
The fuel needs no access during the whole burn-up and it may be kept sealed up as a non-proliferation
safeguard measure. Contrary to Fusion, there are no major technological barriers.
After ≈ 700 years the radio-toxicity left is about 20,000 × smaller than the one of an ordinary
Pressurised Water Reactor (PWR) for the same energy. Geological storage (106 years) is virtually
eliminated or at least strongly reduced [≤ 500 Ci/(GWe × y) after 1000 years]. It could be further
reduced (< 35 Ci) “incinerating” some of the nuclides. Radioactivity dose to individuals truncated to
10,000 years and due to operation is about 1/330 of the one of PWR and about 1/33 of Coal burning.
Geneva, 29th September, 1995
1)
2)
Sincrotrone Trieste, Trieste, Italy
Laboratoire du Cyclotron, Nice, France
2
3
Contents
1.— Introduction. ........................................................................................................... 5
Tables and Figures relevant to Section 1.................................................................. 19
2.— Physics considerations and parameter definition. .......................................... 23
2.1 - Spatial Neutron Distribution. .................................................................... 23
2.2 - EA Uniformisation with a diffusive Medium............................................. 26
2.3 - Numerical example of spatial distributions. . ............................................. 29
2.4 - Fuel breeding............................................................................................... 30
2.5 - Flux dependent effects................................................................................. 32
2.6 - Computing methods.................................................................................... 35
2.7 - Cumulative fission fragment poisoning...................................................... 37
2.8 - Higher Uranium isotopes and other actinides............................................ 38
2.9 - Elementary, analytic formulation of Actinide evolution. ........................... 41
2.10 - Practical considerations. ........................................................................... 42
2.11 - Proliferation issues.................................................................................... 44
2.12 - Burning of different fuels.......................................................................... 45
2.13 - Conclusions............................................................................................... 49
Tables and Figures relevant to Section 2.................................................................. 51
3. —The accelerator complex...................................................................................... 59
3.1 - A three-stage cyclotron facility................................................................... 59
3.2 - Overall design considerations..................................................................... 60
3.3 - The injector cyclotron. ................................................................................ 61
3.4 - The intermediate separated-sector cyclotron (ISSC). ................................. 62
3.5 - The separated-sector booster cyclotron (BSSC). ......................................... 64
3.6 - Beam Transport to the EA. ......................................................................... 65
3.7 - Conclusions................................................................................................. 67
Tables and Figures relevant to Section 3.................................................................. 69
4. —The Energy Amplifier Unit................................................................................. 75
4.1 - Introduction. ............................................................................................... 75
4.2 - Molten Lead as Spallation Target and Coolant. ....................................... 77
4.3 - Corrosion effects due to molten Lead. ......................................................... 79
4.4 - The Proton beam . ....................................................................................... 81
4.5 - Fuel design and Burn-up goals................................................................... 83
4.6 - Core lay-out and main parameters.............................................................. 86
4.7 - Convective Pumping................................................................................... 87
4.8 - Seismic Protection....................................................................................... 90
4.9 - Decay heat removal by natural air convection........................................... 91
4.10 - Miscellanea. .............................................................................................. 93
4.11 - Conclusions............................................................................................... 95
4
Tables and Figures relevant to Section 4.................................................................. 97
5. — Computer simulated operation....................................................................... 105
5.1 - Simulation methods. ................................................................................. 105
5.2 - Simulation of the standard operating conditions...................................... 107
5.3 - Start-up Fuel cycle with “dirty” Plutonium............................................ 111
5.4 - Neutron Spectra and Estimates of the Radiation Damage. ...................... 112
5.5 - Temperature distributions and coolant Flow............................................ 116
5.6 - Safety and Control of Fast Transients. ..................................................... 119
5.7- Compositions at Discharge. ....................................................................... 123
5.8 - Spallation Products................................................................................... 127
Tables and Figures relevant to Section 5................................................................ 129
6. — Closing the Fuel Cycle...................................................................................... 139
6.1 - General Considerations............................................................................. 139
6.2 - Strategy for the Spent Fuel. ...................................................................... 140
6.3 - Fuel reprocessing methods. ....................................................................... 142
6.4 - Spallation induced Radio-nuclides. ......................................................... 146
6.5 - Radio-toxicity emitted in the Environment.............................................. 147
6.6 - Conclusions............................................................................................... 150
Tables and Figures relevant to Section 6................................................................ 151
Acknowledgements. .................................................................................................. 157
References.................................................................................................................... 159
5
1.— Introduction.
The principle of operation of the Energy Amplifier (EA) has been described in
detail in Refs. [1-3]. The present paper is aimed at the demonstration of the practical
feasibility of an EA with power and power density which are comparable to the ones
of the present generation of large Pressurised Light Water Reactors (PWR). This is
only possible with fast neutrons [2].
Greenhouse induced Global Warming concerns related to a massive use of
Fossil Fuels may lead to a new call for nuclear revival. But a much larger share of
energy produced by conventional Nuclear methods (PWR) will sharpen concerns
and enhance many of the problems which must be solved before extending its use.
We believe that most of the criteria for a revival of nuclear power are very tough:
(1) Extremely high level of inherent safety;
(2)Minimal production of long lived waste and elimination of the need of the
geologic repositories;
(3)High resistance to diversion, since latent proliferation is a major concern.
(4)More efficient use of a widely available natural fuel, without the need of
isotopic separation.
(5)Lower cost of the heat produced and higher operating temperature than
conventional PWRs in order to permit competitive generation of substitutes
to fossil fuels [4]. Substitution fuels are necessary to allow a widespread
utilisation of the energy source and to permit retrofitting of existing facilities,
now operating with CO2 producing fuels.
Our design of an EA has these objectives as goals and it is intended as proof
that they can be met fully. The primary fuel is natural Thorium which is completely
burnt after a number of fuel cycles through the EA. Actinides present in the fuel
discharge at the end of a fuel cycle are re-injected in the EA and become the “seeds”
for the subsequent cycle. This ensures a very efficient use of the primary fuel
element1. This objective is identical to the one eventually met by Fast Breeders.
Compared to the consumption of natural fuel material, the EA is about 250 times
more efficient than the present PWRs based on an open fuel cycle.
Nuclear power has successfully developed the methods of retaining large
amounts of radioactivity within the power plant and in isolation with the biosphere.
1
The heat produced burning 70.3 kg of Thorium in the EA is equal to the one of 1 million barrels of oil
6
The limited amount of fuel material of the EA and the sealed, passive nature of the
device further simplifies the realisation of such a concept. The fractions of
radioactivity actually injected in the environment during (1) mining, (2) operation
and (3) reprocessing and refuelling are considered first. Preventive measures to
eliminate unwanted accidents and their possible consequences on the environment
will be considered later on.
The radio-toxicity released by a Thorium driven EA is much smaller than the
one of the PWR related throw-away cycle [1] [2]. In the phase of the fuel extraction
and preparation, it is about 10-3÷10-4 for the same delivered energy, since a much
smaller amount of Thorium is required (0.78 ton vs. 200 tons of Uranium for 3 GW th
× year) in the first place and which is much less toxic to extract [5]. The toxicity
released in form of waste at the back-end of the cycle for Actinides is reduced to the
very tiny fraction lost during fuel re-cycling and reprocessing. Among fission
fragments, excluding the short lived and stable elements, there are a few elements
which are medium lived (τ1/2 ≈ 30 years, 90Sr- 90Y, 137Cs, etc.) and some others (99Tc,
135Cs, 129 I, etc.) which are truly long lived. The policy we propose to follow is to
store in man-watched, secular repositories for several centuries the medium lived in
order to isolate them from the biosphere and to promote a vigorous research and
development of methods of incinerating the bulk of the long lived FFs with the help
of a fraction of the neutron flux of the EA or with dedicated burners [6]. Therefore,
and contrary to the PWR related throw-away cycle, the need for a Geologic
Repository is virtually eliminated.
UNSCEAR [7] has estimated collective radioactivity doses to the population
associated to various forms of energy production. Coal burning emits radioactivity
in fumes and dust, resulting in a typical, collective radiation exposure of 20 man Sv
(GWe y) -1. The practice of using coal ashes for concrete production adds as much as
2.5 × 104 man Sv (GWe y)-1. In the case of the PWR throw-away cycle the estimated
dose is 200 man Sv (GWe y)-1, with the main contribution coming from the mining
and preparation of the fuel2. Accidents which have plagued some of the present
Nuclear Power stations and which are expected to be absent because of the new
features of the EA, have added as much as 300 man Sv (GWe y)-1, bringing the toll of
Nuclear Energy to about 500 man Sv (GWe y)-1. Translating the figures of Ref. [7] to
the conditions of the EA, we arrive at much smaller collective doses, namely 2.75
2The
main nuclide contributions in the nuclear fuel cycle are Radon from Mill Tailings (150 man
Sv/GW/y) and reactor operation and reprocessing (50 man Sv/GW/y). The potential accumulation
of collective radiation doses in the far future from the practice of disposing the long lived waste
(geologic storage) is not included in the UNSCEAR estimates, since it is subject to major uncertainties.
7
man Sv (GWe y)-1 for the local and regional dose and 0.44 ÷ 1.42 man Sv (GWe y)-1
for the global dose, depending on the type of mineral used. The total radioactivity
absorbed by the population is about one order of magnitude smaller than if the same
energy is produced by burning Coal, even if the ashes are correctly handled. In the case
of the Coal option we must add the emissions of pollutants like dust, SO2 etc. and
their toll on the Greenhouse effect.
A novel element of our design is the presence of the proton beam. A recent
experiment has specified the required characteristics of such an accelerator [3]. The
accelerated particles are protons (there is little or no advantage in using more
sophisticated projectiles) preferably of a minimum kinetic energy of the order of
1 GeV. The average accelerated current is in the range of 10 ÷ 15 mA, about one
order of magnitude above the present performance3 of the PSI cyclotron [8]. This
current is lower by one order of magnitude than the requirements of most of the
accelerator-driven projects based on c-w LINAC [9]. In view of the present
developments of high-intensity cyclotrons and the outstanding results obtained at
PSI [8], we have chosen a three-stage cyclotron accelerator. In the design particular
attention has been given to the need of a high reliability and simplicity of operation.
The experience accumulated in the field at CERN, PSI and elsewhere indicates that
this goal is perfectly achievable. The expected over-all efficiency, namely the beam
power over the mains load is of the order of 40%. The penetration of the beam in the
EA vessel is realised through an evacuated tube and a special Tungsten window,
which is designed to sustain safely both radiation damage and the thermal stress due
to the beam heating. As discussed in more detail later on, the passive safety features
of the device can be easily extended to these new elements.
Since the accelerator is relatively small and simple to operate, if more current is
needed, several of these units can be used in parallel, with a corresponding increase
of the overall reliability of the complex. In this case, the beams are independently
brought to interact in the target region of the EA.
For definiteness, in the present conceptual design of the EA we have chosen a
nominal unit capacity of 1500 MW th . This corresponds to about 675 MWatt of
primary electrical power with “state of the art” turbines and an outlet temperature of
the order of 550 ÷ 600 oC. The thermodynamical efficiency of ≈ 45% is substantially
higher than the one of a PWR and it is primarily due to the present higher
temperature of operation. The general concept of the EA is shown in Figure 1.1.
3
An improvement programme is on its way to increase the average current to about 6 mA.
8
The nominal energetic gain4 of the EA is set to G = 120 corresponding to a
multiplication coefficient k = 0.98. The nominal beam current for 1500 MW th is then
12.5 mA × GeV 5. In practice the proton accelerator must be able to produce
eventually up to 20 mA × GeV in order to cope with the inevitable variations of
performance during the lifetime of the fuel. Such accelerator performance is
essentially optimal for a chain of cascading cyclotrons. A significantly smaller
current may not provide the required accelerator energetic efficiency; a higher
current will require several machines in parallel. Hence, this size of the module is
related, for a given gain, to the state of the art of the accelerator. The electric energy
required to operate the accelerator is about 5% of the primary electric energy
production. The choice of k is not critical. For instance an EA with k = 0.96 (G = 60)
can produce the same thermal energy but with a fraction of re-circulated power
about twice as large, namely 10% of the primary electricity, requiring two
accelerators in parallel.
An energy generating module consists of a 1500 MWth unit with its own
dedicated 12.5 mA × GeV accelerator. An actual plant may be made of several such
modules. For instance a cluster of three such modular units will produce about
2,000 MWatt of primary electrical power. Beams from the accelerators can be easily
transported over the site and switched between units: a fourth, spare, accelerator
should be added in order to ensure back-up reliability.
The modular approach has been preferred in several recent conceptual designs
[10] of Sodium cooled fast reactors in the USA (ALMR, American Liquid Metal
Reactor), Japan (MONJOU) and in Russia (BMN-170), for reasons of cost, speed of
construction and licensing. Such modularity permits the use of the devices in
relatively isolated areas. The power plant can be built in a well developed country
and transported to the target area. Decommissioning of the device is also simplified.
The European approach (EFR, European Fast Reactor) is more conservative and is
based on a single, large volume pool for a nominal power in excess of 3,000 MWth.
Such an approach is possible also for the EA. In this case, because of the larger
power, the beams from two accelerators will be simultaneously injected in the core
of the EA. Both designs are robust, cost-effective and they incorporate many features
which are the result of the extensive experience with smaller machines. They are
designed for a number of different fuel configurations and they can easily
4The
energetic gain G is defined as the thermal energy produced by the EA divided by the energy
deposited by the proton beam.
5This notation is justified, since the energetic gain of the EA is almost independent of the proton
kinetic energy, provided it is larger than about 1 GeV.
9
accommodate those appropriate to the EA. We have taken as “model” for our design
many of the features of the ALMR. The ALMR was designed to provide high
reliability for the key safety, including shutdown heat removal and containment. We
intend to follow the same basic design, with, however, the added advantages of (1)
sub-critical operation at all times (2) negative void coefficient of molten Lead (3)
convection driven primary cooling system and (4) non reactive nature of Lead
coolant when compared to Sodium.
The coolant medium is molten natural Lead operated in analogy with our
(Sodium cooled) “models” at a maximum temperature of 600 ÷ 700 oC. In view of
the high boiling temperature of Lead (1743 o C at n.p.t.) and the negative void
coefficient of the EA, even higher temperatures may be considered, provided the fuel
and the rest of the hardware are adequately designed. For instance direct Hydrogen
generation via the sulphur-iodine method [4] requires an outlet temperature of the
order of 800 oC. A higher operating temperature is also advantageous for electricity
generation, since it may lead to an even better efficiency of conversion. Evidently,
additional research and development work is required in order to safely adapt our
present design to an increased operating temperature. In particular the cladding
material of the fuel pins may require some changes, especially in view of the
increased potential problems from corrosion and reduced structural strength. With
these additions the present design should be capable of operating at temperatures
well above the present figures.
A most relevant feature of our design is the possibility of using natural
convection alone to remove all the heat produced inside the core. Convection cooling
has been widely used in “swimming pool” reactors at small power levels. We shall
show that an extension of this very safe method to the very large power of the EA is
possible because of the unique properties of Lead, namely high density, large
dilatation coefficient and large heat capacity. Convection is spontaneously and
inevitably driven by (any) temperature difference. Elimination of all pumps in the
primary loop is an important simplification and a contribution towards safety, since
unlike pumps, convection cannot fail. In the convective mode, a very large mass of
liquid Lead (≈ 10,000 tons), with an associated exceedingly large heat capacity6
moves very slowly (≤ 2.0 m/s inside the core, about 1/3 of such speed elsewhere)
transferring the heat from the top of the core to the heat exchangers located some 20
The heat capacity of liquid Lead at constant pressure is about 0.14 Joule/gram/oC. For an effective
mass of ≈ 10 4 tons=1010 grams and a power of 1.5 GWatt ( full EA power), the temperature rise is of
the order of 1.0 oC/s. The mass flowing through the core for ∆ T ≈ 200 oC is 53.6 tons/sec,
corresponding to some 1.5 minutes of full power to heat up the half of the coolant in the “cold” loop,
in case the heat exchangers were to fail completely.
6
10
metres above and returning at a lower temperature (∆T ≈ – 200 oC) from the heat
exchangers to the bottom of the core.
The geometry of the EA main vessel is therefore relatively slim (6.0 m diameter)
and very tall (30 m). The vessels, head enclosure and permanent internal structures
are fabricated in a factory and shipped as an assembled unit to the site7. The
relatively slender geometry enhances the uniformity of the flow of the liquid Lead
and of the natural circulation for heat removal. The structure of the vessel must
withstand the large weight of the liquid Lead. There are four 375 MW th heat
exchangers to transfer the heat from the primary Lead to the intermediate heat
transport system. They are located above the core in an annular region between the
support cylinder and the walls of the vessel.
The vessel is housed below floor level in an extraordinarily robust cylindrical
silo geometry lined with thick concrete which acts also as ultimate container for the
liquid Lead in case of the highly hypothetical rupture of the main vessel. In the space
between the main vessel and the concrete wall the Reactor Vessel Air C ooling System
(RVACS) is inserted. This system [11], largely inspired from the ALMR design, is
completely passive and based on convection and radiation heat transfer. The whole
vessel is supported at the top by anti-seismic absorbers. Even in the case of an
intense earthquake the large mass of the EA will remain essentially still and the
movement taken up by the absorbers.
The fuel is made of mixed oxides, for which considerable experience exists.
More advanced designs have suggested the use of metallic fuels or of carbides [12].
These fuels are obviously possible also for an EA. We remark that the use of
Zirconium alloys is not recommended since irradiation leads to transmutations into
the isotope 93 Zr, which has a long half-life and which is impossible to incinerate
without separating it isotopically from the bulk of the Zirconium metal. The choice
of the chemical composition of the fuel is strongly related to the one of the fuel
reprocessing method. A relative novelty of our machine when compared to ordinary
PWRs is the large concentration of ThO 2 in the fuel and the corresponding
production of a small but relevant amount of Protactinium. A liquid separation
method called THOREX has been developed and tested on small irradiated ThO2 fuel
samples [13]. The extrapolation from the widely used PUREX process to THOREX is
rather straightforward and this is why we have chosen it, at least at this stage.
Methods based on pyro-electric techniques [14], which imply preference to metallic
7
The shipping weight is about 1500 tons. Removable internal equipment is shipped separately and
installed through the top head.
11
fuels, are most interesting, but they require substantial research and development
work. Since the destination of the Actinides is now well defined i.e. to be finally
burnt in the EA, the leakage of Actinides in the Fission Fragment stream must be
more carefully controlled, since they are the only Actinides in the “Waste”. We have
assumed that a “leaked” fraction of 10-4 is possible for Uranium. The recycled fuel
has a significant radio-activity. We have checked that the dose at contact is similar to
the one of MOX fuels made of Uranium and Plutonium, already used in the Nuclear
Industry.
The average power density in the fuel has been conservatively set to be ρ = 55
Watt/gr-oxide, namely about 1/2 the customary level of LMFBR8 (ALMR, MONJOU,
and EFR). The nominal power of 1500 MW th requires then 27.3 tons of mixed fuel
oxide. The fuel dwelling time is set to be 5 years equivalent at full power. The
average fuel burn-up is then 100 GWatt day/ton-oxide. Since the fissile fuel is
internally regenerated inside the bulk of the Thorium fuel, the properties of the fuel
are far more constant than say in the case of a PWR. As shown later on, one can
compensate to a first order the captures due to fission fragments, operating initially
with a breeding ratio below equilibrium. All along the burn-up, the growth of the
fissile fuel concentration counterbalances the poisoning due to fission fragments.
Therefore neither re-fuelling nor fuel shuffling appear necessary for the specified duration of
the burn-up.
No intervention is therefore foreseen on the fuel during the five years of
operation, at the end of which it is fully replaced and reprocessed. Likewise in the
“all-convective” approach there are no moving parts which require maintenance or
surveillance. In short the EA is a large, passive device in which a proton beam is dumped
and the generated heat is extracted, without other major elements of variability.
Safety and nuclear proliferation are universal concerns. In the case of
conventional Nuclear Power, accidents have considerably increased the radioactivity
exposure of individuals and the population [7]. The total nuclear power generated,
2000 GW × year, is estimated to have committed an effective dose of 400,000 man Sv
from normal operation. Accidents at Windscale, TMI and Chernobyl have added
2000, 40 and 600,000 man Sv respectively. These types of accidents are no longer
possible with the EA concept: Chernobyl is a criticality accident, impossible in a subcritical device and TMI, a melt-down accident, is made impossible by the “intrinsic”
safety of the EA.
8
This choice is motivated by the relative novelty of the “all-convective” approach and the relative
scarce experience with ThO2 , when compared with UO2.
12
A thermal run-off is the precursory sign of a number of potentially serious
accidents. The present conceptual design is based on a swimming pool geometry
where the heat generated by the nuclear cascade is extracted from the core by
convection cooling, completely passive and occurring inevitably because of
temperature differences. . Thermal run-off is prevented, since a significant
temperature rise due for instance to an insufficiency of the secondary cooling loop
and of the ordinary controls will inevitably produce a corresponding dilatation of the
liquid Lead. Because of the slim geometry of the vessel, the level of the swimming
pool will rise by a significant amount (≈ 27 cm/100 oC), filling (through a siphon)
additional volumes with molten Lead, namely :
(1)The Emergency Beam Dump Volume (EBDV), a liquid Lead “beam stopper”
sufficiently massive as to completely absorb the beam some 20 metres away
from the core and hence bring the EA safely to a stop. In the unlikely event that
the beam window would accidentally break, molten Lead will also rise, so as to
fill completely the pipe and the EBDV, thus removing the incoming proton
beam from the core.
(2)A narrow gap normally containing thermally insulating Helium gas, located
between the coolant and the outer wall of the vessel, which in this way becomes
thermally connected to the coolant main convection loop. The outer wall of the
EA will heat up and bleed the decay heat passively through natural convection
and radiation to the environment (RVACS) [11]. This heat removal relies
exclusively on natural convection heat transfer and natural draught on the air
side.
(3)A scram device based on B4C absorbers which are pushed into the core by the
liquid Lead descending narrow tubes. These absorbers anchor the device firmly
away from criticality.
These passive safety features are provided as a backup in case of failure of the
active systems, namely of the main feed-back loop which adjusts the current in order
to maintain constant the temperature at the exit of the primary cooling loop.
Multiply backed-up but simple systems based on current transformers and physical
limitations in the accelerator (available RF power in the cavities, space charge forces,
etc.) sharply limit the maximum current increase that the accelerator can deliver.
Were these methods all to fail, the corresponding increase of temperature will dilate
significantly the Lead, activating the ultimate shut-off of the proton beam from the
accelerator, the emergency cooling and the scram devices, before any limit is
exceeded in the EA.
13
Normally the EA is well away from criticality at all times, there are no control
bars (except the scram devices) and the power produced is directly controlled by the
injected beam current. However in some unforeseen circumstances the EA may
become critical. In itself, this is not an unacceptable though exceptional operation
mode, provided the amount of power produced does not exceed the ratings of the
EA. Indeed even a quite large reactivity insertion is strongly moderated by the large
negative temperature coefficient (Doppler) of the fuel. Since the operating
temperature of the fuel is relatively low, even a rapid increase of the instantaneous
power will increase the temperature of the fuel within limits, large enough, however,
to introduce a substantial reduction of k as to exit from criticality. The safety of
multiplying systems depends to a large extent on fast transients. A kinetic model
dealing with fast transients due to accidental reactivity insertions and unexpected
changes of the intensity of the external proton beam shows that the EA responds
much more benignly to a sudden reactivity insertion than a critical Reactor. Indeed,
no power excursions leading to damaging power levels are observed for positive
reactivity additions which are of the order of the sub-criticality gap. Even if the
spallation source is still active (the accelerator is not shut-off), the power changes
induced are passively controlled by means of the increase of the natural convection
alone (massive coolant response) thus excluding any meltdown of the sub-critical
core.
Any very intense neutron source (≥ 1013 n/s) could in principle be used to
produce bomb grade Plutonium by extensive irradiation of some easily available
depleted Uranium. This is true both for fission and fusion energy generating devices.
We propose to prevent this possibility by “sealing off” the main vessel of the EA to
all except a specialised team, for instance authorised by IAEA. This is realistic for a
number of reasons. The energetic gain of the EA is almost constant over the lifetime
of the fuel, though it changes significantly after a power level variation. Convection
cooling is completely passive and occurring inevitably because of temperature
differences. There are no active elements (pumps, valves etc.) which may fail or need
direct access to the interior of the main vessel. In addition the fuel requires no
significant change in conditions over its long lifetime of five years, since the fissile
material is continuously generated from the bulk of Thorium. The only two
maintenance interventions to be performed are the periodic replacement of the beam
window about once a year and the possible replacement of some failing fuel
elements, performed remotely with the pantograph. Both activities can be carried
out without extracting the fuel from the vessel. We can therefore envisage conditions
in which the EA is a sort of ”off limits black-box” accessed very rarely and only by a
specialised team, for instance authorised by IAEA. The ordinary user (and owner) of
14
the EA will have no access to the high neutron flux region and to the irradiated fuel,
a necessary step towards any diversion which may lead to proliferation or misuse of
the device.
Proliferating uses of the fuel are further prevented by the fact that the fissile
Uranium mixture in the core is heavily contaminated by strong γ-emitter 208Tl which
is part of the decay chain of 232U and by the fact that the EA produces a negligible
amount of Plutonium. As shown later on, a rudimentary bomb built starting with
EA fuel, in absence of isotopic separation, will be most impractical and essentially
impossible to use or to hide.
The EA can operate with a variety of different fuels. Several options will be
discussed in detail in the subsequent sections. A specialised filling can transform
Plutonium waste into useful 233U, for instance, in order to accumulate the stockpile
required at the start-up of the EA. More generally one could envisage a combined
strategy with ordinary PWRs. Presently operating PWRs represent an investment in
excess of 1.0 Tera dollars. It is important to make every possible effort in order to
minimise their impact on the environment and to increase their public acceptability.
A specially designed EA could be used to (1) transform Plutonium waste into useful
233U and (2) reduce the stockpile of "dirty" Plutonium waste. The EA will be initially
loaded with a mixture of Actinide waste and native Thorium, in the approximate
ratio 0.16 to 0.84 by weight. Other Actinides, like Americium, Neptunium and so on
can also be added. The mixture is sub-critical and the EA can be operated with k =
0.96-0.98.
During operation, the unwanted actinides are burnt, while 233U is progressively
produced. The freshly bred 233 U compensates the drop of criticality due to the
diminishing and deteriorating Actinide mixture and the one due to the build-up of
Fission Fragments. A balanced operation over a very long burn-up of up to 200 GW
day/t is thus possible without loss of criticality, corresponding to 5-10 years of
operation without external intervention. The fuel of the EA is then reprocessed, the
233U is extracted for further use. FFs are disposed with the standard procedure of the
EA. The remainders of Plutonium9 and the like, could either be sent to the
Geological Repository to which they were destined or further burnt in the EA,
topped with fresh Thorium. This combination of a PWR and an EA has several
advantages:
The discharge after ≈ 150 GWatt × day/t contains about 50% of the initial Pu, but is highly depleted
of 239Pu (1/5) and 241 Pu(1/4), while other Pu isotopes are essentially unchanged. Am and Cm
isotopes stockpiles are essentially unchanged. Note that the Plutonium is “denatured” of the highly
fissile isotopes, making it worthless for military diversions.
9
15
1) It eliminates permanently some of the Actinide waste of the PWR reducing
the amount to be stored in a Geological Repository.
2) It produces additional power through the EA, thus increasing by about 50%
the energetic yield of the installation.
3) The amount of fissile Uranium, which is by weight about 80% of the
incinerated Plutonium is a valuable asset. It can be used either to start a new,
Thorium operated, EA or it can be mixed with depleted Uranium to produce
more fuel for PWRs. As is well known, 233U is an almost perfect substitute
for 235U in a ratio very close to 1. The yearly Plutonium and higher Actinides
discharge of a typical ≈ 1 GWe PWR operated 80% of the time is of the order
of 300 kg, thus producing via the EA 240 kg of 233U, which in turn can be
used to manufacture ≈ 8 tons of fresh fuel from depleted U with 0.3% 235U
and 3.0 % 233U. This is ≈1/3 of the supply of enriched Uranium fuel for the
operation of the PWR.
We have also considered as an alternative a fast neutron driven EA operated on
Plutonium only, namely without Thorium. Similar schemes, though mostly operated
with thermal neutrons are under consideration at Los Alamos [15], JAERI [16] and
elsewhere [17]. Such potential devices require frequent refills and manipulations of
the fuel, since the reactivity of the Plutonium is quickly deteriorated by the burning
and choked by the emergence of a large relative concentration of FF's. At the limit
one is lead to the "chemistry on line" proposed by the Los Alamos Group [15].
Adding a large amount of fertile Thorium greatly alleviates such problems and the
device can burn Plutonium and the like for very many years without intervention or
manipulation of the fuel, since the bred 233U is an effective substitute to Plutonium to
maintain a viable and constant criticality. In addition FFs are diffused in a much
larger fuel mass. Finally the 233 U recovered at the end of the cycle constitutes a
valuable product.
In principle our method of a Th-Pu mixture could be extended to the operation
of a Fast Breeder used as incinerator [18], however, probably at a much higher cost
and complexity due to the higher degree of safety involved.
We have indicated Thorium as main fuel for the EA since the radio-toxicity
accumulated is much smaller than Uranium and it offers an easier operation of the
EA in a closed cycle. But there are also reasons of availability. Thorium is relatively
abundant on earth crust, about 12 g/ton, three times the value of Uranium [19]. It
ranks 35-th by abundance, just after Lead [20]. It is well spread over the surface of
the planet. In spite of its negligible demand (≈ 400 t/y) the known reserves in the
16
WOCA10 countries are estimated [21] to about 4 × 106 tons (Table 1.1). Adding a
guessed estimate from the USSR, China and so on, we reach the estimate of perhaps
6 × 10 6 tons, which can produce 15,000 TW × year of energy, if burnt in EAs, namely
about a factor 100 larger than the known reserves of Oil or Gas and a factor 10 larger
than Coal. This corresponds to 12.5 centuries at the present world’s total power
consumption (10 TW).
There are reasons to assume that this figure is largely underestimated. Firstly
the demand is now very low and there has been very little incentive to date to search
for Thorium “per se”. Additional resources of any mineral have always been found
if and when demand spurs a more active perspection. The presently exploited
Thorium ores are richer, by a factor 10 ÷ 100, than the ones which are exploitable at a
price acceptable by market conditions applicable to the case of Uranium.
In view of the small contribution of the primary Thorium to the energy cost, one
may try to estimate how the recoverable resources would grow if exploitation is
extended to ores which have a content for instance an order of magnitude smaller,
i.e. similar to the best Uranium ores. Such analysis has been performed for Uranium
[22], assuming that the distribution in the crust follows a "log-normal" (Figure 1.2)
distribution. Other metals for which a better mining history is known, show a
similar trend, though the slope parameter may be different in each case (Figure 1.3).
In the case of Thorium, in absence of better information, we may assume the same
slope as in the case of Uranium. Then, a tenfold decrease in the concentration of the
economically "recoverable" ores 11 would boost reserves of Thorium by a factor of
300, still a small fraction (3 × 10-5 ) of what lies in the Earth crust. Reserves of
Thorium energy would then be stretched to 4.5 million TW × year, corresponding to
≈ 2200 centuries at twice the present world consumption level which can be considered truly
infinite on the time scale of human civilisation.12.
Several other projects have sought the realisation of a “clean” Nuclear Energy.
The project CAPRA [23] focuses on the incineration of Plutonium in a Fast Breeder.
On a longer time scale, Fusion holds the promise of a “cleaner” energy. Amongst the
various projects, Inertial Fusion offers the largest flexibility in design of the
combustion chamber and hence the best potentials of reduction of the activation
10This
stands for World Outside Centrally Planned Activities.
remark that even this 10-fold decrease would make these minerals somewhat more concentrated
than the 2000 ppm "high content ores" used today for Uranium.
12In order to estimate the magnitude of the error in such a “prediction”, we note that the somehow
extreme cases of Tungsten and of Copper have boost factors of 500,000 and 40 respectively. But even
the lower limit of Copper predicts ≥ 300 centuries at twice the today’s world consumption.
11We
17
effects due to neutrons [24]. But neither inertial nor magnetic fusion have so far
achieved ignition13. We have compared the activity of the remnants (Ci) of the EA
with the one of the CAPRA project and of two of the Inertial Fusion concepts, namely
LIBRA [25] and KOYO [26] in which the greatest care has been exercised to reduce
activation. In order to make the comparison meaningful we have to take into account
that the published values of activation for fusion are given in Ci after shut-down and
40 years of operation. Therefore the activities quoted for the fission case (CAPRA,
EA) have been normalised to the same scenario, namely counting the total activity of
remnants (sum of all fuel cycles, in the case of EA excluding recycled fuel) after 40
years of continued, uninterrupted operation. Activities have been normalised 1 GW
of electric power produced (Figure 1.4).
After the cool-down period in the secular repository ( ≈ 1000 years) the activity
of the remnants (40 years of operation) stabilises at levels which are : 1.7 × 10 7 Ci for
CAPRA, 2.35 × 10 4 Ci for LIBRA, 900 Ci for KOYO and 1.3 × 104 Ci for the EA
without incineration. With incineration we reach the level of 950 Ci, out of which
about one half is due to 14 C. The activation for unit delivered power of the EA
without incineration is comparable to the one of LIBRA concept whilst with
incineration we reach a level which is close to the one of KOYO concept based on
second generation design of the combustion chamber. The expected doses after
1000 years of cool-down from Magnetically Confined Fusion are typically three order
of magnitude larger than the quoted values for Inertial confinement due to
substantial differences in the neutron spectra. This improvement is mainly due to the
moderation of neutrons in the blanket consisting of LiPb liquid circulating through
SiC tubes, before they hit the first wall [24]. Therefore we conclude that the EA concept
can reach a level of “cleanliness“ which is well in the range of the best Fusion conceptual
designs.
From the point of view of cleanliness, as well as for the other major goals —
namely non-criticality, non-proliferation and inexhaustible fuel resources — the EA
matches fully the expectations of Fusion. But like CAPRA — which however is about
1000 times less effective in eliminating radioactive remnants — the EA has no major
technological barriers, while in the case of Fusion, major problems have to be solved.
13
The project ITER is aimed at demonstrating Ignition in magnetically confined fusion, presumably
circa 2005. The new large megajoule range optical LASERs in development at Livermore and in
France have the potential for ignition with inertial fusion.
18
19
Table 1.1 - Thorium resources (in units of 1000 tons) in WOCA (World Outside
Centrally Planned Activities) [21]
Reasonably
Assured
Additional
Resources
Total
Europe
Finland
Greenland
Norway
Turkey
Europe Total
54
132
380
566
60
32
132
500
724
60
86
264
880
1290
America
Argentina
Brazil
Canada
Uruguay
USA
America total
1
606
45
1
137
790
700
128
2
295
1125
1
1306
173
3
432
1915
Africa
Egypt
Kenya
Liberia
Madagascar
Malawi
Nigeria
South Africa
Africa total
15
no estimates
1
2
no estimates
18
36
Asia
India
Iran
Korea
Malaysia
Sri Lanka
Thailand
Asia total
Australia
6
18
no estimates
no estimates
343
19
Total WOCA
1754
280
no estimates
20
9
no estimates
no estimates
309
319
30
no estimates
no estimates
no estimates
30
2188
295
8
1
22
9
29
115
479
319
30
22
18
4
10
403
19
4106
This compilation does not take into account USSR, China and Eastern Europe. Out of
23 listed countries, six (Brazil, USA, India, Egypt, Turkey and Norway) accumulate
80% of resources. Brazil has the largest share followed by Turkey and the United
States.
20
21
Figure Captions.
Figure 1.1
General lay-out of the Energy Amplifier complex. The electric power
generated is also used to run the Accelerator (re-circulated power ≤ 5%).
At each discharge of the fuel (every 5 years) the fuel is "regenerated".
Actinides, mostly Thorium and Uranium are re-injected as new fuel in
the EA, topped with fresh Thorium. Fission fragments and the like are
packaged and sent to the Secular repository, where after ≈ 1000 years
the radioactivity decays to a negligible level (see Figure 1.4). For
simplicity the option of incinerating long-lived fragments is not shown.
Figure 1.2
Estimated amount of Uranium mined as a function of the concentration
of metal in the ores.
Figure 1.3
Cumulative amount of metal mined for different metals as a function of
the ore concentration of metal.
Figure 1.4
Accumulated activity of Remnants as a function of the time elapsed after
shutdown for a number of conceptual projects aiming at minimising the
radio-active waste. CAPRA [23] is based on Fast-Breeders similar to
Super-Phenix. LIBRA [25] and KOYO [26] are Inertial Fusion devices
(ICF). The EA concept with and without incineration of long-lived FFs
can reach a level of “cleanliness“ which is well in the range of the best
Fusion conceptual designs. Activities in Ci are given for 40 years of
operation. According to Ref. [24] Magnetically confined Fusion in
general produces activation which are up to three order of magnitude
larger than ICF.
22
( 30 MW )
(27.6 t)
(24.7 t)
(2.9 t)
(2.9 t)
VD, pegmatites,
unconformity deposits
Vein
deposits (VD)
Fossil placers,
sandstones
Fossil placers,
sandstones
Volcanic deposits
Black shales
Shales, phosphates
Granites
Average crust
Evaporites, siliceous,
ooze, chert
Oceanic igneous crust
Ocean water
Fresh water
Zinc
Lead
Copper
Chromium
Molybdenum
Mercury
Uranium
Tungsten
Accumulated Activity after 40 years of continuous Operation
Linear scale
Log scale
CAPRA Project
(Fission)
LIBRA Project
(Inertial Fusion)
EA -This Paper
(No Incineration)
KOYO Project
(Inertial Fusion)
EA - This Paper
(With Incineration)
EA - This Paper C-14
(2.9 grams/year)
23
2.— Physics considerations and parameter definition.
2.1 - Spatial Neutron Distribution. While the neutron distribution inside a Reactor
is determined primarily by the boundary conditions, in the EA the geometry of the
initial high energy cascade is dominant. The two spatial distributions are expected to
differ substantially. The flux distribution is of fundamental importance in order to
determine the generated power distribution and the uniformity of the burning of the
fuel, both of major relevance when designing a practical device.
We shall consider first, in analogy to a Reactor a simple, uniform fuelmoderator medium operated away from criticality [27]. It turns out that in such
"reactor like" geometry, the neutron flux non uniformity associated to sub-critical
regime14 may be so large as to hinder the realisation of a practical device. A radically
different geometry, described in paragraph 2.2, can be used to solve this problem.
We neglect the fine structure of the sub-critical assembly and consider a
fictitious material with uniform properties. We assume no reflector and therefore the
EA is a uniform block of specified size. The high energy beam interacts directly with
the fuel material. The basic diffusion equation for the neutron flux for monoenergetic or thermal neutrons in a steady state is
D∇ 2 φ − Σ a φ + S = 0
where S is the source term, namely the rate of production of neutrons per cm 3 per
second, D = Σ s / 3Σ 2 is the diffusion coefficient and Σ, Σ s and Σ a respectively the
macroscopic total, elastic and absorption cross sections, all homogenised over the
fuel-moderator mixture. This formula is strictly applicable only to mono-energetic
neutrons of velocity v and then only at distances greater than two or three mean free
paths from boundaries.
Let k∞ be the number of neutrons produced at each absorption in the fuelmoderator mixture. The source term is decomposed in two parts, namely
S = k∞ Σ a φ + C where the first term is due to fission multiplication in the fuel and the
second is the inflow of neutrons (per cm 3 and second) emitted by the high energy
cascade. Upon dividing by D and rearranging terms the diffusion equation becomes
14
As shown later on, a subcritical device far from criticality has a neutron flux distribution which is
exponentially falling from the target region, while a critical reactor has the well known cos-like
distribution. The exponential is obviously falling very fast and the burn-up is therefore highly non
uniform and concentrated around the beam area.
24
∇2φ −
C
1 − k∞
φ+ =0
2
D
Lc
[1]
where L2c is equal to D /Σ a. Boundary conditions are determinant. The neutron
density at the outer boundary of the medium is quite small. It cannot be exactly zero
because neutrons diffuse out of the medium. In analogy with Reactor theory [27] we
shall use the boundary condition that at the extrapolated distance d = 2 / 3Σ s from
the boundaries of the medium the flux must vanish, φ = 0 .
r
In order to solve Eq. [1] we find it useful to introduce a new function ψ ( x)
r
where x ≡ (x, y, z) which is defined by the following differential equation, in which
only the geometry of the device is relevant:
r
r
∇ 2 ψ ( x) + B2 ψ ( x) = 0
[2]
r
The boundary conditions ψ ( x) = 0 at the extrapolated edges introduce a quantization
r
in the eigen-values of B2 and the corresponding eigen-functions ψ ( x) . Therefore we
have a numerable infinity of solutions.
For instance in the case of rectangular geometry, namely a parallelepiped with
r
dimensions a, b, c and origin at one edge, such as ψ ( x) = 0 for the planes x = a, x = 0,
y = b, y = 0, and z = c, z = 0, we find
r
8
πx
πy
πz
ψ l,m,n ( x) =
sin l sin m sin n
abc
a
b
c
l 2 m2 n2
2
= π2 2 + 2 + 2
Bl,m,n
a
b
c
Analogue expressions can be given for different geometries. The eigenr
functions ψ ( x) are normalised to one and constitute a complete ortho-normal set.
Hence it is possible to express any function as the appropriate series of such eigenfunctions, provided the boundary conditions are the same. In particular the high
r
energy neutron source C( x) produced by the beam interactions (zero outside, in
order to satisfy boundary conditions) is expanded to
r
r
1
r
r
ψ l,m,n ( x)C( x)dV
where cl,m,n =
C( x) = D∑ cl,m,n ψ l,m,n ( x)
∫
D volume
l,m,n
It is then possible to express the neutron flux as a series expansion with the help of
Eq. [1] and of Eq. [2]:
c
r
r
1 − k∞
where
Γ=
φ ( x) = ∑ 2 l,m,n ψ l,m,n ( x)
[3]
2
L
B
+
Γ
c
l,m,n
l,m,n
Note that the only parameter which is not geometry related is Γ. The criticality
condition can be defined as a non zero flux for the limit of cl,m,n → 0. Therefore one
2
of the denominators Bl,m,n
+ Γ of Eq. [3] must vanish, which of course implies Γ < 0 or
2
equivalently k∞ > 1. The smallest value of Bl,m,n
and therefore the smallest value of
k∞ which makes the system critical occurs for l = m = n = 1, namely the fundamental
25
mode of Eq. [2]. This result exhibits the well known sinusoidal distribution of the
neutron flux of a Reactor and the classic condition for criticality, k∞ − 1 = B02 L2c , where
B02 is the “buckling“ parameter.
2
The significance of Bl,m,n
is further illustrated if one considers the neutron
(i)
(i)
absorption and escape rates or probabilities for the mode i ≡ (l, m,n), Pabs
and Pesc
respectively. Let us consider a case in which the i-th eigen-mode of the wave
function is dominant. It is easy to show that
(i)
(i) D
(i) 2 2
Pesc
= Pabs
Bi2 = Pabs
Lc Bi
Σa
where Lc is the (already defined) diffusion length. The (small) escape probability for
(i)
each mode Pesc
is then simply equal to Bi2 in units of the inverse of the square of the
diffusion length. Note that since Bi2 is a rapid rising function of the mode i, higher
modes escape much more easily from the volume. Therefore the containment of the
cascade is improved if the source geometry is such as to minimise the excitation of
the higher eigen-modes.
This interpretation of Bi2 makes also more transparent the classic condition for
criticality of a Reactor, k∞ − 1 = B02 L2c . Evidently in order to have criticality, the number
of neutrons produced at each absorption k∞ must exceed 1 precisely by Pesc ≈ L2c B02 ,
the fraction of neutrons escaping the active volume. To extend this formula to the EA
it is then natural to introduce the mode dependent multiplication coefficient
ki = k∞ − L2c Bi2 , in which the escape probability has been taken into account. In the
case of the fundamental mode, the corresponding k-value has the classic significance
of the Reactor Theory. This makes even more transparent the significance of the
denominator of Eq. [3], which becomes
1
1
Bi2 + Γ = 2 ( L2c Bi2 + 1 − k∞ ) = 2 (1 − ki )
Lc
Lc
We can then re-write Eq. [3] as
c
r
r
φ ( x) = L2c ∑ l,m,n ψ l,m,n ( x)
1 − kl,m,n
l,m,n
where the “(1-k) enhancement” of each mode is further emphasised. The formula can
be used to readily calculate the neutron flux distribution in the uniform EA starting
from the known initial cascade distribution.
In contrast with the case of the critical reactor in which only the fundamental
mode is active, any reasonable source configuration in an EA will excite a large
number of different modes, each with its different criticality coefficient k i. The
2
neutron distribution will be wider than the source distribution only because Bl,m,n
grows with increasing order and therefore expansion coefficients are indeed different
26
from cl,m,n . In general the distribution of neutrons inside a uniform medium operated
as an EA reasonably far from criticality will remain strongly non uniform. One can
show that far from the source it decays approximately exponentially rather than
having the characteristic cos-like shape of a Reactor.
Since the neutron inventory is very critical, the neutron containment inside the
EA must be as complete as possible. Inevitably this implies a large fraction of the
volume with a low neutron flux and hence with a small specific energy production.
An EA made of a uniform volume of fuel with the beam interacting in the central
region will therefore be highly impractical.
2.2 - EA Uniformisation with a diffusive Medium. One can overcome this difficulty
by embedding discrete fuel elements in a large, diffusing medium of high neutron
transparency. In Figure 2.1 we show the capture cross sections at the typical energy
of the neutrons in the EA as a function of the element number. One can remark very
pronounced dips, which are due to the occurrence of closed shell in the nuclei. This
is why their “nuclear reactivity” is minimal. These dips are somehow the equivalent
of the Noble Gases in the atomic shell structure. The unique properties of the Lead
and Bismuth are evident. The uniformisation of the fuel burn up is then ensured by
the long migration length of the diffusing medium. Since the present design of the
EA is based on fast neutrons, the medium must have also a very small lethargy, i.e. a
high atomic number. Two elements appear particularly suited: Lead and Bismuth.
In general Lead will be preferable because of its lower cost, smaller toxicity and
smaller induced radioactivity. Both elements have the added advantage that the
neutron yield of the high energy beam is large: the same medium can therefore be the
high energy target and the diffuser at the same time.
While 209 Bi is a single isotope, natural Lead is made of 204 Pb (1.4 %), 206Pb
(24.1%), 207Pb (22.1 %) and 208Pb (52.4 %), which have quite different cross sections.
Isotopically enriched 208 Pb would be very attractive because of its smaller capture
cross sections. However, we shall limit our considerations to the use of natural Lead.
Assume a large, uniform volume made of Lead, initially without fuel elements.
The proton beam is arranged to interact in the centre, producing a relatively small,
localised source of spallation neutrons. The solution of the diffusion equation (Eq. (2)
in the case of an infinite diffusing medium and a small source of strength Q(n/s) is
given by [27]:
27
Q e−κr
Qκ e − κ r
=
4 πD r
4 πD κr
where D is the diffusion coefficient and κ the reciprocal of the diffusion
length with (κ 2 = Σ abs / D ). In the case of Lead, D is very small (D ≈ λ s/3 ≈ 1.12 cm)
and 1/κ very large, about 1 metre, the exact values depending on the energy
dependent cross sections. Neutrons will then fill a very large volume of few
1/ κ units and they will execute a brownian motion, stochastically "stored" in the
medium by the very large number of diffusing collisions.
φ (r) =
Spallation neutrons above a few MeV are rapidly slowed down because of the
large (n,n') cross section. Once below threshold (≈ 1 MeV), the well known slowingdown mechanism related to elastic collisions takes over. The logarithmic average
energy decrement for Pb and Bi is very small ξ = 9.54 × 10 -3 and the mean number of
collisions to slow down the neutron for instance from 1 MeV to 0.025 eV (thermal
energies) is very large, ncoll = ln(1 MeV/0.025 eV)/ξ = 1.8 × 103 . The elastic cross
section, away from resonances is about constant, around 10 b corresponding to a
scattering mean free path of λs = 3.38 cm (700 °C). The total path to accumulate ncoll
is then the enormous path of 62 metres! The actual average drift distance travelled is
of course much smaller, of the order of 1 metre, since the process is diffusive.
During adiabatic moderation, the neutron will cross in tiny energy steps a
resonance region, located both for Pb and Bi in the region from several hundred KeV
to few KeV. We introduce the survival probability Ps (E 1 , E2 ), defined as the
probability that the neutron moderated through the energy interval E1 → E 2 is not
captured. The probability that a neutron does not get captured while in the energy
interval between E and E + dE is [1 – (Σabs/(Σabs+Σsc)) (dE/Eξ)] where Σsc and Σabs
are the macroscopic elastic scattering and absorption cross sections. Evidently such
probability is defined for a large number of neutrons in which the actual succession
of energies is averaged. Combining the (independent) probabilities that it survives
capture in each of the infinitesimal intervals, Ps(E1, E2) is equal to the product over
the energy range:
E2
1 E1 Σ abs dE
I
dE
Σ abs
Ps (E1 , E2 ) ≅ ∏ 1 −
= exp – res
= exp – ∫E2
Σ sc + Σ abs E
Σ sc + Σ abs ξ E
ξ
E1
ξ
where the resonance integral Ires is defined as
Σ abs dE
E2 Σ + Σ
sc
abs E
Ires = ∫
E1
If the cross sections are constant, the integral is easily evaluated
Σ abs
1 E1
Ps (E1 , E2 ) = exp −
ln
Σ sc + Σ abs ξ E2
28
which evidences the large enhancement factor due to the slow adiabatic process,
ln(E1/E 2 )/ξ = 104.8ln(E1/E 2 ) with respect to a single scattering. For instance, if
E1/E2 = 50, the effective value of the absorption cross section Σ abs is increased by a
factor 410. The values of the resonance integral Ires for the Lead isotopes are given in
Table 2.1 for E1= 1.0 MeV and several final energies E2. Natural Lead and Bismuth
have similar properties, while a pure 208 Pb will be vastly superior. The temperature
coefficient of the survival probabilities is (slightly) negative, since Doppler
broadening increases the extent of the resonances. About 20% of the fission neutrons
are absorbed in pure diffusing medium before they reach an energy of 100 keV,
which is the typical energy in a practical EA. In reality the presence of a substantial
amount of fuel in the EA will reduce such a loss: typically one expects that about 5%
of the neutrons will end up captured in the diffusing medium.
Let us assume that a localised, strongly absorbing fuel element is introduced in
the diffusing medium. The effects on the flux due to its presence will extend over a
volume of the order of the migration length, as one can easily see describing the
localised absorption as a "negative source". Hence one can in a good approximation
use averaged properties for a diffuser-fuel region.
In a fuel-diffuser mixture with a relatively small concentration η of fissile
diff
fuel
The survival
material,
Σ sc ≈ Σ diff
whilst Σ abs ≈ η Σ abs
= η(Σ n,fuelγ + Σ fuel
sc
fiss ) >> Σ abs .
probability is therefore strongly reduced, namely due to the large probability of
absorption in the fuel. Adding fuel elements in the otherwise "transparent" medium
makes it "cloudy". Evidently a large fraction of the absorptions will occur in the fuel
even if in relatively small amounts, because of the very high transparency of the pure
medium.
Once the capture in the added materials becomes dominant, a larger fuel
concentration with respect to the diffuser concentration implies an earlier neutron
capture and hence a higher average neutron energy. This leaves a large freedom in
the quantity of fuel to be used, depending on the power required for the application.
An analytical analysis of such a composite system is necessarily approximate,
lengthy and outside the scope of the present paper. For more details we refer to Ref.
[28]. (The actual behaviour of some specific designs will be derived with the help of
numerical calculations).
The conceptual design of the diffuser driven EA consists of a large volume of
diffusing medium in which one can visualise a series of concentric regions around
the centre, where the proton beam is brought to interact (Figure 2.2):
29
i) A spallation target region, in which neutrons are produced by the high energy
cascade initiated by the proton beam. This region is made of pure diffuser.
The proton beam is brought in through an evacuated pipe and a thin
window.
ii) A buffer region, again of pure diffuser in which neutrons are migrated and the
energy spectrum is softened by the (n,n') reactions. This ensures that the
structural elements (fuel assembly) is not exposed to high energy neutrons
from the proton beam which may produce an excessive radiation damage.
iii) A fuel region in which a series of discrete fuel elements are widely
interspersed in the diffusing medium. The outer part of the fuel region can
be loaded with non-fissile materials to be bred (breeder region).
vi) A reflector region made of pure diffuser, with eventually an outer retaining
shield, which closes the system, ensuring durable containment of neutrons.
In order to ensure appropriate containment, the Lead or Bismuth volume must
be of the order of 2000÷3000 tons, arranged in a sort of cylinder or cube of some 6 m
each side. Since the neutron containment is essential, this order of magnitude of
diffuser volume is required in all circumstances. The amount of fuel to ensure
dominance of the capture process needs instead to be much smaller. A realistic EA is
already possible with 6-7 tons of fuel, corresponding to a ratio fuel/diffuser η ≥ 2.5
10 -3 . On the other hand larger fuel amounts are possible for large power
applications. From the point of view of the neutronics, η ≤ 0.01 is ideal. The neutron
leakage out of the diffuser is then typically less than 1% and the fraction of captures
in the Lead nuclei of the order of 4 ÷ 6%, i.e. much smaller than in the case of a pure
diffuser.
2.3 - Numerical example of spatial distributions. .In order to evaluate the actual
neutron flux distribution in practical cases, analytic calculations are either too
approximate or too cumbersome. It is preferable to use the Montecarlo computer
method described in paragraph 2.6. The burn-up radial distribution for three
different values of k and a typical EA geometry15 of Figure 2.2 has been calculated
with the full Montecarlo method (see paragraph 2.6) and it is shown in Figure 2.3.
The value of k has been varied changing the pitch of the hexagonal fuel lattice and
hence the fuel density. One can see clearly how the neutron flux distribution changes
from exponential for k=0.95 (pitch 1.40 cm) to an almost perfect cos-like distribution
15The
outer radius are as follows: Spallation Target and Buffer: 40 cm, Main core and
Breeder : 1.67 m. The height of the core is 1.5 m and the containment box a cylinder of 6 m diameter
and 6 m high. The fuel is a compact hexagonal lattice with fuel pins as described in Table 4.4. The fuel
is made of ThO2 with 10% by weight of 233UO 2 . The cladding is made of HT-9, low activity steel.
30
for k = 0.99 (pitch 1.138 cm), indicating the emerging dominance of the fundamental
mode. At k = 0.98 (pitch 1.243 cm) which is the chosen working point for our
conceptual design, one is somehow in a transitory region. The concavity of the curve
passes through a zero and a linear fit is a good approximation.
A number of different machine geometries have been explored in order to
assess the effects of higher modes in a more general way. In general one can say that
lowering the k produces a faster decay in the exponential mode, in agreement to what
is found in the elementary theory. The actual transition value of k from pure
exponential to linear and eventually to cos-like depends on the geometry of the
spallation source and of the core. A geometry with several spallation sources
(beams) or a widely diffused source can be beneficial in order to improve the
uniformity, especially if the source distribution follows a symmetry pattern such as
to cancel the contribution of the most offending higher modes.
2.4 - Fuel breeding. For many reasons illustrated for instance in Ref. [1], the by
far preferred fertile material is 232Th, although applications based on other Actinides
are of interest for burning Plutonium, depleted Uranium and similar surpluses.
Neutron captures in the fertile element lead to production of fissile material. The
main chain of events for 232 Th is then
−
−
,22 m
,27.0 days
232
→ 233Pa β
→ 233U
γ → 233Thβ
Th + n
In steady neutron flux conditions, the chain will tend to an equilibrium, namely in a
situation in which each fissioned 233 U nucleus is replaced by a newly bred fuel
nucleus. To a first order, the equilibrium condition can be summarised by the
equations:
N( 232 Th)σ γ ( 232 Th)φ = N( 233Pa) / τ( 233Pa→ 233U) = N( 233U)σ fiss+ γ ( 233U)φ
where cross sections are averaged over the neutron spectrum of integrated flux φ.
Such a "breeding" equilibrium is naturally attained with a specific value of the
fuel/breeder concentration ratio determined solely by the ratio of cross sections
σ γ ( 232 Th)
N( 233 U)
ξ = 232
=
N( Th) σ fiss + γ ( 233U)
This equation assumes no alternatives besides the main chain, justified as long as the
rate of neutron captures by 233Pa competing with natural decay is kept negligible
with a sufficiently low neutron flux. This is the "decay dominated" regime [1] in
contrast with the high flux, "capture dominated" regime investigated by Bowman et
al [15] where the 233Pa must be quickly extracted to avoid capture.
The breeding ratio at equilibrium is about ξ =1.35×10-2 for thermal energies and
it rises to ξ = 0.126 for fast neutrons and cross sections of Table 2.2. An EA based on
31
fast neutrons (F-EA) will then require a fuel concentration which is about nine times
the one of a device based on fully thermalised neutrons (T-EA). However, it can
operate with much higher burn-up rates and hence the total mass of fuel is
correspondingly reduced: for the same output power, the stockpiles of 233 U are in
general comparable.
During the actual burn-up of the fuel following an initial fuelling, the
equilibrium equation above is only approximately attained, since the concentration of
the bulk, fertile material is decreasing with time. Solving the related Bateman
equations with an initial breeding material exposed to a constant neutron flux shows
that correction terms have to be introduced to the asymptotic value of the breeding
ratio16:
σ γ ( 232 Th)
σ γ ( 232 Th)
N ( 233 U )
1
=
=
+
ξlowflux
N ( 232 Th) σ fiss + γ ( 233U ) σ fiss + γ ( 233U )
ξ=
(
N( 233 U)
= ξ lowflux 1 + φσ γ ( 232Th)τ( 233Pa→ 233U)
232
N( Th)
)
The first correction is negligible for a T-EA, but it increases significantly (by 10%) the
breeding equilibrium of the F-EA. The second, flux dependent term is smaller but
not negligible ( ∆ξ = 0.31× 10-3 for a burn-up rate ρ = 60 W/g and cross sections of
Table 2.2) and it compensates partially the flux dependent losses due to captures of
the intermediate state 233Pa.
The energetic gain G, namely the energy produced in the EA relative to the
energy dissipated by the high energy proton beam is given by the expression [1]
G
2Go
G= o =
1 – k 2 – η(1 – L )
where Go is the gain proportionality constant, typically 2.4 ÷ 2.5 for a well designed
EA; k is the fission-driven multiplication coefficient k = η(1 – L ) / 2 ; L is the sum of
fractional losses of neutrons (absorbed in a variety of ways, like captures in
structures and coolant, in fission-product poisons, diffused outside the EA and so
_
on); η is the (spectrum averaged) number of fission neutrons produced by a neutron
absorbed in the fissile isotope17. The parameter η (E) has a rather complicated
neutron energy dependence, with a somewhat lower value in some parts of the
resonant region, before rising to larger values for fast neutrons.
16In our treatment we do not include the captures in 233Pa, which of course are also a rate dependent
effect. These losses are instead counted in L.
17This equation is easily worked out realising that at the breeding equilibrium the number of neutron
captures in 233U and in 232 Th at each generation must be the same and normalised to 1 neutron are
equal to (1–L)/2, since, by neutron conservation, [captures in 233 U] + [captures in 232 Th] + [Losses]= 1
= (1–L)/2+(1–L)/2+L = 1. As the number of next generation neutrons η(1–L)/2 generated by 233U
fissions is also, by definition, the multiplication coefficient k, we conclude that k = η(1–L)/2.
32
As is well known, in order to achieve criticality the denominator must become
zero, η = 2 / (1 – L ) . More precisely, criticality is achieved when neutron losses are
reduced to the value Lcrit = 1 − 2 / η . Note that since L > 0 in order to reach criticality
_
η > 2, one neutron being required to maintain the chain reaction and the second
being absorbed by the fertile material.
The F-EA has the advantage, when compared to a T-EA that it operates in a
_
region where η is significantly larger. In addition because of the higher energies,
additional neutrons are produced at each generation by different processes, like for
instance fast fissions in the fertile material 232Th and (n,2n) reactions in the fuel and
the moderator. In order to take into account these contributions it is customary to
_
_
replace the parameter η with η ε where ε (fast fission factor) is the ratio of all
neutrons produced to the ones from the main fission reaction. For a F-EA we expect
_
η ε ≈ 2.4 ↔ 2.5, conveniently and significantly larger than 2 and larger than
_
η ε ≈ 2.1 ↔ 2.2 [2] appropriate for a T-EA. The larger allowance for losses (f.i.
Lcrit = 1 − 2 / ηε = 0.167 ↔ 0.200 vs. Lcrit = 0.048 ↔ 0.091 ) is an important asset of the
F-EA, even if operation is always with L > Lcrit . As discussed in more detail later on,
these extra neutrons do not necessarily have to be thrown away: they may for
instance be used to breed additional fuel or to eliminate radio-toxic substances [6]. It
is also convenient to start operation of a F-EA with a 233U concentration smaller than
the one corresponding to the breeding equilibrium. During operation, the increase of
criticality due to the build-up of the 233 U relative concentration can be used to
compensate growing neutron losses due to captures by fission fragments, thus
ensuring a more uniform gain during a longer period of operation without
interventions.
2.5 - Flux dependent effects. It has been pointed out [1] that there are sharp
limitations to the neutron flux at which an EA can operate in acceptable conditions.
The power produced is directly proportional to the neutron flux. We define with
ρ the specific power, in units of thermal Watt produced by one gram of Thorium in
fuel18. At the breeding equilibrium the fluxes for thermal and fast neutrons are given
by
ρ −2 −1
ρ −2 −1
cm s ; φ fast = 3.88 × 1013 ×
φthermal = 1.80 × 1012 ×
cm s
W / g
W / g
18
In this chapter we define the power density with reference to the main Thorium content, unlike the
rest of the paper where we have taken as reference the unit weight of the actual chemical mixture of
the fuel.
33
where for the latter we have used the cross sections of Table 2.2. Let us estimate
some orders of magnitude. For thermal neutrons (E = 0.025 eV), a power of ρ = 15.0
W/g corresponds to a flux φ = 2.7 × 1013 cm-2 s-1, which is considered optimal for a TEA [1]. In practice the flux in a T-EA will depend somewhat on the energy spectrum
of the neutrons, which in turn depends on the operating temperature of the device
and on the choice of the moderator. For the same power yield, the neutron flux in a
F-EA is approximately 20 times larger. As is well known, it simply reflects the fact
that at higher energies cross sections are generally smaller. A practical burn-up rate
of a F-EA is about ρ = 60 W/g : the flux will then be φ = 2.33 × 1015 cm -2 s-1, about 80
times larger than the one optimal for a T-EA.
There are several flux dependent effects which have a direct influence on the
value and the stability during operation of the multiplication factor k, and hence on
the gain:
1)
2)
Neutron capture by the intermediate elements of the breeding process and
specifically by the 233Pa which destroys a nascent 233U atom at the price of an
extra neutron. Such a loss involves a competition between neutron capture and
radioactive decay, and it is proportional to the total flux φ through the
parameter ∆λ 1 = σ a( 233Pa) × τ( 233Pa→ 233U) × φ << 1 where τ is the mean life. The
absorption cross section σ a( 233Pa) is about 43 b at thermal energies, it has a
resonance integral of 850 b and it is equal to 1.12 b for fast neutrons (Table 2.2).
The corresponding value for a T-EA is ∆λ 1 ≈ 1.45 × 10 −16 φ , corresponding to a
contribution to L of ∆L = (1 − L) ηε ∆λ 1 / 2 ≈ 3.78 × 10 −3 for the typical flux of 2.7
× 1013 cm-2 s-1. For fast neutrons the cross section is much smaller but the flux
is correspondingly larger: for a given burn-up rate ρ, ∆λ 1 is 0.56 times the value
for thermal neutrons. Note however that the allowance for neutron losses is
much greater for the F-EA and therefore larger burn-up rates are practical: for ρ
= 60 W/g, ∆λ1 = 8.81 × 10-3 which is quite acceptable.
A consequence of the relatively long mean life of 233Pa (1/e decay after τ = 39
days) is that a significant reactivity increase occurs during an extended EA shutdown. Conversely, any prolonged increase in burn-up rate produces a
temporary reduction of reactivity until the 233 Pa inventory has been reestablished. The magnitude of such a reactivity change following a shut-down
need not be a problem, but appropriate measures would be required to correct
its effects. The density of 233Pa is given by
N( 233Pa) = τ( 233Pa→ 233U)σ γ + fiss( 233U)N( 233U)φ =
[
= (1 + α )τ( 233Pa→ 233U) × N( 233U)σ fiss( 233U)φ
]
34
where α is the ratio of the non-fission (n,γ) to fission reactions and the last term
N( 233U)σ fiss( 233U)φ is directly proportional to the 233U burn-up rate, ρ. If the
accelerator beam is shut down, following the characteristic decay lifetime
τ( 233Pa→ 233U), the concentration of 2 3 3 U will increase by an amount
asymptotically equal to N( 233Pa), essentially independent of the mode of
operation of the EA for a given equilibrium burn-up rate. However since in the
case of the F- EA the equilibrium concentration ξ of 233U is about nine times
larger, its effect on reactivity max(∆k k) = N( 233Pa) / N( 233U) will be only 1/9 of
the one
for a T-EA.
For the chosen examples of burn-up rates,
−2
max(∆k k) ≈ 5.2 × 10 for the T-EA and only max(∆k k) ≈ 2.08 × 10 −2 for the FEA, in spite of the factor four in ρ in favour of the present option.
3)
Neutron losses due to the high cross section fission product 135 Xe are well
known [29]. The Xenon poison fraction is neutron flux dependent, since it
relates, like in the case of 233Pa to an equilibrium between captures and decays.
For thermal neutrons and at the breeding equilibrium, the fraction of neutrons
captured by 135Xe is given by ∆λ 3 ≈ 0.9 × 10 −19 φ / (2.1 × 10 −5 + 3.5 × 10 −18 φ ) which
tends to an asymptotic value ∆λ3 ≈ 0.021 for a flux φ ≈ 2.7 × 10 13 cm-2 s-1.
Following a reactor shutdown or reduction in power, the Xenon poisoning
temporarily increases even further [29] because decays producing Xe continue
to occur, passing through a maximum 10 to 12 hours after the shutdown. The
magnitude of this transient additional poisoning is also dependent on the
neutron flux. Although the temporary loss is not significant, a reactivity
reserve, if normally compensated by control rods, would represent a permanent
loss of neutrons. The Xenon type poisoning effect is essentially absent in the
case of F-EA, since there is no fission fragment nucleus which has the required
features in the energy domain of importance.
As one can see in a F-EA the importance of these effects is much smaller. The
estimated effects at the burn-up rate ρ = 60 W/g are given in Table 2.3.
The reactivity increase due to 233 Pa decays is quoted for a 10 day cooling
period, since such a time is largely sufficient to overcome any imaginable technical
problem, assuming that the "scram" system fails in blocking the reactivity. The most
direct consequence of this fact is that a larger value of k is operationally conceivable,
with a consequently higher energetic gain, (see paragraph 2.6). As discussed further
on, the temperature coefficient of criticality is negative, corresponding to ∆k= + 0.01
for a temperature drop of 700 o C. Adding linearily the effect of such a large
temperature swing to the 10 day intervention limit suggests that the largest, practical
35
maximum value of operational reactivity of a subcritical F-EA is about k ≤ 0.98. It
should be noted however that already for k = 0.96 the recirculation power through
the accelerator is less than 10% of the delivered, useful electric power.
2.6 - Computing methods. The exact definition of the parameters of the F-EA
implies an appropriate account of the resonance or otherwise complex energy
behaviour of the cross sections of the many elements which intervene in the cascade
reactions.
As in Ref. [1] we have adopted a Montecarlo method in which a large number
of individual neutrons are followed from their birth to absorption. We make use of
the concept of neutron generation and introduce the effective multiplication
coefficient k eff, the fraction of neutrons which are regenerated at each generation.
Both fissions and (n, 2n) reactions are considered. Cross sections are finely
interpolated from the most complete sets of cross section data available today [30]
and include all main channels, like for instance inelastic (n,n’) scattering. Thermal
movement of the target nuclei (Doppler broadening) is included in the simulation.
The elementary structure of the EA is subdivided in a number of different
regions, which reflect the geometrical properties of the device. The composition of
each of these regions is allowed to change as a function of time taking into account
the changes in concentrations of the newly produced elements due to (1) the nuclear
transformations and (2) the spontaneous decay chain. A complete database of all
known elements with their decay modes and rates is used [31] and new elements are
introduced to the list whenever a decay or a reaction channel justifies it.
Particular attention has been given to fissions, since they are the dominant,
driving process for the multiplication. The energy dependence of the neutron
multiplicity has been parametrized from existing data [30].
One important feature of the programme is the one of calculating the evolution
of the (poisoning) fission fragments. In order to do so effectively many hundreds of
different elements must be followed during the calculations. This very complete
method of simulation has been made possible only recently due to the availability of
more powerful computers. It is still somewhat limited in the statistical accuracy due
to lack of computing power [32].
In practice, the computer programme requires that one defines the different
geometrical regions, their initial composition and their operating temperatures. One
36
has to define then the scale of time and of reaction activity. The programme then
calculates the time evolution of the system — based of course on a much smaller
random neutron population but with changes of concentrations scaled to the actual
flux — and calls on further elements whenever required. The calculation can be
coupled with a Montecarlo programme which simulates the high energy cascade.
Hence the Montecarlo emulates the whole process initiated by an incoming beam of
specified characteristics. More often it is used as a stand-alone module to determine
the multiplication coefficient keff, starting from an initial spectrum due to fission
neutrons.
The Montecarlo method has the advantage over other methods that in principle
it provides a very realistic evolution of the system. However the computing time is
long and the results affected by statistical errors. Therefore it has been coupled with
another, simpler evolution programme, which permits a faster exploration of the
main features of an EA. This programme makes use of some of the information from
the full Montecarlo, namely
1) the averaged cross sections for all relevant elements are extracted as the
average over the energy and the fuel volume of the flux as computed by the
Montecarlo. Since (see paragraph 2.2) the flux is rather uniform over the fuel
elements, the spatial average is a good approximation. The averaging over
energy may introduce some approximations in presence of strong
resonances, where the flux may be locally affected. The extent of this
approximation has been checked comparing true Montecarlo with the
evolution programme and found acceptable for our purposes.
2) the parameter L, namely the sum of fractional losses of neutrons (absorbed in
a variety of ways, like captures in structures and coolant, diffused outside
the EA and so on) is divided into two components, namely a term which is
constant, but geometry dependent and another (mainly due to fissionproduct poisons, spallation and activation nuclei etc.) which is linear in the
burn up. This parametrization is in excellent agreement with the Montecarlo
results. Actual values to be used in the evolution programme are fitted from
the Montecarlo simulation. Hence they take into account all burn-up
dependent neutron losses.
The time evolution in a slab of material subject to a neutron flux and with
spontaneous decays cannot be calculated following the classic Bateman evolution
equations [33]. This is due to the fact that the Bateman's description assumes an
open, successive chain of decay nuclei, eventually leading to the final stable isotopes,
namely a specific path in the (A,Z) plane. Under the simultaneous action of neutrons
37
and decays, nuclei can both rise (neutron induced reactions) and fall in the atomic A,
Z number (spontaneous decays). Hence the decay paths in the (A,Z) plane perform
loops which may bring back the same nucleus an arbitrary number of times and
imply products of an infinite number of terms, although with a decreasing
probability. For this reason our time evolution programme is based on numerical
step-wise methods. In our analysis both programmes are used and give consistent
results. Furthermore the neutron flux and criticality predicted by the Montecarlo
programme is in good agreement with the results of standard, non evolutionary
programmes [34].
2.7 - Cumulative fission fragment poisoning. One of the most serious limitations in
the T-EA comes from the losses of neutrons due to slowly saturating or non
saturating fission fragments (FFs). In contrast to 135Xe and 149Sm, which have a very
large neutron cross section and therefore reach saturation in a short time, the
majority of the fission products have cross sections which are comparable or smaller
than the one of the fuel itself. Hence the aggregate poisoning effect of such fission
products is roughly proportional to the fractional burn-up of the fuel. The
accumulated effect depends significantly on the past history of the fuel. Computer
calculations have been used to analyse the poisoning as a function of the integrated
burn-up for a variety of different conditions.
One important result is that losses due to fission fragment poisoning are much
less important for a F-EA, when compared to a T-EA (Figure 2.4). In both cases
however the build up of FFs implies a progressive reduction of criticality.
An important feature of the F-EA is that it is possible to operate the device for a
long time (several years) without intervention on the fuel. In order to enhance such a
feature we have investigated the possibility of starting with a 233U concentration
smaller than at the breeding equilibrium ξ and thus compensate as much as possible
the drop of criticality due to fission fragment poisoning with the help of the
increasing fraction of bred 233U.
In Figure 2.5 we have considered with the help of the evolution programme the
criticality coefficient k for the EA device described in paragraph 2.3 as a function of
burn-up for a constant neutron flux and given initial 233U concentration. Since the
neutron flux will in practice depend on time, the criticality coefficient will be slightly
affected also by the dependence of the 233Pa concentration with flux. The initial
criticality coefficient is adjusted "ad hoc" to k = 0.965 by slightly increasing the
38
neutron losses L. The initial filling of 233U is set to ξ =0.117, significantly lower than
the breeding ratio at equilibrium. The graph shows three different fluxes and hence
power yields, ρ. The general behaviour of the curves shows an initial drop related to
233 Pa production, followed by a rise due to the increment of ξ due to breeding.
Fission fragment captures eventually become important and bring down k. A higher
ρ gives lower k values since early captures in 233 Pa reduce the breeding yield.
Curves without fission fragment poisoning are also shown. One can conclude that
(1) a very smooth running is possible up to a burn up of the order of 150 GW
day/ton, essentially without intervention and (2) a power yield of the order of ρ ≈
100 W/g is perfectly acceptable19. An extended shut-down will move to the curve
for ρ → 0, still sufficiently far away from criticality. Of course, as already pointed
out, in view of the long 233Pa lifetime, there is plenty of time to introduce corrective
measures.
For a fixed beam power the flux is time dependent, and will vary proportionally
to gain. Since gain is related to the 233Pa concentration and in turn to its capture
probability, the dependence of k as a function of burn up is even smoother. In Figure
2.6 we show the typical k behaviour for a somewhat larger initial value of k. Almost
constant conditions can be ensured without intervention over a burn up of 100 ÷ 150
GW day/t, namely over several years.
2.8 - Higher Uranium isotopes and other actinides. Higher Uranium isotopes and
higher Actinides are produced by successive neutron captures. The time evolution of
an initially “pure” 232Th and 233U fuel mixture can be easily calculated and is given
in Ref. [1] for a T-EA. The build-up of the several isotopes introduces more captures
and some fissions. Hence in principle the multiplication coefficient k is also
modified. It was shown in Ref. [2] that the asymptotic mixture preserves an
acceptable value of k for initial 232Th both in thermal and fast neutron conditions,
while for initial 238U only fast neutrons preserve an acceptable gain.
In the EA the initial fuel is completely burnt in a closed, indefinite cyclic chain in
which Actinides of the spent fuel become the "seeds" of the next fuel cycle [1]. At
each discharge an appropriate amount of fresh fuel is added to compensate for the
burn-up and the accumulated nuclear species, products of the fission (fission
fragments, FFs) are removed. The initial fuel nuclei (either Th232 or U 238 or
19Note
that in the present design, we have conservatively set the power density to about one half of
this value.
39
eventually a mixture of both) undergo a series of transformations induced by neutron
captures and spontaneous decays, until they achieve ultimate fission. The first of
these transformations is the initial "breeding" reactions which continue to be the
dominant source of fissions (233U or 239Pu respectively) even after a long burn-up.
However a rich hierarchy of secondary processes builds up at all orders. These
secondary processes become essential in determining the atomic concentration vector
c( A, Z ) of Actinides and hence the neutron economy of the cascade. For stationary
conditions the atomic concentration vector c( A, Z ) (φ ) tends asymptotically, (i.e. after
long burn-ups) to a limiting equilibrium value.
In order to estimate the actual evolution of c( A, Z ) (φ ) we have studied the time
evolution of some fuel exposed to the average flux of an F-EA with the help of the
evolution programme and using the cross sections of Table 2.2. Results have been
checked with the full Montecarlo programme. The chain of many successive refillings has been simulated. Although the results are widely independent of the
power density, for definiteness the value ρ = 100 W/g has been used. After a preassigned burn-up of 150 GW day/t, Actinides are discharged and the fuel topped-up
with fresh 232Th. Since the amount of fuel burnt is not negligible the stockpile of
233 U is affected by the over-all reduction of the fuel mass, even if the relative
concentration with respect to 232 Th has remained constant (at the breeding
equilibrium) or significantly increased (if initially below the breeding equilibrium). It
is therefore necessary in general to add to the renewed fuel an amount of 233U which
is larger than what is recovered at the discharge. For this reason a small breeder
section has to be added to the EA: initially made of pure Thorium, it is designed to
supply such a needed difference. The total 233U stockpile as a function of burn up
has been calculated with the full Montecarlo for the geometry given in paragraph 2.3
and shown in Figure 2.7. With the help of such an extra breeding, it is realistic to
expect that the initial volume of 233U can be made available at the end of the cycle.
Therefore in our simulation of the evolution of c( A, Z ) (φ ) we assume that both 232Th
and 233U are topped up to the initial values at each filling. The new fuel will contain
in addition all the remaining Actinides produced by the previous combustion.
In Figures 2.8a, 2.8b and 2.8c we show the Actinide distribution at discharge, as
a function of the discharge number. The relative concentrations are listed in Table
2.4. All elements clearly reach an asymptotic concentration, in which production and
incineration are in equilibrium. Concentrations of higher actinides tend to a stable
equilibrium condition which is a fast decreasing function of A and Z. This is due to
the fact that almost at each step of the neutron induced evolution ladder, fissions
subtract a significant fraction of nuclei. The most offending isotopes, because of their
40
amount and their radio-toxicity, namely 231Pa and 232U are practically close to the
asymptotic values of 1.06 × 10-4 and 1.30 × 10-4 already at the first discharge. Note
also the large concentration of 234 U which quickly reaches an asymptotic
concentration which is about 38% of 233U. The Uranium composition at (asymptotic)
discharge is therefore 9.354 × 10-4 of 232U, 63.88 % of 233U, 24.12 % of 234U, 5.870 % of
235U, 6.01 % of 236U and 1.03 × 10-4 of 238U, which constitutes about 14% of the spent
fuel mass. Likewise the Neptunium and Plutonium, produced in negligible amounts
during the first fillings grow to asymptotic values of 0.2% and 0.1 % respectively.
Plutonium is dominated by the isotope 238 Pu which has the short half life of 87.7
years and therefore has no practical military application. Higher Actinides,
Americium and Curium, never reach concentrations of significance. Note that for
instance after 20 refilling the fuel seeds have produced an integrated burn up of the
order of 3000 GW day/t and therefore these contaminating amounts, once
normalised to the produced energy are totally negligible. For instance the Plutonium
concentration at the discharge of an ordinary PWR is about 1.1% for 33.0 GW day/t.
The amount of trans-uranic Actinides produced per unit of energy delivered is about
three orders of magnitude less than in an ordinary PWR.
We have compared the evolution of k as a function of burn-up obtained with
the simple evolution programme and the "exact" calculations of the Montecarlo
programme. As shown in Figure 2.9, the agreement is excellent.
The behaviour of the multiplication coefficient k as a function of the burn-up
during successive refills is given in Figure 2.10. One can see that in spite of the
significant change of the fuel composition, the value of kremains remarkably
constant.
We conclude that the fuel can be indefinitely used in an open ended chain of
cycles. Indeed the fuel can survive the lifetime of the installation and be re-used as
long as there is demand for EAs, with very small or no loss of performance. In
contrast with an ordinary reactor the EA produces no "Actinide Waste" to speak of,
but only valuable "Seeds" for further use and once the asymptotic concentrations
have been reached, there is no significant increase with operation of the radio-toxicity
of the Actinide stockpile (see next paragraph).
2.9 - Elementary, analytic formulation of Actinide evolution.
A number of
simplifying assumptions permits calculating analytically the essential features of the
evolution of the concentration vector c( A, Z ) (φ ) . We ignore the discontinuity of the
41
refills and assume a constant inflow of the father element and neglect the (n,2n) and
other channels which may introduce "loops" in the (A,Z) evolution plane, as already
mentioned. We assume that in the presence of the neutron flux φ, for all elements
there is only one transformation channel (either with neutron capture averaged cross
(i)
section σ capt
or radioactive decay with decay rate λ(i) , whichever is dominant) and a
dissipative, fission channel with spectrum averaged cross section σ (i)
fiss . For very high
values of A spontaneous fission and other forms of nuclear instability will contribute
to such dissipative terms. The rate of transformation in a neutron flux φ is φσ and
(i)
(i)
(i)
= φσ (i)
if the transformation is decay
the total rate µ (i) = φ (σ capt
+ σ (i)
fiss ) or µ
fiss + λ
dominated. The survival, chaining coefficient, which represents the probability of
continuation to the next step of the evolution chain is defined as
(i)
(i)
(i)
= λ(i) / (λ(i) + σ (i)
α (i) = σ capt
/ (σ capt
+ σ (i)
fiss ) or α
fiss × φ ) respectively. The procedure is
schematically shown below:
Chain
P→
N1 →
↓
→
N2
↓
N3 →
↓
→
Ni
↓
Initial
amount
N1 (0)
0
0
0
Removal
rate
φσ (1)
fiss
φσ (2)
fiss
φσ (3)
fiss
φσ (i)
fiss
Transfer
rate
φσ (1) , [λ(1) ]
capt
φσ (2) , [λ(2) ]
capt
φσ (3) , [λ(3) ]
capt
φσ (i) , [λ(i) ]
capt
Survival
coeff. α (i)
(1)
σ capt
(1)
σ capt
+ σ (1)
fiss
(2)
σ capt
(2)
σ capt
+ σ (2)
fiss
(3)
σ capt
(3)
σ capt
+ σ (3)
fiss
(i)
σ capt
(i)
σ capt
+ σ (i)
fiss
Total
rate µ (i)
(1)
φσ (1)
fiss + λ
(2)
φσ (2)
fiss + λ
(3)
φσ (3)
fiss + λ
(i)
φσ (i)
fiss + λ
Assuming first no refill (P = 0 ) and an initial number of nuclei N1 (0), the time
evolution is given according to the Bateman equation (i >1):
j =i
j =i −1
j =i −1
( j)
exp(− µ t)
N (i) (t) = N (0) (t) ∏ α ( j ) × ∏ µ ( j ) × ∑ k =i
(k )
( j)
j =1
j =1
j =1
µ
µ
(
−
)
∏
k =1
k≠ j
If alternatively, there is refill at the constant rate P per unit time and no initial nuclear
sample, i.e. N1 (0) = 0, the formula becomes (i > 1)
42
j =i
j =i −1
j =i −1
( j)
1 − exp(− µ t)
N (i) (t) = P ∏ α ( j ) × ∏ µ ( j ) × ∑
k =i
j =1
j =1
j =1 µ ( j ) (µ ( k ) − µ ( j ) )
∏
k =1
k≠ j
In practice, both refilling and initial nuclei are present and the actual number of
nuclei will be simply the sum of the two above terms. Note that for ρ ≈ 100 W/g,
φ ≈ 5 × 1015 cm-2 s-1 and that the sum of cross sections is of the order of magnitude of
≈ 2 × 10-24 cm2, leading to an evolution time constant 1 / µ (i) of the order of ≈ 3 years.
The asymptotic distribution is reached at the limit t → ∞ . At this stage the
process is dominated by the refill term P and one can easily calculate the equilibrium
amounts:
j =i−1 ( j)
∏α
j =1
µ (1) j =i−1 ( j)
(1)
(i)
N (t → ∞) = P
= N (t → ∞) (i) ∏ α
µ (i)
µ j =1
The time required by N (i) to grow to N (i) (t → ∞)(1 − 1 / e)is approximately given
by ∑1 /µ ( j) where the sum is extended up to i. Since the order of magnitude of the
time constant is typically 3 years, equilibrium is reached after ≈ 3 (i-1) years where
we have used i-1 to take into account that the step through the 233Pa is fast. The fast
decrease of N (i) (t → ∞) with the rank in the chain is due to the product of the α << 1
terms. To a fast decreasing degree of concentrations, the whole table of elements is
eventually involved. As already pointed out, in practice the chain is not open-ended
since spontaneous fissions and other instabilities ensure very small α –values toward
the end.
2.10 - Practical considerations. Strictly speaking, continuing operation of the EA
requires merely the recycling of the Uranium isotopes. However at each refill of the
fuel, inevitably, individual Actinides are separated during the reprocessing.
Furthermore their relative incineration rate is independent of the concentration.
Therefore, although their elimination requires permanence in the EA for a long time,
it is not mandatory to dilute these extra products in every fuel refill of each EA. They
can be accumulated and inserted instead in a dedicated device. Whichever strategy
is chosen, the already calculated evolution of the trans-uranic stockpile as a function
of the integrated burn up (Figures 2.8a-c ) remains valid.
In order to positively destroy such trans-uranic Actinides, the exposure time is
long, extending over many refilling steps. Since their relative amount is very small it
is possible to concentrate them in a few, dedicated fuel bars, to be inserted
43
somewhere in the bundles of ordinary fuel, which is then made of Uranium and
Thorium only. After irradiation, such dedicated bundles do not need further
reprocessing, since even if the local Fission Fragment concentration becomes very
high, it will not affect the over-all criticality of the device which is not appreciably
different than if they were generally distributed. Therefore it may be sufficient at
each refill of the main fuel to bleed the gaseous fragments produced and to add a
new protecting sleeve or otherwise ensure the continuing mechanical strength of
such specialised fuel bars: it will make sense not to reprocess them any more, until
all actinides are positively transformed into fission fragments and their incineration
completed.
Therefore a practical scenario will consist in (1) reprocessing of the bulk of the
spent fuel at each refill, with separation of Thorium and Uranium which are to be
used to fabricate the next fuel refill and (2) separation at each reprocessing stage of
the trans-uranic Actinides and of Protactinium in a small stockpile which is then
introduced in the neutron flux of the EA once and for all and up to its total
incineration, with gas bleeding and strengthening of the cladding at each refill.
The amount of elements at the discharge depends critically on the concentration
of 236 U, which acts as the gateway to 237 Np. Therefore we have considered the
production of trans-uranic elements after 150 GW day/t, starting from the
asymptotic mixture of Uranium in the fuel. Much smaller amounts will be produced
during the early fillings, as seen from Figures 2.8a-2.8c. Results are listed in Table
2.5. The discharge consists primarily of 237Np (66.0 %), 231Pa (4.24 %), medium lived
238Pu (26.1 %, half-life of 87.7 years) and 239Pu (3.3%) and it is ridiculously small,
namely 276 grams/ton of fuel, or 4.14 kg for a 15 ton discharge. The radioactive heat
of this discharge is ≈ 600 W, primarily due to 238Pu, and quite manageable. The
relative radio-toxicity of such trans-uranic products is also very modest, when
normalised to the produced energy. The volume is only a few percent of the
production of a PWR for the same energy. As already pointed out, once inserted in
an appropriate fuel containment rod, they will not be handled again until fully
incinerated. In view of the simplicity of such a procedure, geologic storage of transuranic waste from an EA is unnecessary. Clearly the best place to put the unwanted
long lived waste is the EA itself, where an incineration lifetime of years is at hand.
2.11 - Proliferation issues. A great concern about Nuclear Power is that military
diversions may occur with the spent fuel. The present EA scheme offers much better
guarantees against such a potential risk. We assume that the procedure of fuel
loading and reprocessing is the one described in the previous section. Critical
44
Masses (CM) and other relevant parameters for bare spheres of pure metal are listed
in Table 2.6. The addition of a neutron reflector, a few inches thick may be used to
reduce the CM by a factor two or so.
One can see that three chemical elements of the discharge, namely the
asymptotic Uranium Mixture, Neptunium and Plutonium exhibit potential nuclear
explosive features. However several other features limit the feasibility of an actual
explosive device. We consider them in turn, following the arguments given in Ref.
[35]:
1) Decay heat produced by the α-decays of the material in some instances is
much larger than the eight watts emitted from the approximately three
kilograms of weapon grade plutonium which is suggested to be in a modern
nuclear warhead. Since the high-explosive (HE) around the fuel would have
insulating properties (≈ 0.4 W m oC-1), only 10 cm of HE could result in an
equilibrium temperature of about 190 oC for 100 W of heat. Apparently the
breakdown rate of many types of HE becomes significant above about
100 o C. Although methods could be envisaged to add heat sinks to the
device, we assume that α-heat yield much larger than 1000 W will not be
acceptable.
2) Gamma activity from some of the decay products of the chain are making the
handling of the device during construction and deployment very risky and
eventually impossible. In particular the hard γ-ray emitted by 208Tl is very
hazardous. The corresponding dose rate of 30 kg of Uranium mixture with
103 ppm of 232U contamination is asymptotic after 103 days [36] and is about
3.6×104 mSv/hour which corresponds to a 50% lethal dose after 10 minutes
exposure to the bare mass.
3) Spontaneous fissions produce neutrons which could cause the pre-initiation
of the chain reaction and thus dramatically reduce the potential yield of the
device. Gun-type implosion systems, which are the easiest to realise, are
particularly sensitive to pre-ignition. This effect for instance discourages the
use of such simple systems in the case of weapon grade Plutonium, which
has a yield of 66 n g-1 s-1 , where high power explosives providing an
implosion speed of one order of magnitude larger must be used. We assume
therefore that fuels with a neutron yield much larger than 1000 n g-1 s-1 are
not practical, leading to a too small "fizzle yield", namely the smallest
possible yield resulting from pre-initiation.
As already mentioned, the total discharge of Neptunium and Plutonium is of
the order of 4 ÷ 5 kilograms after a long burn-up (5 years of operation ) of a typical
45
EA. Hence in order to accumulate the amount of explosive to reach a single CM the
full discharges of many decades of operation, and the result of the reprocessing of
hundreds of tons of spent fuel must be used. Note that according to our scenario,
this is impossible since the spent fuel is re-injected in the EA right after reprocessing
and completely incinerated. Clearly the accumulation of a CM demands suspending
such a procedure for decades. In addition it will be a very poor explosive, since as
one can see from Table 2.6, both cases will have a very small "fizzle yield" which will
require HE ignition. This effect is particularly large in the case of Neptunium, since
the CM will produce 1010 n/s! In the case of Plutonium, this effect is also large, but
the ignition method will be heavily hampered by the large heat production of the
short-lived (half-life 87.7 y) 238Pu isotope, 4.4 kW for the CM.
Therefore the main concern stems from the possible diversion of the Uranium
Mixture, which is abundantly produced. It has been suggested to denature the
Uranium adding a significant amount of 238U. In our view such a method is not
foolproof since the 238U will quickly produce ample amounts of 239Pu which is a well
proven, widely used explosive and which could be extracted maliciously during
reprocessing, as is the case of ordinary PWRs. Instead we believe that the very strong
γ-radiation from the 208Tl contaminant constitutes a strong deterrent and an excellent
way to "denature" the fuel. A new technology in constructing, assembling and
handling the weapon must be developed, which we believe is highly selfdiscouraging, with respect to other ways of achieving such a goal.
2.12 - Burning of different fuels. As one can see from Table 2.2 the majority of
Actinides have a large cross section for fission. Therefore the required level of subcriticality can be attained with a very large variety of different fuels. Clearly the
choice is application dependent and an almost infinite number of alternatives are
possible. In this report we shall limit ourselves to a number of specific cases.
1) Fuel based on 238U, in which the fissile element bred is Plutonium, which
might be of interest in view of the huge amount of unused depleted Uranium.
The main draw-back of this fuel, when compared with Thorium is the large
amount of Plutonium and higher Actinides produced. However they are
eventually incinerated and the stockpile remains constant, just as in the case
of the previous example based on Thorium.
2) Initial mixture of Thorium and "dirty" Plutonium from the large amount (≥
1000 tons) of the surplus Plutonium stockpile, presently destined to the
geologic storage. In this way one can actually "transform" Plutonium into
233U with about 85% efficiency, to be used for instance to start-up other EAs,
46
besides incinerating the unwanted ashes and producing a considerable
amount of useful energy.
We shall briefly review the basic properties of the breeding cycle based on 238U,
γ)
β−
β−
→ 239Np
→ 239Pu. Such a burning cycle is of interest in view of
→ 239U
U + n(n,
the huge amount of surplus of depleted Uranium, but it implies a major concern in
view of the larger radio-toxicity of the spent fuel and of the possible military
diversion of the large amounts of Plutonium. It has been shown in Ref. [1] that the
thermal EA cannot use this fuel, since the asymptotic fuel has a reactivity k∞ which is
238
smaller than the one of Thorium. With fast neutrons, however, this cycle has "per se"
some advantages over the Thorium cycle, namely an even higher reactivity k∞ which
in principle could permit envisaging even a critical device and a shorter half-life (2.12
days) of the intermediate 239Np which considerably reduces the reactivity changes
with power, as shown in Table 2.7.
Cross sections have been integrated over the neutron spectrum calculated with
Montecarlo methods on a realistic model (see paragraph 2.6). The breeding ratio ξ is
somewhat larger than the one for Thorium, while the amount of intermediate state
239Np is much smaller, mainly because of its shorter lifetime. The main consequence
is that the variation Max(∆k) subsequent to an extended shutdown and the breeding
loss due to premature captures in 239Np are much smaller. Note that the value of k∞
at breeding equilibrium is for the binary mixture 238U – 239Pu. As we shall see the
Plutonium mixture will rapidly evolve in a mixture of several isotopes, which reduce
the value of k∞ at the asymptotic limit.
Notwithstanding, as already pointed out in the introduction, the large value of
k ∞ at first sight would indicate that for instance a traditional Fast Breeder might
suffice to exploit the fuel cycle [37][18]. But in the case of an EA the excess criticality
could be used to extend the burn up, typically in excess of 200 GW day/t, in presence
of fission fragments, starting the EA with a mixture well below the breeding
equilibrium. The radiation damage of the fuel sleeves and the gas pressure built up
have to be periodically taken into account, for instance by a periodic renewal of the
fuel encapsulation and gas bleeding. These procedures are much simpler than a full
reprocessing and in principle do not have to be exposed to the full radio-toxicity of
the fuel.
Reprocessing and in general the fuel handling strategy implies that several
components of the spent fuel are assembled into a renovated fuel, eventually with the
external supply of additional fuel (i.e. "dirty" Plutonium) and/or with additional
fissile material produced in the breeder section. A simplified, elementary method of
47
estimating the relevant multiplication coefficient can be formulated assuming that
the neutron spectrum in the EA is not appreciably affected by the variations in the
mixture. This is only approximately valid in the case of strong resonances which
may produce "screening", namely local "dips" in the spectrum. Also large variations
of fuel concentration will affect the spectrum and hence the performance of the
system since the fraction of captures and the lethargy effects in the Lead diffuser will
change. Notwithstanding, such a treatment could be very useful to understand at
least qualitatively the general evolution during burn-up and refills.
The multiplication coefficient k∞ of a small amount of element mixture of two
components exposed to an "external" neutron flux φ(Ε) is given by
n
k∞(1+2) =
∑ Niσ (i)fiss ν (i)
1
n
(
(i)
∑ Ni σ (i)fiss + σ capt
1
)
=
k
n
1
k +1
n
(i)
(i)
φ ∑ Ni σ (i)
+ φ ∑ Ni σ (i)
fiss ν
fiss ν
k
(
)
(
(i)
(i)
(i)
φ ∑ Ni σ (i)
fiss + σ capt + φ ∑ Ni σ fiss + σ capt
1
k +1
)
n1k∞(1) + n2 k∞(2)
n1 + n2
=
where ν (i) is the spectrum averaged neutron multiplicity due to fissions and the
multiplication coefficients for the two media are, as obvious
n
k
k∞(1) =
∑ Niσ (i)fiss ν (i)
1
∑ N (σ
k
i
(i)
fiss
(i)
+ σ capt
1
)
; and
k∞(2) =
∑Nσ
i
(i)
fiss
ν (i)
k +1
∑ N (σ
n
i
k +1
(i)
fiss
(i)
+ σ capt
)
The weights are given simply by the relative absorption rates (per unit time) in the
two media
k
(
(i)
n1 = φ ∑ Ni σ (i)
fiss + σ capt
1
)
n
and
(
(i)
n2 = φ ∑ Ni σ (i)
fiss + σ capt
k +1
)
In order to simplify the algebra we have limited our consideration to the
dominant contribution due to fission. The discussion can be easily extended to other
processes, like (n,2n) and so on. Generalising, the multiplication coefficient of a
mixture of n-elements is simply given by the "stoichiometric" weight of the
coefficients of the components. In particular, after n cycles with refills of fuel with no
external additions (each after a predetermined flux exposure β = ∫ φ dt ) the
multiplication coefficient can be easily estimated as stoichiometric sum of the same
fuel which is subject to a series of successive exposures corresponding to
nβ ,(n − 1)β ,(n − 2)β ⋅⋅⋅⋅⋅⋅⋅⋅, β . If at each cycle some fresh amount of fuel is added or
eventually some component is removed, its contribution must obviously be added or
subtracted stoichiometrically.
Linearization of the problem permits using simple "chemistry" considerations
which are very useful for instance in defining the strategy of the refills. The definition
of the elements of the mixture is of course dependent on the problem one wants to
48
solve. They can be either the refill mixture or even single isotopes. Each of the
elements will then independently evolve inside the fuel i.e. Ni will change with time.
In our approximation the total number of nuclei ∑ Ni will decrease because of
fissions. Clearly the gain G is not a linearized quantity and it must be estimated with
the help of the parameter k. In order to calculate k, one has to introduce the effect of
the losses L as discussed in the previous paragraphs, starting from the value of k∞.
The total burn up of the fuel is the sum of the burn-ups of the elements, since
the power produced is the sum of the power delivered by each of the elements,
−11
joules is the energy produced by
ρ = ∑ ρ (i) = φε fiss ∑ Ni σ (i)
fiss , where ε fiss = 3.2 × 10
each fission.
We have estimated the evolution of some of the primary ingredients of the fuel
strategy. Spectra are taken from the exemplificative designs of section 2.3. They
should be a good representation of the actual situation, with the above mentioned
provision. We have considered sub-fuel elements made of pure 232Th, 233U, 235U,
239Pu and the typical trans-uranic discharge of a PWR after 33 GW day/t of burn-up,
in which Np, Pu, Am and Cm isotopes have been included. In Figure 2.11 we have
plotted k∞ as a function of the days of exposure to a flux φ = 4.0×1015 n cm-2 s-1. One
can distinguish the difference between the fissile elements which have a k∞
decreasing with the isotopic evolution of the mixture and the breeder elements in
which k∞ starts very small (some fission is present even for pure elements) and grows
because of the progressive breeding of fissionable elements.
In order to estimate the value of k∞ for a mixture of such elements as a function
of the burn-up one has to introduce the stoichiometric weights ni. In Figure 2.12 we
(i)
plot rabs
the relative absorption rates (per unit time) for 1 initial gr/cm3 of each
element, which must then be multiplied by the actual initial concentration of each
element di to compute ni.. Likewise the power produced for 1 gram of the mixture
by the flux φ is easily calculated with the help of Figure 2.13, in which ρ i, the
power/gram of each element is given as a function of the integrated flux. The
irradiation dependence and the power/gram of the mixture are then
(i)
k∞(i)rabs
di
ρi di φ cm −2 s −1
∑
∑
k∞ =
and ρ[W / gr ] =
(i)
di
∑ rabs
∑ di 4 × 1015
[
]
Note that in practice one might prefer to set the more relevant parameter ρ and
derive the consequent flux, which is trivially done with the above formula. Finally in
Figure 2.14 we give the disappearance rate of nuclei due to fissions as a function of
the integrated flux. Note that the burn-up for full disappearance is about 950 GW
day/t and therefore the burn-up for a given integrated exposure can be calculated
49
with the appropriate weights directly from the Figure 2.14, rather than integrating ρ .
Fission fragment captures must be evaluated in order to calculate k from k∞ . An
approximate formula has been derived from the full Montecarlo calculation and
gives a linear dependence of the fraction of neutrons vs. burn-up, with L = 0.065 for
100 GW day/t.
As one can see from Figure 2.11 to Figure 2.14, the features amongst the various
fissionable elements on one hand and of the two main breeding materials on the
other are surprisingly similar. This means that a large flexibility exists in substituting
a fissionable material for another or in building a convenient mixture of them: a
wide spectrum of choices is possible, depending on the availability of fuels and on
the application. The same EA can be used (even simultaneously) (1) to produce
energy (2) to transform fuels, like for instance Plutonium discharge into 233U and (3)
to incinerate unwanted Actinides. In general using mixtures other than 232Th/233U
would, however, produce fuel discharges with a much greater radio-toxicity.
2.13 - Conclusions. In order to ensure a practical utilisation of the fuel, the
neutron distribution in an EA must be sufficiently uniform. This in turn requires
abandoning the classic homogeneous fuel-moderator mixture geometry of an
ordinary reactor and instead inserting sparse fuel elements in a strongly diffusive
medium. Lead or Bismuth appear to be ideal materials for such purposes, at least for
a F-EA. Other media with similar properties, like for instance Graphite or Heavy
Water could be used for a T-EA.
The energetic gain of a T-EA, as discussed in Ref. [1] is of the order of
G = 30÷50. In practice this is realised operating the EA at an effective multiplication
k in the range 0.92 < k< 0.95. Fission poisoning limits the burn-up of the T-EA to
some 30-50 GW day/t. There are other reasons which suggest operation of the T-EA
with relatively small values of k, namely its relatively large variations due to decay
mechanisms after shut-down or power variations ( 233 Pa and 135 Xe) so as to leave
enough margin from risk of criticality.
The same type of considerations would however suggest a much greater gain
for a F-EA [2], for which an operating point in the vicinity of k = 0.98 is an optimal
operating point, corresponding to an energetic gain in the interval G= 100÷150. A
first reason for this choice stems from the much larger value of εη ≈ 2.5, which
implies k ∞ ≥ 1.20 and ∆ L = 8.6 10-3 for k = 0.980. On the other hand the fission
poisoning is much smaller and linearly growing with the burn-up, amounting to
50
about ∆L = 0.05 after 100 GW day/t. The flux dependent 135Xe effect is absent and
the time dependent k variation due to 233 Pa decays is much smaller for a given
power density. All these considerations suggest k ≈ 0.98 as quite appropriate for a FEA.
The multiplication factor k∞ is such as to permit to reach such a k value with a
233U concentration below the breeding equilibrium, thus permitting to compensate
the growth due to fission fragment captures during operation with the increase of k∞.
In this way, very long burn-ups are possible without intervention and in
exceptionally stable conditions.
At the end of each of these very long cycles, reprocessing is necessary in order
to remove Fission Fragments and replace the burnt fuel mass with fresh Thorium.
Uranium isotopes are chemically recovered and reused as seeds for the next fuel
load. The rest of the trans-uranic Actinides are of modest amount (few kilograms)
and they should be stored indefinitely in the EA where they are progressively
incinerated. Thus, Geological Storage of Actinides is unnecessary.
Although the optimal performance of the EA is ensured with the Thorium cycle,
a variable amount of other isotopes could be used instead, with very little or no
change in performance. For instance depleted Uranium (238U) of which vast amount
of surplus exists, could be used to replace 232 Th. The fissionable 233U could be
replaced in part or totally with 235U, 239Pu or even the trans-uranic discharge mix of
a PWR. Burning such unwanted "ashes" of the present PWR power plants is not only
providing a very large amount of extra energy from an otherwise useless waste
destined to geologic storage, but also helps to eliminate permanently materials that
nobody wants.
51
Table 2.1 - Resonance Integral and Survival Probability for Lead and Bismuth (E1 = 1
MeV, T = 20 oC)
204 Pb
206 Pb
207 Pb
208 Pb
E2=1 eV
.0781
.00787
.0272
.000685 .00974
.00621
E2=10 eV
.0649
.00728
.0125
.000676 .00626
.0054
E2=100 eV
.0607
.0071
.00783
.000673 .00516
.00512
E2=1 keV
.0568
.00706
.00635
.000672 .00475
.00331
E2=10 keV
.0287
.0065
.00516
.000671 .00283
.00223
E2=100 keV
.0124
.00435
.00395
.000636 .0018
.00195
.000278 0.438
0.0578
0.930
0.360
0.521
E2=10 eV
.00111
0.466
0.269
0.931
0.519
0.567
E2=100 eV
.00172
0.475
0.440
0.931
0.582
0.584
E2=1 keV
.00259
0.477
0.514
0.931
0.607
0.706
E2=10 keV
.04940
0.506
0.582
0.932
0.743
0.791
E2=100 keV
0.272
0.633
0.661
0.935
0.828
0.815
Element
Nat Pb
209 Bi
Integral Ires
Surv.prob.,Ps(E1,
E2)
E2=1 eV
52
Table 2.2 - Averaged cross sections (barn) of Actinides relevant to the fast EA.
Element
230Th
232Th
231Pa
233Pa
232U
233U
234U
235U
236U
237U
238U
237Np
238Np
239Np
238Pu
239Pu
240Pu
241Pu
242Pu
243Pu
244Pu
241Am
242Am
243Am
242Cm
243Cm
244Cm
245Cm
246Cm
247Cm
248Cm
249Bk
249Cf
250Cf
251Cf
252Cf
253Cf
Capture Fission
0.198672 0.018918
0.386855 0.005966
3.309176 0.179791
1.121638 0.038989
0.731903 2.096317
0.289003 2.783923
0.615564 0.248950
0.574071 1.972008
0.490142 0.068786
0.492199 0.610042
0.428265 0.025351
1.674921 0.233176
0.089278 0.595202
2.083201 0.353837
0.756840 1.025175
0.557041 1.780516
0.667103 0.288079
0.425030 2.577470
0.535288 0.190578
0.403097 0.810772
0.236048 0.157011
1.963967 0.190469
0.079728 0.530819
1.582431 0.146245
0.372092 0.105767
0.265210 2.655223
0.909153 0.318102
0.335178 2.475036
0.230261 0.181669
0.348536 1.926754
0.265514 0.218438
1.447988 0.113146
0.667223 2.707975
0.614795 0.944213
0.368920 2.488528
0.320039 0.573875
0.180410 0.716114
Elastic
(n->2n)
(n->n')
14.060925 0.000598 0.989135
10.923501 0.000560 0.699221
9.133289 0.000398 1.110933
8.093003 0.000162 1.754808
9.368297 0.000281 0.433875
8.919141 0.000211 0.280445
10.031339 0.000054 0.718069
8.858968 0.000457 0.640860
11.125422 0.000294 0.855951
9.189025 0.000920 0.491900
11.254804 0.000529 0.832077
9.157094 0.000115 0.759934
10.439487 0.000000 0.000000
9.184162 0.000135 0.865835
11.046388 0.000152 0.342888
9.156214 0.000237 0.770227
10.331735 0.000083 0.573045
8.104389 0.000880 0.801986
11.024648 0.000229 0.667679
9.283313 0.002254 0.623218
10.805879 0.000808 0.813081
9.580900 0.000004 0.565741
10.233513 0.000462 0.073528
10.003948 0.000028 0.935282
10.362508 0.000007 0.724242
10.012800 0.000456 1.005476
10.515990 0.000135 0.540912
8.750109 0.000831 0.862513
10.844025 0.000174 0.780190
9.117731 0.001353 0.372127
11.295776 0.000234 0.813142
10.220059 0.000052 1.186927
9.064980 0.000189 0.425589
8.927651 0.000406 0.468860
8.815815 0.001573 0.417832
11.865360 0.000335 0.414425
9.940411 0.000000 0.000000
Total
15.268245
12.016131
13.733619
11.008615
12.630690
12.272738
11.613976
12.046378
12.540620
10.784104
12.541045
11.825250
11.123966
12.487206
13.171463
12.264245
11.860045
11.909761
12.418422
11.122661
12.012833
12.301095
10.844059
12.667938
11.564615
13.939172
12.284297
12.423669
12.036336
11.766518
12.593122
12.968192
12.865973
10.955943
12.092679
13.174031
10.836935
53
Table 2.4 - Relative concentrations of Actinides at the discharge after 150 GW day/t
of burn up. The power density was ρ = 100 W/g, corresponding to a cycle of about 5
years. Concentrations are normalised to the fuel mass which is made of
corresponding oxides.
Element
First
discharge
5th
discharge
10th
discharge
15th
discharge
Asymptotic
limit
230Th
1.408 E-7
1.378 E-6
2.586 E-6
3.271 E-6
3.642 E-6
232Th
7.637 E-1
7.637 E-1
7.637 E-1
7.637 E-1
7.637 E-1
231Pa
9.246 E-5
1.055 E-4
1.059 E-4
1.061 E-4
1.061 E-4
232U
7.942 E-5
1.298 E-4
1.304 E-4
1.305 E-4
1.306 E-4
233U
8.919 E-2
8.919 E-2
8.919 E-2
8.919 E-2
8.919 E-2
234U
1.403 E-2
3.102 E-2
3.340 E-2
3.365 E-2
3.368 E-2
235U
1.851 E-3
7.242 E-3
8.101 E-3
8.185 E-3
8.196 E-3
236U
2.420 E-4
4.475 E-3
7.428 E-3
8.214 E-3
8.395 E-3
238U
3.239 E-8
3.145 E-6
9.390 E-6
1.296 E-5
1.440 E-5
236Np
2.626 E-10
1.047 E-7
5.787 E-7
1.228 E-6
1.924 E-6
237 Np
1.669 E-5
9.127 E-4
1.832 E-3
2.104 E-3
2.168 E-3
238Pu
3.163 E-6
5.975 E-4
1.545 E-3
1.875 E-3
1.958 E-3
239Pu
2.274 E-7
1.422 E-4
4.706 E-4
6.029 E-4
6.374 E-4
240Pu
1.172 E-8
3.709 E-5
2.144 E-4
3.307 E-4
3.703 E-4
241Pu
5.192 E-10
5.084 E-6
3.756 E-5
6.172 E-5
7.034 E-5
242Pu
1.694 E-11
9.800 E-7
1.536 E-5
3.508 E-5
4.572 E-5
244Pu
2.494 E-17
8.631 E-12
3.155 E-10
1.163 E-9
1.999 E-9
241Am
2.924 E-11
7.003 E-7
7.218 E-6
1.316 E-5
1.547 E-5
243Am
5.577 E-13
1.406 E-7
3.575 E-6
9.807 E-6
1.372 E-5
243 Cm
1.647 E-14
4.741 E-9
7.930 E-8
1.646 E-7
2.010 E-7
244Cm
4.859 E-14
5.683 E-8
2.479 E-6
8.489 E-6
1.303 E-5
245Cm
2.185 E-15
9.850 E-9
6.417 E-7
2.550 E-6
4.158 E-6
246Cm
3.693 E-17
9.783 E-10
1.519 E-7
1.023 E-6
2.329 E-6
247Cm
3.660 E-19
4.102 E-11
1.038 E-8
8.604 E-8
2.166 E-7
248Cm
5.510 E-21
3.492 E-12
2.011 E-9
2.743 E-8
9.618 E-8
54
Table 2.3 - Neutron flux dependent effects in the F-EA based on the 232Th cycle. The
parameter ρ is the power density produced per unit fuel mass at breeding
equilibrium.
Quantity
Values for
ρ = 60 W/gr
Ratio N(233Pa)/N(233U)
Variation of the breeding ratio, ξ
Neutron Flux cm-2 s-1
Effects of 135Xe, 149Sm etc.
Breeding loss due to premature capt. in 233Pa
Criticality rise after 10 days shut-down ( 233Pa)
Criticality rise after infinite shut-down ( 233Pa)
0.0208
+ 0.388 × 10 −3
2.33 × 10 15
< 10−4
– 0.00480
+ 0.00413
+ 0.0203
∆ξ
φ
Max(∆k)
∆k
∆k
Max(∆k)
Table 2.5 - Trans-uranic and Protactinium from discharge for asymptotic fuel
concentration. Integrated burn up is 150 GW day/t.
Element
231Pa
Partial density (gr/cm3)
Total Cm
0.9179
0.9179
0.5469
0.1428
0.1428
0.5640
0.7141
0.6185
0.3924
0.1887
0.6420
0.2638
0.8461
0.2722
0.4182
0.5500
Total discharge
2.1618 E-3
Total Pa
236Np
237Np
Total Np
238Pu
239Pu
240Pu
241Pu
242Pu
Total Pu
241Am
243Am
Total Am
242Cm
E-04
E-04
E-07
E-02
E-02
E-03
E-04
E-05
E-06
E-07
E-03
E-07
E-09
E-07
E-09
E-09
55
Table 2.6 - Some properties of Actinides from EA discharge having relevance to
possible military diversions of fuel.
Element from EA
Critical mass (CM),kg
Decay Heat for CM,Watt
Gamma Activity, Ci/CM
Neutron Yield, n g-1 s-1
Uranium Mix
Neptunium
Plutonium
28.0
24.3
790
very small
56.5
1.13
small
2.1 105
10.4
4400
small
2.6 103
Table 2.7 - Neutron flux dependent effects in the F-EA base on 238 U cycle. The
parameter ρ is the power density produced per unit fuel mass at breeding
equilibrium.
Quantity
Neutron Flux cm-2 s-1
φ
Breeding ratio, zero flux N(239Pu)/N(238U)
ξ
Rate variation of the breeding ratio, ξ
∆ξ
Ratio N(239Np)/N(239Pu)
Fuel intrinsic mult. factor at breeding equil.
k∞
Effects of 135Xe, 149Sm etc.
Max(∆k)
Breeding loss due to premature capt. in 239Np
∆k
Criticality rise after infinite shut-down ( 239Np) Max(∆k)
Values for
ρ = 120 W/gr
5.967 × 10 15
0.190
– 6.00× 10-4
3.66 × 10-3
1.250
< 10−4
– 3.816 × 10 −3
3.256× 10 −3
56
57
Figure Captions.
Figure 2.1
Capture Cross sections at 65 keV, as a function of the element number.
Figure 2.2
Conceptual design of the diffuser driven EA.
Figure 2.3
The burn-up radial distribution for different criticality coefficients,
namely for (a) for k=0.99, (b) for k=0.975 and (c) for k=0.950. Open
points have not been included in the fits.
Figure 2.4
Fraction of neutrons capture by the fission fragments as a function of the
integrated burn-up, for thermal and fast EA.
Figure 2.5
Criticality coefficient k as a function of the integrated burn-up for
different power yields. The effect on k due to the neutron captures by
the fission fragments is also shown.
Figure 2.6
Behaviour of k as a function of the integrated burn-up.
Figure 2.7
233U stockpile as a function of the integrated burn-up.
Figure 2.8a 231 Pa and 232 U stockpile as a function of the discharge number
(integrated seeds burn-up).
Figure 2.8b Other actinides s tockpile as a function of the discharge number
(integrated seeds burn-up).
Figure 2.8c Trans-uranic production/unit energy relative to ordinary PWR as a
function of the discharge number (integrated seeds burn-up).
Figure 2.9
Comparison of keff calculated analytically and by Montecarlo.
Figure 2.10 Behaviour of k as a function of the burn-up for different fillings.
Figure 2.11 Behaviour of k∞ as a function of the irradiation time at a constant flux of
4.0 × 1015 neutrons s–1 cm-2.
Figure 2.12 Relative absorption rates for different isotopes as a function of the
irradiation time at a constant flux of 4.0 × 1015 neutrons s–1 cm-2.
58
Figure 2.13 Power delivered per gram of different isotopes as a function of the
irradiation time at a constant flux of 4.0 × 1015 neutrons s–1 cm-2.
Figure 2.14 Rate of disappearance of different isotopes as a function of irradiation
time at a constant flux of 4.0 × 1015 neutrons s–1 cm-2.
Odd Z target nuclei
Even Z target nuclei with
even-even component weighted by
multiplying by factor of 2.4
Lead
reflector
Fuel and
breeding
region
Beam
Spallation
target
region
Buffer
region
Cos-like Distribution
Spallation target
Core
Linear Fit
Spallation target
Core
Exponential Fit
Spallation target
Core
Thermal neutrons
All fission fragments
Fast neutrons
All fission fragments
Thermal neutrons
Xe-135 only
Without fission fragment
captures
With fission fragment
captures
Without fission fragments
With fission fragments
Total
Fuel
Breeder
Plutonium
Americium
Curium
Points: Montecarlo Calculation
Continuous Line: Analytic
1st fill.
10th fill.
5th fill
U233
Pu239
"Dirty" Pu
U238
Th232
U235
U233
U235
Pu239
"Dirty" Pu
Th232
U238
U233
U235
Pu239
"Dirty" Pu
Th232
U238
U238
Th232
"Dirty" Pu
U235
Pu239
U233
59
3. —The accelerator complex.
3.1 - A three-stage cyclotron facility. The accelerator has to provide a proton
beam of 10 ÷ 15 mA, one order of magnitude lower than the one of most of the
accelerator-driven incineration projects based on continuous-wave (c-w) LINAC [9].
The relatively modest requirement of the present application, primarily related to the
high gain of the F-EA, allows alternative and much simpler solutions based on
circular machines producing a continuous beam, such as ring cyclotrons [38] [39]
which have a lower cost and a much smaller size.
Taking into account the recent development of high-intensity cyclotrons and the
outstanding results obtained at PSI [8], we have chosen a scheme based on a threestage cyclotron accelerator (Figure 3.1), namely in succession: (1) the injector, made of
two 10 MeV, C ompact Isochronous C yclotrons (CIC). Beams are merged with the
help of negative ion stripping; (2) the intermediate stage, a cyclotron with four
separated sectors (ISSC) bringing the beam up to 120 MeV; (3) the final booster with
ten separated sectors and six cavities (BSSC), raising the kinetic energy up to about 1
GeV.
The main novelty of our design, besides the about tenfold increase of the
accelerated current, well within the expectations of the present knowledge of space
charge effects and beam instabilities, is the increased power efficiency. This
extrapolation can be made with confidence and relies primarily on the performance
of the RF cavities, which is confirmed by specific model studies that we have made.
In particular we believe that the increased beam loading can be adequately handled.
This conclusion has been confirmed by a similar study of the PSI Group [8].
The main parameters of the two separated sector cyclotrons are given in Table
3.1. An essential aspect of the accelerator complex is the overall efficiency which
depends mainly on the RF performances. Power estimates have been made assuming
a 70 % yield of the RF power amplifiers and taking into account measurements on
cavity models for the RF losses. Further optimisations of the cavity shape which are
in progress show that a global efficiency slightly greater than 40 % is within the
reach.
An important aspect of the Accelerator complex when used in conjunction with
the EA is the high level of reliability required. Based on previous experience with
60
similar machines and possible improvements within reach we believe that the
unscheduled down-time of the accelerator can be kept to the level of 3÷5 %.
3.2 - Overall design considerations. Acceleration of intense beams requires a very
efficient extraction. To this effect, the main parameters of the accelerators should
follow several design criteria:
1) Injection energy should be high enough in order to reduce the longitudinal
space charge effects especially during the first turns after injection in the
intermediate stage.
2) Separated sectors magnets with small gap (5 cm) to obtain good vertical
focusing and to provide plenty of free space between sectors for accelerating
structures, injection and extraction devices. A high energy gain per turn is
important in order to reduce the number of turns to reach the extraction
radius. The number of sectors is mainly determined by engineering
considerations (number of RF cavities as well as extraction channel
problems).
3) Flat-topping RF cavities: in order to decrease the energy spread flat-topping
accelerating cavities are added, namely, two additional RF resonators
working on a harmonic of the main RF cavity frequency in order to obtain an
"as flat as possible" accelerating voltage wave form. These cavities operate on
a third (or fifth) harmonic mode with a peak voltage between 12 and 14% (or
4 and 5%) of the main RF cavities.
4) Single turn extraction: In order to get a high extraction efficiency, it is
necessary to achieve a large radial separation of the last turns. In turn this
requires choosing a large extraction radius, i.e. a low average field and a high
energy gain per turn. The effective turn separation depends somewhat also
on the phase width of the beam; for 20 o (30 o) it is 12.9 mm (12.4 mm) in the
intermediate (ISSC) cyclotron and 9.0 mm (8.4 mm) for the final booster
(BSSC).
5) Matching the three stages: in order to avoid any beam loss, matching
conditions must be satisfied between the different stages. To simplify the
overall design of the RF system, a good choice is to operate all three machines
at the same frequency, i.e. 42 MHz in the proposed design, and to accelerate
protons on the same harmonic number at least in the ISSC and BSSC, since at
the same time the magnetic fields can be kept sufficiently far away from
saturation.
61
The main parameters of the Accelerator complex for the RF option at 42 MHz
are given in Table 3.2. Equilibrium orbits and related properties have been calculated
numerically using realistic magnetic field maps.
3.3 - The injector cyclotron. It consists of a four sector isochronous cyclotron
capable of delivering 5 mA in the acceptable phase width of the intermediate stage.
The beams of two such injectors working at the same frequency are then merged
before injecting them into the intermediate stage (ISSC) and the final booster.
Commercial compact cyclotrons accelerating negatively-charged H– ions [40] operate
routinely with an internal ion source (i.e. an injection at low energy, about 30 KeV) at
about 2 mA intensities. In our case a higher current is required and therefore the
injection energy must be increased to about 100 keV in order to avoid space charge
limitations in the source-puller gap. Taking into account the possibility to inject large
currents from an external source at high voltage [41], we have chosen an axial
injection system at about 100 kV for various reasons :
1) A high extraction voltage for the source.
2) A multicusp ion source for the production of negatively charged ions. This
source is cumbersome and therefore it could not be installed in the central
region of the cyclotron.
3) A high brightness beam accelerated by the cyclotron requires a careful 6D
matching (the two transversal and the longitudinal phase space); in
particular, it is necessary to use a buncher in a way to avoid too strong effects
of the space charge.
4) Increasing the reliability of the cyclotron: the absence of an internal source
assures a better vacuum in the cyclotron, which allows higher RF peak
voltages.
5) Refined 3-D computations of the magnetic field have been carried out, in
particular in the injection and extraction regions. As opposed to the
intermediate and booster cyclotrons, a closed magnet configuration with a
return yoke is used in order to make the cyclotron more compact.
6) The RF system consists of two accelerating and two flat-topping cavities. The
fourth harmonic of the particle frequency has been chosen to make the
cyclotron rather compact. In order not to worsen space-charge effects by
phase compression, a constant voltage distribution along the cavity gaps is
desired.
62
Table 3.3 summarises the main parameters of the injector cyclotrons. A general
view of the injector cyclotron is visible in Figure 3.2. Bunches of the two 5 mA beams
produced by each of the two injectors are merged in order to obtain a single 10 mA
beam to be injected in the ISSC. Both injectors operate with negative ions (H – ). A
H+ beam extracted by stripping H– ions and an H– beam, extracted by a
conventional channel, are synchronised so that bunches are superposed (in phase
space) in a straight portion of the ISSC injection line. A stripper is installed at the end
of the injection line, before the beam enters the ISSC magnetic field to convert the H–
beam into a H+ beam. As a result the particle density in the phase space injected in
the ISSC is about doubled, leading to an injected current of 10 mA at no increase of
the single beam emittance. The method can be easily extrapolated to the merging of
currents of even a larger number of injector cyclotrons.
3.4 - The intermediate separated-sector cyclotron (ISSC). The general view of the
ISSC is given in Figure 3.3. A four-separated-sector cyclotron has been chosen as the
intermediate stage because of the following reasons :
1) the acceleration to a sufficiently-high injection energy for the booster can be
achieved in about 100 turns due to the possibility to install, between the
sectors, cavities providing a high accelerating voltage without prohibitive
losses.
2) the flat-topping of the RF voltage is easy to achieve.
3) the strong magnetic focusing provided by the four identical C-shaped sector
magnets with a constant small magnetic gap (5 cm).
4) the possibility to install an efficient extraction channel in the field-free valleys.
The choice of the injection energy into the ISSC is certainly one of the most
important parameters which influences the overall performances of the cyclotron
complex. The space charge effects are strong at low energy. They are present in both
transversal and longitudinal directions of the beam. Figure 3.4 shows the simulation
of the evolution of the accelerated beam in the radial-longitudinal plane during the
first 16 turns under the following conditions: intensity 20 mA, injection energy 10
MeV, energy spread 0.05 MeV, normalised emittances π mm.mrad in both radial and
vertical directions. Flat-topping with a third harmonic voltage and a shift in phase
(-10 RF deg.) with respect to the accelerating voltage have been used in order to
compensate the linear effects of the space charge and increase the longitudinal
acceptance (± 15 RF deg.) of the bunch. It has been observed that the beam shape in
the r-φ plane seems to stabilize after a certain number of turns (cf. Figure 3.4). The
63
beam radial spread is about ± 15 mm in the extraction region. The result of these
simulations is that a nominal 10 mA beam can be handled at an injection energy of
the order of 10 MeV.
Acceleration of the beam is provided by two main resonators located in
opposite valleys giving an energy gain per turn of 0.6 MeV at injection and 1.2 MeV
at extraction, increasing the beam energy from 10 MeV to 120 MeV. The RF
frequency of the accelerating (main) cavities has been chosen equal to 42 MHz, which
corresponds to the sixth harmonic of the particle revolution frequency in the
cyclotron. Due to the large (30 RF deg.) beam phase width, flat-topping cavities
would operate on the third harmonic of the main cavities i.e. on the eighteenth
harmonic of the revolution frequency.
Double-gap cavities have been selected (as opposed to single-gap) because their
radial extension is much smaller, thus leaving more space in the centre of the
machine for the bending and injection magnets and the beam diagnostics. A voltage
(or phase compression) ratio of 2.0 is used between injection and extraction. In order
to reduce the number of turns in the cyclotron and to have sufficient turn separation,
accelerating voltages of 170 kV and 340 kV are required at injection and extraction.
The main characteristics of the RF cavities are given in Table 3.4.
The shape of the cavities has been defined with the help of the 3D
electromagnetic code MAFIA [42]. Models of the main and flat-top cavities have
been respectively built at 1:3 and 1:1 scales in order to check the computations with
MAFIA. These models are of the low-power type and are mainly made of wood and
copper. Photographs of the accelerating and flat-topping cavity model during
assembling and measurements are shown in Figure 3.5.
For a current of 10 mA, the power to be delivered to each main cavity of the
ring cyclotron is estimated to be about 770 kW ( 550 kW beam power and 220 kW
cavity loss), which correspond to about 1.1 MW electrical power load (assuming a
70% DC to RF conversion efficiency). The beam power to be absorbed by each cavity
is 65 kW, which is about seven times the power dissipated in the walls (9 kW).
The injection channel of the ISSC cyclotron brings the beam from outside the
cyclotron to the first RF cavity gap where it is accelerated. It starts after the stripper
which is located at the end of the beam line that transports the combined H+ /H –
beam from the injectors. The stripped H + beam is injected in the cyclotron through a
valley along a flat-top RF cavity as shown in Figure 3.6. When it reaches a radius
lower than the injection radius it is deflected in a first bending magnet BMI1 in the
64
clockwise direction (seen from above). It is then deflected counter-clockwise, first by
a second bending magnet BMI2 and by a electromagnetic channel EMDI located in
one of the cyclotron sector gap so that it reaches the first RF cavity gap where beam
acceleration starts. Injecting at 10 MeV allows to take benefit of enough room to
locate the deflecting magnets and use a simple set of deflecting elements with
moderate magnetic field requirements. The main parameters of the injection channel
are given in Table 3.5. The location of the injection and extraction channel elements
of the ISSC are given in Figure 3.6.
The extraction channel allows deflecting the accelerated beam outside the
cyclotron. In order to achieve an extraction efficiency of nearly 100% so as to reduce
induced radioactivity, the extracted orbit at the channel entrance should be fully
separated from the last internal orbit. It consists of an electrostatic deflector (ESDE),
an electromagnetic deflector (EMDE) and a bending magnet (BME). The three
channel components are located in two successive valleys. After the beam is kicked
outwards from the last internal orbit, by the electrostatic deflector located at the exit
of a main RF-cavity it passes through the magnet sector. It is then further deflected
to the entrance of the next valley by the electromagnetic deflector. The last section is
a conventional bending magnet which is located in the valley behind the RF flat
topping cavity as shown on Figure 3.6. Table 3.6 gives the main parameters of the
extraction channel.
3.5 - The separated-sector booster cyclotron (BSSC). A general view of the booster
can be seen in Figure 3.7. The magnet of the final booster consists of 10 identical Cshaped sector magnets with a strong spiral needed in order to obtain sufficient
vertical focusing at high energies. Each sector is made of a pair of spiral pole tips
whose angular aperture is increasing with the radius. The width of the sector at low
energies fixes the magnetic field level Bs needed in the magnet for isochronism and
the value of the vertical focusing frequency νz. The sector width should not be too
large so that devices like the RF cavities and the extraction channel elements can be
installed in the valleys. All these considerations have led us to select a 10 degree
sector angle width at low radii. The corresponding values of the vertical focusing
frequency and sector field are respectively 1.2 T (without space-charge) and 1.8 T. As
in the ISSC cyclotron design, no trimming coils are used for generating the radial
magnetic field increase required by isochronism. This effect is obtained by increasing
the sector width with radius. The characteristics of the magnet are presented in Table
3.7.
65
Acceleration of the beam is provided by 6 main resonators located in the
valleys. They should provide an energy gain per turn of 3.0 MeV at injection and 6.0
MeV at extraction, increasing the beam energy from 120 MeV to 990 MeV. In order to
compensate the effects of the space charge forces, two flat-topping cavities are
needed. The RF frequency of the accelerating (main) cavities has been fixed equal to
42 MHz, which corresponds to the sixth harmonic of the particle revolution
frequency in the cyclotron. Since the beam phase width can be reduced to 15 degrees
at the intermediate cyclotron exit, fifth harmonic operation has been selected for the
flat-top cavities. This enables to decrease the flat-top cavity power compared to
operation on the third harmonic. Single-gap cavities are the most suitable candidates
because azimuthal space is restricted and they have high quality factors. This type
would be used for both accelerating and flat-topping cavities. A voltage (or phase
compression) ratio of 2.0 is used between injection and extraction in order to reduce
the number of turns in the cyclotron and to have sufficient turn separation at
extraction. The main characteristics of the accelerating cavities are given in Table 3.8.
Measurements on the accelerating cavity model (1:3 scale) which can be seen on
Figure 3.8 where the upper part has been removed, have been carried out in order to
check and determine precisely the cavity characteristics. A very good agreement has
been found between theoretical calculations and experimental results.
The power to be delivered to each main cavity of the ring cyclotron is estimated
to be about 2.05 MW (1.45 MW beam power and 0.60 MW cavity loss), which
corresponds to about 2.9 MW electrical power (assuming a 70% DC to RF conversion
efficiency). The beam power to be absorbed by each flat-top cavity is 220 kW, which
is about 20 times the power dissipated in the walls (10 kW). Operating on the fifth
harmonic allows to reduce the power absorption in flat-top cavities by a factor
slightly larger than 2. All the figures above are given for a current of 10 mA.
The injection channel of the BSSC cyclotron is the system that allows to bring
the beam from outside the cyclotron to the first RF cavity gap where it is accelerated.
Its layout can be seen in Figure 3.9, where both injection and extraction channel
components are visible. The main parameters of the injection channel are given in
Table 3.9. The main parameters of the extraction channel are given in Table 3.10.
3.6 - Beam Transport to the EA. The beam extracted from the cyclotron complex
has a typical transverse invariant emittance of ε inv = 2 π 10 -6 rad m (the true
emittance is ε = ε inv / βγ where βγ is the usual relativistic factor), and a momentum
spread of the order of a few 10 -4. The current density is roughly uniform in the
66
transverse phase-space, leading to an approximately parabolic current density in a
focal point. It is not difficult to transport such a beam over significant distances and
to the EA. This can be accomplished with the help of standard bending magnets and
quadrupoles. The momentum of a 1.0 GeV kinetic energy protons is 1.696 GeV/c
corresponding to a magnetic curvature radius of 3.77 metres in a field of 1.5 Tesla
and to βγ = 1.807 . In particular the “goose neck” required to bend the beam from
horizontal to vertical into the EA requires a total bending strength of 8.88 Tesla
× metre. This magnet is also used to separate the beam transport from the neutrons
escaping the EA through the beam pipe. An appropriate beam catcher is used to
remove them far away from the proton beam path.
As is well known, the beam transverse radial dimensions in each plane are
determined by the so-called betatron function ∆x ( z ) = β ( z )ε / π . Over the beam
transport channel, typically β ( z ) ≈ 20 m and the beam radius is ∆x ≈ 5.0 mm. At the
EA beam window we want ∆x ≈ 7.5 cm and therefore β ( z ) ≈ 4000 m. This is realised
by creating a focal point some L = 30 meters away from the window and letting the
beam spread-out naturally because of its emittance. In absence of magnetic fields,
the evolution of the β-function at a distance L from the focal point is given by the well
known formula β ( z ) = β (0) + L2 / β (0) ≈ L2 / β (0) . Setting β ( z ) =4000 m we find
β (0) ≈ L2 / β ( z ) = 0.225 m, which is within reach with the help of an ordinary
quadrupole triplet20. The beam radius at the focal point is very small,
∆x(0) = β (0)ε / π = 0.70 mm. In short the idea is the one of enhancing the angular
divergence of the beam by making a very tiny focal spot 21. A long drift space
following such a focal point will traduce this angular divergence into a large spot.
An appropriate collimator is limiting the aperture available to the beam in this
point to about 10 times its nominal radial size, large enough in order to let the beam
through with no loss in ordinary conditions. In case of the accidental mis-steering of
the beam or of a malfunctioning of the focusing lenses, the spot will grow in size and
the beam will be absorbed by the collimator. In this way the beam window can be
protected against accidental “hot spots” caused by the wrong handling of the beam.
It has been verified that the defocusing forces due to the beam current do not
appreciably affect the beam optics22.
20It
may not seem entirely obvious to obtain such a low beta value with a beam transport if the actual
emittance from the accelerator were less than what is quoted. If so, one could easily increase the
emittance of the beam through the beam transport with the help of multiple scattering or with a pair
of orthogonal small steering magnets operated at high frequencies (Lissajous pattern).
21From phase-space conservation in fact through the beam transport the product of the beam size and
angular divergence is a constant.
22For instance the CERN-PS Booster routinely handles and transports peak currents of the order of 100
mA, about one order of magnitude larger than the present case.
67
The beam must be transported under a reasonable level of vacuum. In our
design the last part of the beam tube is filled with Pb vapour at the pressure of about
5 × 10-4 Torr, the vapour tension of the coolant at the operating temperature.
Differential pumping and a cold trap will remove these vapours which may be
radioactive before they reach the accelerator. There are no appreciable effects of this
residual pressure on the beam propagation. The need of clearing electrodes will be
further studied, but it appears unnecessary at this level.
The extracted beam current and positions are carefully monitored with nondestructive probes, beam profile monitors and pick-up electrodes. In case of a
malfunctioning of the beam, the accelerator current can be cut-off very easily on the
axial injection line of the injectors in times of the order of microseconds (the
transition time from the ion source to the final focus), thus avoiding any damage of
the hardware due to beam mis-steering. An alternate beam dump should be
provided to which the beam could be dumped during accelerator tuning and the like.
3.7 - Conclusions. The above preliminary studies have shown that a 3-stage
Cyclotron facility could provide a solution for a ≈ 10 GeV × mA beam to drive the
Energy Amplifier. Detailed design studies are now being undertaken in order to
clarify the following points in beam dynamics:
1) detailed calculations on the beam dynamics in the injectors in order to assess
the intensity limits of this kind of injector.
2) more refined calculations of the merging of the 2 beams (H+ and H– ) coming
out of the injectors in order to define the beam characteristics at injection in
the ISSC.
3) detailed beam dynamics in the ISSC with space charge effects taking into
account the particle distribution after stripping.
Besides this, technical design studies on the three accelerators have to be
started, in particular mechanical design studies (vacuum chamber of the large SSCs,
optimisation of the shape of the main cavities of the SSCs, etc.). Finally, a conceptual
study aiming at increasing the final energy towards 1200 MeV is in progress.
68
69
Tables and Figures relevant to Section 3.
Table 3.1 - Main parameters of the two ring cyclotrons
Accelerator
External diameter
Magnet iron weight
Magnet power
RF power
ISSC
BSSC
10.5 m
1000 tons
0.6 MW
1.54 MW
16 m
3170 tons
2.7 MW
12.5 MW
Table 3.2 - Main parameters for the 42 MHz design
Accelerator type
Injection
Extraction
Frequency
Harmonic
Magnet gap
Nb. sectors
Sector angle (inj/ext)
Sector spiral extraction
Nb. cavities
Type of cavity
Gap Peak Voltage injec.
Gap Peak Voltage extrac.
Radial gain per turn ext.
Injector
Intermediate
Booster
100 KeV
10 MeV
42 MHz
4
6 cm
4
15 /34 deg
0 deg
2
delta
110 KVolt
110 KVolt
16 mm
10 MeV
120 MeV
42 MHz
6
5 cm
4
26/31 deg
0 deg
2
delta
170 KVolt
340 KVolt
12 mm
120 MeV
990 MeV
42 MHz
6
5 cm
10
10/20 deg
12 deg
6
single gap
550 KVolt
1100 KVolt
10 mm
70
Table 3.3 - Main parameters of the injector cyclotrons
Injection energy
Extraction energy
Number of sectors
Pole radius
Total yoke height
Maximal field in the sectors
Number of main RF cavities
RF frequency
Harmonic number
Peak Voltage
Losses per cavity
Number of flat-top cavities
RF frequency of flat-top cavities
Peak Voltage of flat-top cavities
Axial Deflector field
100 keV
10 MeV
4
0.75 m
1.2 m
1.5 T
2
42 MHz
4
113 kV
17 kW
2
126 MHz
13 kV
15 kV/cm
Table 3.4 - Main characteristics of the ISSC cyclotron RF cavities
Number of cavities
Type of cavity
Frequency
Cavity height
Cavity length
Voltage at injection
Voltage at extraction
Quality factor
Losses/cavity
Beam power/cavity
Total power/cavity
Total electric power/cavity
(70% efficiency)
Main cavities
Flat-top cavities
2
λ/2, double-gap,
tapered walls
42.0 MHz
2.6 m
2.6 m
2×170 kV
2×340 kV
13000
220 kW
550 kW
770 kW
2
λ/2, double-gap,
tapered walls
126.0 MHz (h=3)
1.0 m
2.45m
2×20 kV
2×40 kV
11000
9 kW
-65 kW
-56 kW
1.1 MW
13 kW
71
Table 3.5 - ISSC Injection channel characteristics
Element
BMI1
BMI2
EMDI
Length (m)
Magnetic field DB (T)
0.4
0.6
0.8
0.4
1.0
0.25
Table 3.6 - ISSC Characteristics of the extraction channel elements
Element
ESDE
EMDE
BME
Length (m) Electric field (kV/cm)
0.4
0.9
1.2
Magnetic field DB (T)
80
0
0
0
0.25
1.0
Table 3.7 - Main characteristics of the booster magnets
Number of sectors
Angular aperture at injection
Angular aperture at extraction
Spiral angle at extraction
Magnetic gap in the sector
Overall external diameter
Total iron weight
Maximum field in the sector
Total electric power
10
10 deg
20 deg
12.0 deg
50 mm
15.8 m
3170 tons
1.8 T
2.7 MW
Table 3.8 - Main characteristics of the booster cyclotron accelerating cavities
Frequency (MHz)
Number of cavities
Type of cavity
Voltage at injection
Voltage at extraction
Quality factor
Losses (estimated)
42.0
6
λ/2, double-gap, curved walls
550 kV
1100 kV
31000
600 kW
72
Table 3.9 - BSSC Injection channel characteristics
Element
Length (m)
Field drop DB (T)
BMI1
BMI2
BMI3
BMI4
BMI5
EMDI
0.90
0.50
0.50
0.50
0.50
0.90
1.70
1.30
1.70
1.70
1.30
0.25
Table 3.10 - BSSC Extraction channel characteristics
Element
Length (m)
B-Field drop (T)
E-Field (kV/cm)
ESDE
EMDE
BME
0.80
0.30
1.30
0.16 T
1.0 T
55
-
73
Figure Captions.
Figure 3.1
General lay-out of the accelerator complex.
Figure 3.2
General view of the injector.
Figure 3.3
General view of the ISSC.
Figure 3. 4 Beam evolution in the r-φ plane for the first 16 turns.
Figure 3.5
Photographs of the cavity models (top: main cavity during assembling,
bottom: flat-topping cavity during assembling.
Figure 3.6
Location of the injection and extraction channel elements of the ISSC.
Figure 3.7
General view of the booster ring cyclotron.
Figure 3.8
Photograph of the model of the accelerating cavity of the booster.
Figure 3.9
Location of the injection and extraction channel elements of the booster
ring cyclotron.
74
;
@
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FIG. 3.2 General view of the injector cyclotron
Figure 3.3
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Figure 3.4
FIG. 3.5 Photographs of the cavity models (top : flat-topping cavity during
assembling ; bottom : main cavity during assembling.)
Figure 3.7
FIG. 3.8 View of the model of the accelerating cavity of the booster
75
4. —The Energy Amplifier Unit.
4.1 - Introduction. The general layout of the EA unit is shown in Figure 4.1a-b.
The main design parameters are given in Table 4.1. In short it consists of a main
vessel, about 6 m in diameter and 30 m tall, filled with molten Lead. The vessels,
head enclosure and permanent internal structures are fabricated and shipped as an
assembled unit to the site. The shipping weight is then about 1500 tons. Removable
internal equipment is shipped separately and installed through the top head. The
relatively slender geometry enhances the uniformity of the flow of the molten Lead
and of the natural circulation for heat removal.
A high energy beam is injected through the top and made to interact in the Lead
near the core. The heat produced by the nuclear cascade is extracted by the Heat
Exchangers. Most of the inside of the vessel is free of obstructions, in order to permit
a healthy circulation of the cooling liquid. The circulation of the Lead in the vessel is
ensured exclusively by natural convection.
There are four 375 MWth heat
exchangers to transfer the heat from the primary Lead to the intermediate heat
transport system. They must be designed in such a way as to introduce a small
pressure drop in order not to slow down too much the convective cooling flow. The
liquid once cooled by the heat exchangers, descends along the periphery and feeds
the lower part of the core and the target region. A thermally insulating wall
separates the two flows. In order to have an effective circulation at the chosen power
level (1500 MWth), the temperature gradient across the Core must be of the order of
250 oC. Consequently the volume inside the vessel can be ideally divided in three
separate regions, namely (1) the target/core/breeder region, (2) the convection draft
generating region and (3) the heat exchangers region. A remotely controlled
pantograph transfer machine is used to transfer fuel between the core, storage racks
located in the convection generating region and the transfer station, where they can
be inserted or removed from the EA vessel by a transfer cask23. The fuel storage
region can be used also as a cooling down region for spent fuel. Fuel bundles can be
extracted or introduced into the vessel with the help of appropriate tooling through
the top cover of the vessel 24. According to previous experience with such
23Refuelling
machines of this type have been applied in the UK’s PFR, Italy’s PEC and Japan’s
MONJOU. The conceptual design for the ALMR transfer machine was provided by Ansaldo (Italy).
24As already pointed out, in order to reduce the proliferation risk, the fuel extraction or injection
operation may be restricted to the user (owner) of the plant and allowed only to specialized team. This
is possible since refuelling occurs only once about every 5 years and there are no major, active
elements which need access during operation.
76
pantographs, widely used in existing Fast Reactors, the refuelling time may require
of the order of 1-2 weeks. As described in the text, it is to be performed about once
every five years or so.
The proton beam enters the vessel through a long cylindrical evacuated tube of
about 30 cm diameter, which restricts to 20 cm before entering the core region. The
beam diameter at the window is about 15 cm. The life expectancy of the beam
penetration window is estimated to be about 1 year, namely it requires periodic
replacement, performed extracting the full beam tube. The window is cooled by the
main Lead circulation in the vessel. Accidental breaking of the window will fill the
beam tube with molten Lead. This will bring the Energy Amplifier to a halt, since the
injected lead will act as a beam stopper. The design of the beam penetration channel
is more amply discussed further on.
There are no control bars and the power produced is controlled with the beam
current. A feed-back system ensures that the inlet temperature of the heat exchangers
is maintained to the specified value. For further safety however the ultimate shut
down assembly which drops CB4 by gravity, is retained, following the ALMR design,
but slightly modified since the buoyancy of the Lead is much greater than the one of
Sodium. This simple scram system is however used to anchor the EA solidly away
from criticality when not operating. In contrast with an ordinary Reactor, in the EA
there are no main elements of variability in the neutronics of the device.
Accidental thermal run-off is ultimately prevented using the natural expansion
of the coolant. In case of an overheating of the EA, its lead level rises at the rate of
27 cm/100 oC. Such a level rise (see Figure 4.1b) is used to activate an overflow path
which
(1) fills through a siphon a cavity located about 25 m above the Core, in which
the proton beam is safely absorbed. Natural convection is sufficient to
remove the residual power of the proton beam, which represents about 1/6
of the amount of the initial decay heat.
(2) fills with molten Lead the narrow gap between the vessel liner and the
containment vessel, ordinarily filled with Helium25 gas at normal pressure
(Figure 4.1b). The thermal conductivity increases from the 0.03 W/m/K of
Helium at 1 bar pressure to 16 W/m/K for Pb. This allows the surplus heat to
be dissipated away into the environment through air convection and
radiation (RVACS),
25
The choice of helium gas is justified by the fact that the more commonly used Argon will mix with
the radio-active nuclide 42Ar produced by the spallation cascade.
77
(3) scrams the EA to a low k- value. Safety is also enhanced by the strong
negative void coefficient and the negative temperature coefficient (Doppler)
of the fuel which operates at relatively low temperatures.
These passive safety features are provided as a backup in case of failure of the
active systems, based on the ultimate shut-off of the proton beam from the
accelerator, which brings to an immediate stop the fission generated power of the
Amplifier. These functions are achieved by passive means without operator action.
The key processes underlying these functions are governed by thermal expansion,
natural circulation of molten Lead, natural air circulation on the outer containment
surface, and thermal radiation heat transfer which becomes very effective at elevated
temperatures. Our design integrates all these effects into an efficient passive safety
system which can accommodate primary coolant flow loss and loss of heat removal
of secondary transport system with benign consequences on the Core, which can
survive with no damage.
The various main components constituting the EA will be separately discussed.
4.2 - Molten Lead as Spallation Target and Coolant. Lead constitutes an ideal
spallation target, since its neutron yield is high, and it is very transparent to neutrons
of energies below 1 MeV. It has also excellent thermodynamical properties which
make it easy to dissipate the intense heat produced by the beam. As illustrated in the
previous sections, Lead has also the required properties in terms of small lethargy
and small absorption cross sections to perform the function of main coolant. Its very
high density and good expansion coefficient make convection sufficient even for
large power production. Finally it is an excellent shielding material and most of the
radiation produced by the EA core is readily and promptly absorbed. There is no
need to add additional internal shields or reflectors like in the case of Liquid Sodium
to protect structurally important elements inside the vessel. The radiation dose
transmitted to the outer Main vessel is very small. Hence, unlike for instance in
PWRs, its active life is very long since the neutron fluence is about 1020 n/cm2/ year
its radiation damage is negligibly small (see Table 5.5).
Molten Lead when compared to Sodium, has considerable advantages on
safety. The void coefficient of Sodium is notoriously positive, namely creation of
bubbles increases the reactivity. In Lead the void coefficient is negative. The absence
of void coefficient problem allows for instance a less flattened shape of the fuel core.
Hence the fuel pins in our design are substantially longer. The boiling point of Lead
78
(1743 oC) is also much higher than the one of Sodium (880 oC) and it does not react
like Sodium in contact with air. Thermodynamic properties of both molten metals
are given in Table 4.2. Saturation vapour pressure and evaporation rate against
vacuum are shown in Figure 4.2. Since these quantities are very small (respectively
5 × 10-4 Torr and 10-5 g cm-2 s-1 ) it is possible to keep molten Lead in an evacuated
region: this feature is very important to ensure safety for the proton beam. In
general, in order to have the same pressure and temperature changes through the
core for a given specific power production, the speed of circulating Lead must be
about 0.38 times the one of Sodium and the pitch in the fuel lattice must be enlarged
in order to provide a flow area which is 1.8 times larger. The flow speed of Lead in
the core is typically of the order of few m/s. The mass flow through the core is
approximately doubled with respect to Sodium. Once these changes are easily
implemented the two fluids become essentially equivalent.
Notwithstanding there is little or no experience in the use of Lead as a coolant
in Reactors, with the exception of Military applications in the former USSR. For
instance the use of molten Lead requires further studies to overcome corrosion. As
discussed further on, such a problem appears fully manageable.
Natural Lead exposed to an intense neutron flux in the EA will become
activated. Since the Lead is circulating in the EA this activity will spread from the
core to the rest of the device. Fortunately the main activation channels are benign.
Natural Lead is made of several isotopes, 208Pb (52.4%), 206Pb (24.1%), 207Pb (22.1%)
and 204Pb(1.4%). If the target is ideally made of pure 208Pb, a neutron capture will
produce 209Pb, which quickly (t1/2 = 3.25 h) decays into the stable 209Bi (with a β−
decay of 645 keV end point and no γ-ray emission) which will remain as eutectic
mixture with the target material. Reactions of type (n, 2n) occur at a level which is
few percent of captures and create 207Pb, also stable. Both daughter nuclei are stable
elements and excellent target material themselves. A target with natural Lead will
produce an appreciable amount of 205Pb from captures of 204Pb and to a smaller level
from (n, 2n) of 206Pb. This element is long lived (t1/2 = 1.52 107 y) and decays into
stable 205Tl by electron capture (i.e. by neutrino emission) and no γ-ray emission.
The Q of the decay is only 51 keV. Therefore its presence is relatively harmless.
Neutron capture properties of 205Pb are unknown and therefore it is impossible to
estimate the possibility of further transformations. However it is likely that the main
channel will be neutron capture, leading to the stable 206Pb. Finally 203Pb from (n,
2n) of 204Pb is short lived (t1/2 = 51.8 h) and decays into stable 203Tl by electron
capture and γ-ray emission. Reactions of the type (n,p) which are very rare since they
occur only for high energy neutrons, transform Pb isotopes into the corresponding
79
Thallium isotopes (208Tl, 207Tl, 206 Tl and 204 Tl) which all β-decay quickly into Pb
nuclei again.
The situation is more complex in the case of a Bismuth target. Neutron captures
lead to short lived 210Bi which decays (t 1/2 = 5.0 d) in 210Po which, in turn, decays
with t1/2 = 138 days to stable 206Pb. There is a long lived (t1/2 = 3×106 y) isomeric
state 210mBi, also excited by neutron capture, which decays by α-decay to short lived
206 Tl (RaE), which in turn β-decays in stable 206 Pb. Reactions of the (n,2n) type
would produce the long lived (t 1/2 = 3.68 10 5 y) 208Bi, which ends up to stable 208Pb
via internal conversion. Therefore a Bismuth moderator may present significant
problems of radio-toxicity which must be further examined before seriously
considering such material as target. Consequently the use of Bismuth or of BismuthLead eutectic mixtures is not considered as main coolant, since Bismuth via the
leading single neutron capture produces sizeable amounts of Polonium which is
radio-toxic and volatile at the temperatures considered for the present study.
However such mixture is envisaged for secondary cooling loops because of its lower
boiling point (125 oC).
Additional fragments are produced by the spallation processes due to the high
energy beam (see Table 5.10). The toxicity problem is investigated later on, although
there is expectation that no major problems should arise, provided the appropriate
precautions are taken.
4.3 - Corrosion effects due to molten Lead. Molten lead has a significant solubility
for many metals ( Ni and Mn > 100 ppm; Fe, Cr, Mo, 1 ÷ 10 ppm at 600 oC), which is
a rising function of temperature (Figure 4.3). As a consequence, after prolonged
immersion some metals and alloys exhibit a significant deterioration. This is a
relevant problem and it must be mastered. Some experience on the use of Lead and
Bismuth coolants in Nuclear Reactors exists in the former Soviet Union. Extensive
studies of corrosion of Lead-Lithium mixtures have been carried out in the context of
Fusion, where a neutron multiplying, Tritium breeding blanket is necessary. For
instance a steel type HT-9 immersed in liquid Lead for 50,000 hours exhibits a
corrosion loss of about 80 µm at about 500 o C [43]. In general Ferritic steels are
moderately corroded by lead and in particular they do not exhibit inter granular
damage (typically 30 µ after some 3000 hours at 575 oC for EM 12). The effect is more
pronounced for austenitic steels (typically 120 µ after the same period at 700 oC for
800 H, where also mass transfer from the hot to cold regions is observed). Several
80
successful methods have been devised and demonstrated effective in order to
suppress corrosion due to prolonged hot Lead Immersion:
1) Purification and additives to the liquid metal. When a de-oxidant (225 ppm Mg) is
added to lead, no corrosion (0 µ) is observed [44] for 15 CD 9-10 loops after
28000 hours (3.2 years) of tests at 550 oC. In comparison, the same conditions
and no additive would result in a corrosion in excess of 300 µ. Similar results
are obtained with Titanium or Zirconium additions to the liquid Lead, where no
corrosion is observed after 750 hours at 950 oC [45], in contrast to a 400 µ for an
uncoated steel. Their beneficial effect is probably related to the formation of
nitrides at the interface Steel/Lead. The nitrogen is contained in the Steel, if not
treated beforehand. If the Zirconium is maintained constantly the film is selfhealing and its long term effectiveness is preserved.
2) Coating materials. Amongst all the coated materials which have been tested,
some seem to give the best results (i) 15 CD 9-10 low chromium steel coated
with plasma sprayed Molybdenum [46][47], where no cracking or dissolution is
observed after 1500 hours at 720 oC; (ii) Aluminium on low Chromium steel [46]
where no evolution of the specimen is observed after 1500 hours at 750 oC. The
coated material is prepared by heating the specimen in contact with a mixture of
aluminium oxide and Aluminium. The coating probably reacts with traces of
Oxygen to form a self-healing protective Alumina film; (iii) Z6 CN 91-9 coated
with ZrN: this coating is self-healing if Zirconium is added to Lead. These last
two possibilities are considered the most promising in view of to their selfhealing capacity.
A small amount of embrittlement may also occur for some alloys (45 CD 4 and
35 CD 7) mostly around the melting point of Lead. Liquid metal embrittlement is a
reduction of the fracture strength of a metal stressed in tension while in contact to a
surface active liquid metal. This effect is enhanced when some elements such as Sn,
Sb and Zn are added to the Lead. As for 15 CD 9-10, no significant embrittlement
effect has been evidenced, even in the 320-350 o C temperature range. Hence
specifications on the maximum concentration of certain elements in Lead must be
established.
In conclusion there is no doubt that some type of additives and/or coating can
effectively stop corrosion in the domain of interest [37]. But an important experimental
work has to be done (non isothermal experiments, effects of cyclic load and so on).
81
4.4 - The Proton beam. The proton beam (≈ 10 mA) after acceleration and beam
transport is brought to the Amplifier by conventional beam transport and a 90
degrees bending on top of the vessel. The amount of power of the beam is
comparable to the one envisaged in Neutron Spallation sources under design [48].
The magnetic bending helps also in separating leakage neutrons, which are absorbed
in an appropriate beam dump. By switching off the bending magnets of the last
bending, the beam can be safely diverted to an appropriate beam dump. An
appropriate but conventional design of the beam channel allows to perform the
switch to the beam dump in a time of the order of 1 millisecond, which is extremely
short in view of the thermal inertia of the Amplifier. The beam, focused by
conventional quadrupoles, traverses the whole beam penetration tube and enters in
the lead coolant and target through a window made of Tungsten ≈ 3 mm thick. The
material has been chosen for its high melting temperature (3410 oC), its excellent
thermal conductivity, its high mechanical strength26 and acceptable activation
properties. In addition it exhibits a negligible corrosion by molten Lead [49].
The beam spot size is determined by the physical distance from the focal point
(≈ 30 m), where a narrow collimator has been installed (see paragraph 3.6). This
arrangement ensures that the beam size at the window cannot become abnormally
small, for instance as the result of a miss-steering or a failure of the beam transport.
The proton beam window has a spherically curved profile and it is cooled by the
bulk of the Lead coolant circulating in the target region at a speed of the order of a
few m/sec. At the window the proton beam spot size has a parabolic profile,
2I p / πro2 1 − r 2 / ro2 with 2ro = 15cm corresponding to a peak current density of 113.2
µA/cm2 for Io = 10 mA. Montecarlo calculations show that the beam deposits about
1% of its kinetic energy in passing through the window, mostly due to ionisation
losses, namely ≈ 95 kWatt, with a peak power density in the centre of 113 W/cm2,
which is comparable to the peak power density of the fuel rods. The same
Montecarlo calculations, in excellent agreement with experimental data [50] have
been used in conjunction with a fluid-dynamic code to predict the temperature and
flow of the coolant and the conditions of the window27. The maximum temperature
rise for the Tungsten and the surrounding Lead is respectively ∆T = 137 oC and ∆T =
[
26The
]
use, for example, of alloys like Tungsten-Rhenium can further enhance the mechanical
resistance of the window and its weldability. In particular such an alloy has a higher re-crystallisation
Temperature (1650 °C vs. 1350 °C for pure Tungsten). However it has a considerable disadvantage,
namely the thermal conductivity is about a factor 2 lower. Note that the operating temperature of the
window is about 540 °C and the incipient re-crystallisation temperature is considerably higher
(1150 °C)
27The thermal hydraulic model has been built using the code STAR-CD [51] and describes at the same
time, the thermal behaviour of the lead (liquid) and of the beam window (solid).
82
107 o C. Thermal stresses associated with beam intensity variation have been
estimated and found largely within the limits set by the properties of the material28.
We have reduced such thermal stresses by reducing the thickness of the window
from 3 mm in the welding of the pipe to 1.5 mm in the centre of the hemisphere,
along the beam axis and were most of the energy is released (see Figure 4.4). More
generally the energy deposited by the beam predicted by the Montecarlo calculations
is pictured in Figure 4.5. The temperature profiles of the window and of the
surrounding Lead are shown in Figure 4.6 for a local Lead speed of 5 m/s. The main
parameters of the final beam transport in the Vessel are listed in Table 4.3.
The window should safely withstand accidental power densities which are
more than one order of magnitude larger than the design value. The expected peak
radiation damage in the window after 6000 hours at full beam intensity is of 171.1
d.p.a. and the associated gas production are of 1.1 × 104 He (appm) and 9.97 × 104 H
(appm). These values are reasonable but suggest that the window should be
periodically replaced. A high quality vacuum ( ≤ 10-4 Torr ) in the final beam
transport and in the Accelerator is easily ensured by differential pumping and a Cold
Trap in which Lead vapour will condense. The low Lead vapour pressure in the last
part of the beam transport (≈ 5 × 10-4 Torr at 600 °C) has no appreciable influence on
the proton beam which has a high rigidity and penetrating power.
In the unlikely possibility that the proton beam will persist even for instance if
the main cooling system of the Amplifier would fail, a totally passive system (Figure
4.7), driven by the thermal dilatation of the Lead coolant will ensure that an enlarged
volume region, sufficiently massive to stop the proton beam will be automatically
filled with liquid Lead, the Emergency Beam Dump Volume (EBDV). A shut-off
valve at the bottom of the volume ensures that the whole beam pipe is not filled with
Lead. This measure has no character of necessity, but only of convenience. Indeed in
the unlikely case that the Tungsten window would break, liquid Lead will rise, such
as to fill completely the pipe and the Emergency Beam Dump Volume, though at a
slightly lower level, but still sufficient to kill the beam and bring the Amplifier safely
to a halt. It has been verified that convection cooling can safely transfer the heat
produced in the EBDV (10 MW) to the main Lead coolant. This method is applicable
because of the high density (10.55 g/cm3) and the low vapour pressure (≈ 5 × 10-4
Torr at 600 oC) of the molten Lead (Table 4.2 ).
28
The static structural analysis of the window has been performed using the code ANSYS [52]. The
model developed used detailed pressure and temperature maps coming from the thermal hydraulic
calculations.
83
4.5 - Fuel design and Burn-up goals. Fuel and Breeder elements are loaded in the
form of thin rods (pins). Pins are clustered in sub-assemblies, each with a predetermined number of pins, arranged at constant pitch roughly in an hexagonal
configuration. Pins are made of small oxide pellets inserted in a robust steel cladding.
Each pin has two extended void regions, called “plenums”, one at each end, intended
to accumulate the gaseous fission fragments. The pins are kept separate by a wire
wrapped around the pin, which also improves the coolant flow. The main
parameters of the fuel assemblies are listed in Table 4.4. They are quite similar to the
ones used in Fast Breeders (FB). But in order to adapt these well proven designs to
our case we must (1) modify the pitch between pins to the different thermodynamical
properties of the Lead coolant when compared to Sodium and (2) reduce the coolant
pressure losses through the plenum region. The temperature and pressure drop
across the core must be adjusted to the requirements of convective cooling. We have
chosen two different sub-assemblies with different pitches: a wider pitch is used in
the central part of the core where the specific power is larger. The flat to flat distance
is the same for all sub-assemblies but the number of pins is slightly different to
accommodate the two different pitches.
The burn-up of an ordinary reactor varies from the 7 GW × day/t of a natural
Uranium fuel of CANDU reactors to the 30 ÷ 50 GW × day/t of enriched Uranium in
PWRs. The fuel burn-up of the EA is of the order of 100 GW × day/t, averaged over
the fuel volume. The most exposed pins, if no intermediate shuffling is performed
will accumulate about 200 GW × day/t. The practical final burn-up is determined
not only by the losses of fuel quality due to FF captures, but also by (1) radiation
damage of the supporting structures; and (2) pressure build-up of gaseous fission
fragments. These two effects are briefly reviewed:
1) Radiation damage of the pins. Note that for a given power yield, the flux in the
case of 233U is smaller than the one of 239Pu in a FB by a factor 0.64 due to the
difference in cross sections. Therefore 150 GW × day/t for a Thorium based EA
produce an integrated neutron fluence through the cladding ∫ φ dt equals to the
one after about 96 GW × day/t in a FB. Considerable experience exists in burnup tests for fuel pins in FB. Based on this extensive experience, a limit of about
100 ÷ 120 GW × day/t is a current goal value for most of these designs. A
reasonable goal for the radiation damage in the Amplifier will then be 160 ÷ 180
GW × day/t for the most exposed pins. A burn-up of 100 GW × day/t in our
case corresponds to an integrated neutron fluence through the cladding of ∫ φ dt
84
= 3.3 × 1023 n/cm2. The most exposed pins will accumulate about twice such a
fluence. The effects on the properties of the HT-9 steel used have been
examined [53]. The conclusion is that we expect ≈ 34 d.p.a./year for the most
exposed pins. A reasonable ultimate limit applicable to this material is 225
d.p.a. A five year lifetime is therefore reasonable. Likewise other effects,
namely He production and embrittlement appear fully acceptable.
2) The fuel material in form of (mixed) Oxides will undergo considerable damage
and structural changes in view of the considerable fraction which is burnt and
transformed into FFs. The behaviour of ThO2 is not as well known as the one of
the UO 2 which is presently universally used. However, the thermal
conductivity, the expected mechanical properties and the melting point of ThO2
are more favourable than in the case of UO 2 and we do not anticipate any major
problem. For these reasons we have chosen at least at this stage the rather
conservative average power density of ρ = 55 W/g29. The most exposed pins
will operate at ρ = 110 W/g. The temperature of the fuel averaged over the core
is then 908 o C. The average temperature of the most exposed pins is then
1210 oC and its corresponding hottest point 2350 oC, well below the melting
point of ThO2 which is 3220 oC.
3) Some space must be provided for the fission fragments, which have in general a
significant mobility, especially at high temperatures. The pressure build-up is
not very different for different fissionable fuels and therefore the volume of the
plenum for the gases due to FFs has been calculated taking into account the
mechanical properties of the cladding under a specified pressure increase,
assuming that all gaseous products escape the fuel. The plenum fractional
volume turns out to be essentially the same as the one of the conventional pin
designs for Fast Breeders (ALMR, EFR etc.). The hottest point of the cladding is
707 oC, well below the structural limits of the steel of the cladding30. Note also
that, when compared to Sodium cooled pins, we are dealing with a single phase
coolant with negative void coefficient.
We have therefore taken as reference parameters for our design pins (Figure 4.8)
which are essentially the same as those used in our “ FB-models” designs with,
however, the following changes:
(1) longer fuel pins to improve neutron containment in the core (1.5 m);
29This
30
value is about one half of what is currently used in SuperPhenix and Monjou.
The corresponding value for Monjou is 675 oC.
85
(2) a larger, variable pitch to accomodate the differences in hydraulics of molten
Lead in a convective regime. Two different pitches have been used, a wider
one for the Inner Core and a tighter one for the Outer Core;
(3) an appropriate “plenum” to ensure the required burn-up, but with smaller
diameter and correspondingly more elongated in order to reduce the
pressure drop through the core;
(4) cladding made of steel with low activation and small corrosion rate by
molten lead (HT-9). More research work is still required to ensure an
effective protection against corrosion ( see paragraph 4.3).
The general layout of the two fuel subassemblies is shown in Figure 4.9. Many of
these subassemblies which have all the same flat to flat dimensions are arranged in a
continuous, quasi circular geometry with an empty central region for the Spallation
Target assembly and the molten Lead diffusing region. A few hexagonal elements
are left empty for the scram device and other control functions.
The Breeder is designed to compensate for the reduction of the 233U stockpile
during the long burn-up and the inevitable losses due to reprocessing. Especially if
the EA is started well below the breeding equilibrium, such an additional amount is
small. Hence the breeder mass is typically some 20% of the total fuel mass. For
simplicity, the pin and subassembly geometry have been taken to be the same as in
the case of the Fuel elements. Toward the end of the fuel cycle, some significant
power is produced also by the Breeder (ρ = 3.0 W/g), though much smaller than in
the Fuel.
During successive fuel cycles, the isotopic composition of the Uranium changes,
especially due to the production of a substantial amount of 234 U. In order to
accomodate the extra mass some additional 20 cm of the fuel pin are left initially
empty and progressively filled. Hence for asymptotic fuel composition, the active
length of the fuel pins may be increased to as much as 1.70 m.
Small amounts of Trans-uranic elements (Np, Pu and Am) and long lived 231Pa
are separated out during each reprocessing and re-injected in the EA for final
incineration. It is convenient to insert these materials in special “incineration” pins
which undergo no successive periodic reprocessing at least until a major fraction of
the isotopes is incinerated. These pins have a much shorter fuel section and a much
larger “plenum” section, to allow build-up of fission fragments. The lifetime of the
cladding is limited by radiation damage. We have already estimated that the
ordinary fuel exposure accumulates ≈ 34 d.p.a./year. Assuming an ultimate
cladding lifetime of 250 d.p.a. these pins may last 7/8 years. After this time they
86
must be reinforced with a second, fresh cladding or equipped with a new one. In
order to ensure the fastest incineration these pins must be located where the flux is
the highest, namely near to the target region.
The operating temperature of the plant is application dependent. In our basic
design we have retained the choices of the reference design, which calls for a fuel
outlet temperature of about 600 oC. It must be noted however that in principle the
Lead coolant could permit a somewhat higher operating temperature, which is
advantageous to increase the efficiency of the conversion into electricity and
eventually to produce synthetic Hydrogen [4]. Evidently additional research and
development work is required in order to safely adapt our present design to an
increased operating temperature. In particular the cladding material of the fuel pins
may require some changes, especially in view of the increased potential problems
from corrosion and reduced structural strength31.
4.6 - Core lay-out and main parameters. The EA is based on a highly diffusive
structure (molten Lead) in which a number of fuel elements are inserted. In absence
of fuel, spallation neutrons produced roughly in the centre of the device will diffuse
and loose adiabatically energy until either they are captured or they escape. If fuel is
inserted gradually in the molten Lead medium, both the captured fraction in Lead
and the escape probability will decrease. The fuel properties will gradually influence
the neutronics. We consider as reasonable design parameter an escape probability
≤ 1% and captures in the Lead moderator of the order of 5-6% (Table 4.5). Note that
in an EA the neutron inventory is of primary importance and that these losses must
be as small as possible. While in an ordinary PWR losses can be easily compensated
with a more enriched fuel, the necessity of full breeding does not offer much degrees
of freedom in an EA. On the other hand the void coefficient for molten Lead is
negative and therefore the rather awkward measures ordinarily taken in a Sodium
cooled device are no longer necessary. In particular one does not need to make the
shape of the fuel core “pancake” like. A more spherical profile improves the neutron
containment and hence the losses in the moderator.
Because of the long migration length in the Lead medium, these parameters are
largely independent on the detailed geometry of the fuel and depend primarily on
the fuel and diffuser masses. The core can be ideally divided into three concentric
31
Titanium based alloys have been studied for the Fast Breeder and may be an interesting
development for our application. In particular the corrosion of molten Lead on Titanium is very low.
87
regions. The first region (the Spallation Target) has no fuel and it is naturally filled by
the molten lead. In this volume beam particles interact to produce primary neutrons.
The radial size of such a volume has to be sufficiently ample in order to ensure that
the neutron spectrum is made softer by the occurrence of (n,n’) inelastic interactions
in Lead. In this way the spectrum at the first fuel element is softened sufficiently as
to ensure a minimal radiation damage to the structural materials and to uniformise
by diffusion the vertical illumination of the fuel pins. We have chosen a radial
distance of the order of ≥ 40 cm. With this choice, the calculated spectrum at the edge
of the target region is not appreciably different from the one in the core. The second
region is the Main Fuel region, in which a variety of fuels can be inserted (generally
subdivided in two parts, the Inner Core and the Outer Core with different pitches),
followed by a third region, the Breeder region, initially loaded with pure ThO2
breeding material.
The nominal power of 1500 MW th requires 27.3 tons of mixed fuel oxide at the
average power density of 55 W/g. The duration of the fuel is set to be 5 years
equivalent at full power. The average fuel burn-up is then 100 GWatt day/ton-oxide.
The main parameters of the Fuel/Breeder core are listed in Table 4.4. As already
pointed out the breeding equilibrium concentration of 233U, referred to 232Th is ξ =
0.126. With such a high concentration there is obviously no problem in setting the
wanted value of k and eventually even of reaching criticality. However with
continued burn-up the fraction of captures due to FFs, ∆L ff will grow linearly with
time, absorbing for instance about 6% of all neutrons at 100 GW × day/t and causing
a corresponding reduction in the criticality. The reduction of the multiplication
coefficient ∆k ff = −( ηε / 2)∆L ff will be very large. For instance, if initially we have k =
0.98 and G= 120, after 100 GW × day/t, k = 0.908 and G = 26.0. Such fivefold decrease
of gain would be completely catastrophic. It is therefore preferable to start with a
233U concentration lower than the breeding equilibrium and let it grow toward such
a limit during burn-up. As already pointed out in paragraph 2.7 one can realise a
first order cancellation between the approximately linear rise of the FF captures and
the exponentially approaching breading equilibrium. This leads to a much smaller
initial 233U concentration, x = 0.105.
4.7 - Convective Pumping. Convection pumping is realised with the help of a
sufficiently tall Lead column in which the warm coolant from the Core rises as a
result of the large value of the Lead expansion coefficient, 1.32 kg m –3 K-1 . The
coolant returns to the Core after being cooled down to the initial temperature by the
88
heat exchangers. The pressure difference generated in the loop by the convective
pumping action is given by ∆P = K ∆T h g , where ∆T is the temperature change, K is
the coolant expansion coefficient, h is the height of the column and g the gravity
acceleration constant. Typically for ∆T = 200 oC, h = 25 m, we find ∆P = 0.637 bars!
Such a pressure difference is spent in order to put into movement the coolant and in
stationary conditions it is equal to the sum of the pressure drops in the loop,
primarily the pressure drops across the Core and the Heat exchangers. The pumping
power required to move a volume V = 10 m3/s of coolant with a pressure difference
∆ P across the Core is W pump = V∆P = 0.647 MWatt. Such power must evidently be
produced by the convective pump.
In order to dissipate a power q produced by nuclear reactions in the pin with a
resulting temperature difference ∆T, the coolant must traverse the core with a speed
v given by
q
υ=
f a ∆Tρ c p
where f a is the flow area and ρ and c p are respectively the density and specific heat
of the coolant. For cylindrical pins of radius r ≡ [r f ;r p ] of the fuel and the plenum
respectively arranged in an infinite hexagonal lattice of pitch p, the flow area is
f a = 3p 2 / 2 − π r 2 . Neglecting end effects and the temperature dependence of the
parameters, the pressure drop through the core ∆P consequent of a given flow speed
v in the fuel which the pump must supply is given by
1.25
1.75
−0.25
l f l p de, f f f
ρ υ de
2 χη l ρ υ 2
4 fa
∆P =
; η = 0.079 ×
; χ= +
; de =
de
l de, p f p
l
2 πr
µ
where χ is a geometry dependent factor, l = l f + l p the pin length, divided in the fuel
section and the plenum section; η is the friction factor, function of the Reynolds
number, which in turn depends on the viscosity µ; de ≡ [de, f ;de, p ] is the effective
diameter of the fuel and the plenum and, function of the coolant flow area
f a ≡ [ f f , f p ] and of the so-called wetted perimeter. Additional corrections which
typically amount to a maximum of 8% are due to the abrupt changes of the coolant
flow area:
2
2
2
2
ff
fp
f p f f
2 χη l ρ v 2 ρ v 2
f0 f f
1− + 1− + 21− + 21−
∆P =
+
ff
fp
fo f p
de
4
fp fp
where f o is the free flow area. With these corrections, the results of the formula [54]
are in excellent agreement with the full hydrodynamic code COBRA [55].
In practice we take the temperature difference ∆T as an input design parameter,
which determines the primary pressure difference ∆ P pump for a given convective
pump column of length L. Such pressure difference must get the coolant through the
89
Core, the heat exchangers and the full loop (> 2L long) at a sufficiently high speed as
to transfer the large amount of heat produced from the Core to the secondary loop.
In order to provide sufficient margin for the other pressure drops, somewhat
arbitrarily we have set the pressure drop across the core to 0.7 ∆Ppump, setting in this
way the pressure and the temperature differences across the core. The pitch size of
the lattice can be adjusted next in order to set the coolant speed v through the core to
the value required by the actual power density and by ∆ T. The resulting pitch and
coolant speed as a function of the power density in the pins is given in Figure 4.10a
and Figure 4.10b for L= 25 m and different temperature differences in the range 150
oC to 250 oC. They appear quite acceptable.
Since the power density produced in the fuel rods is falling about linearly with
the inverse of the radius, the resulting pitch will be a smooth function of the core
radial co-ordinate, leading to a pitch size decreasing with radius. In practice and in
order to permit the same flat to flat dimensions for the fuel bundles across the core
and a given fuel pin radius, we have actually quantified the pitch into discrete values
corresponding to different number of integer rounds of hexagonal shape. This leads
to some residual radial dependence of ∆ T, which is partially absorbed by natural
mixing along the convective column and it should be compensated restricting the
flow for instance at the entry of the fuel bundles. Evidently a radial pitch variation
affects also the neutronics of the core, which in turn has effects onto the power
density. Hence, all these parameters have to be recurrently adjusted to their optimal
values.
The motion of the warm coolant in the convective column is the key to the
convective pumping and it has been carefully simulated with help of the full
hydrodynamic code. The actual temperature and speed distributions at the exit of
the core have been used as input in a simulation of the rising liquid. The speed and
temperature of the coolant gently homogenise along the path through the column as
shown in Figure 5.12 in the following section. The programme described in
paragraph 5.5 to which we refer for more details reproduces the main results of our
simpler analysis.
The previous calculations are made for the nominal power of the EA and
stationary conditions. It has been verified that correct cooling conditions persist over
the full range of conceivable powers, including decay heat and major transients. In
general, convective cooling has “self-healing” features, namely the pumping action is
directly related to the amount of power to be transported.
90
In stationary conditions and at the nominal power, the ≈ 10,000 tons of coolant
will flow through the core at the rate of some 52 t/s, corresponding to a turn-around
time of the order of 200 seconds for a total length of the loop of the order of 50
metres. In view of the large mass of the coolant, a considerable momentum is stored
in the coolant during normal operation and it has considerable effect in (fast) changes
of conditions.
4.8 - Seismic Protection. As already pointed out in order to reduce capital costs
and increase flexibility large portions of the EA plant should be standardised.
Furthermore, to gain public acceptance, the plant must be reliable and should have
passive inherent features. Seismic design can play a major role in achieving a
standardised design which could accommodate a range of seismic conditions. One
approach to standardisation would be to design a plant using traditional methods for
a Safe Shutdown Earthquake (SSE) which envelopes the responses of 90 percent of
existing nuclear sites in the USA. This is the present licensing seismic basis (RC 1.60)
and it calls for a maximum horizontal and vertical acceleration (PGA) of 0.30 g.
This approach, however, would lead to high seismic loads, especially in
components and equipment, and would still exclude for instance California sites and
limit the export potential of these plants to high seismic countries such as in the
Pacific Rim region. Liquid Metal designs which consist of thin walled vessels
designed to accommodate large thermal transients under low operating pressures are
more sensitive to seismic loads and thus the EA would be particularly penalised by
this approach. An appropriate design of a modular EA requires to be able to
accomodate a variety of seismic conditions expected at a wide range of sites, from
deep soil sites with a minimum shear wave velocity to stiff rock sites.
The alternative is to seismically isolate the plant. Several studies performed in
Japan have shown that it would not be possible to design large LMR plants which are
economical in areas of high seismicity without incorporating seismic isolation [56]. In
an isolated plant, the design and qualification of equipment and piping and their
supports become a simpler task than it is today and the impact of seismic design on
preferred equipment layouts is minimised. Since the response of isolated structures is
highly predictable, the risk of accidents due to uncertainties in the input motions is
reduced, safety margin is increased, and plant investment protection is enhanced.
Additionally, if seismic design criteria are upwardly revised, for example due to the
discovery of unexpected geo-tectonic conditions, the standard plant design would
91
probably not have to be altered and only the isolation system would need to be
upgraded.
Seismic isolation is a significant development in earthquake engineering that is
gaining rapid world-wide acceptance in the commercial field [57]. This approach
introduces a damped flexible mechanism between the building foundation and the
ground to decouple the structure from the harmful components of earthquake
induced ground motion, thus resulting in significant reductions in seismic loads on
the structure and more significantly on equipment within the structure. In recent
years, seismic isolation of nuclear structures has been receiving increased attention.
To date, six nuclear power plant units in France and South Africa have been isolated.
It is expected that seismic isolation will play a major role in the design of the
advanced nuclear plants of the future in the US as well as in Japan and Europe.
Several technological advancements are responsible for making seismic
isolation a practical alternative. These include the development of highly reliable
elastomeric compounds used in seismic bearings which are capable of supporting
large loads and accommodating large horizontal deformations during the earthquake
without becoming unstable. Additionally, the development of high damping
elastomers and other mechanical energy dissipators has provided the means to limit
the resulting displacements in the isolators to manageable levels. Other factors
include the availability of verified computer programmes, the compilation of reliable
test results of individual seismic isolators under extreme loads, shake table tests for
evaluating system response, and validation of computer programmes and
confirmation of the response of isolated buildings during earthquakes [58].
Seismic isolation has been included in the EFR and in the ALMR designs. Most
of this work is relevant also to our case. The ALMR design calls for a seismically
isolated platform which supports the reactor module, containment, the reactor vessel
auxiliary cooling system and the safety related reactor shut-down and coast-down
equipment. The total mass to be insulated is of the order of 25,000 tons. The fragility
of components appears greatly improved by insulation [59]. Some model tests have
confirmed the results of these estimates [60]. Our present design can include most of
the features of the ALMR design.
4.9 - Decay heat removal by natural air convection.
Nuclear industry has
developed a number of passive natural convection air cooling systems to remove
decay heat in the unlikely event that all active cooling systems of a reactor fail [11]
92
[61]. We have applied the design made for the ALMR (RVACS) to the EA, in order to
study the behaviour of our system in case of such an event32.
The application of the RVACS to the Fast Energy Amplifier is illustrated in
Figure 4.1b.
In the unlikely case of a scram event in which all the active cooling systems fail
to operate, the heat produced by the fission products decay in the core increases the
average temperature of the lead contained in the vessel. Lead expands (the level
rising at the rate of 27 cm/100 ˚C) and when its temperature exceeds a determined
safety margin, it overflows into a narrow gap between the main vessel and the
containment vessel. This gap is normally filled with Helium which ensures a
reasonable thermal isolation during normal operations.
The containment vessel is in contact with ambient air entering the system
through a cooling channel. Air reaches the bottom of the vessel through a
downcomer channel which is thermally isolated from a riser channel, in direct
contact with the vessel.
When the lead fills the gap, a good thermal contact is established between the
main and the containment vessels, and heat can be transferred to the air in the riser
channel. Air temperature increases, and a natural circulation starts. Air draft is
enhanced if a long chimney (about 30 m) is added at the end of the riser channel. The
downcomer and riser channels consist of two annular regions around the vessel of
respectively 18 and 57 cm thickness. In such conditions, for a vessel temperature of
500 ˚C, the air velocity attained in the hot channel is of the order of 10 m/s,
corresponding to a flow rate of 53 m3/s. The average outlet temperature of the air is
about 177 ˚C and the heat removal rate of the order of 6.5 MW, which is linearly
dependent on the vessel temperature.
Decay heat is therefore extracted by a simultaneous process of internal (lead)
and external (air) natural convection, conduction (through the steel of the vessels)
and radiation (from the external vessel into the riser channel).
The core decay heat generation and the RVACS heat removal rates during a
scram event are shown in Figure 4.11. At the beginning the decay heat generation is
at a much higher rate than the heat removal. Consequently, the lead heats up very
32We
built a thermal-hydraulic model using the code STAR-CD [51]. The numerical model simulates
the natural convection of air in the system, by taking into account convective and radiative heat
transfer from the surface of the vessel to the air cooling channel.
93
slowly, thanks to the large thermal capacitance of the F-EA. The RVACS heat
removal rate increases slowly with the gradual increase in the reactor vessel
temperature. When the decay heat generation rate and the heat removal rate are
equal, the system reaches its highest temperature. From then on, the removal rate
exceeds the decay heat generation rate, and the average temperature of the vessel
slowly decreases.
The thermal transient experienced by the F-EA vessel for different starting
temperatures is shown in Figure 4.12. It consists of a slow increase over many hours
to a peak temperature followed by a gradual cool down. The peak temperature is
reached much earlier (and has a lower value compared to the starting temperature)
in the case of higher starting temperatures, since the heat removal rate is higher.
The RVACS is based on the natural mechanism of lead dilatation and air
convection. It is therefore completely independent on active components or operator
actions, and insensitive to human errors.
4.10 - Miscellanea. The on-line, continuous determination of the multiplication
coefficient k is essential in order to monitor the correct operation of the EA. The
method we propose is based on the lifetime of the fast neutrons after a sudden shutoff of the proton beam (source). This is easily performed gating-off the ion source for
a period of time of the order of a few hundred microseconds. The effects on the RFcavities of suddenly removing the beam load is still being investigated, but it should
be manageable by the control system. The time of the neutron activity is roughly
exponential, with a time constant proportional to 1/(1-k). Monitoring of the k-value
can be performed continuously as a part of the standard operation mode of the
Accelerator.
Scram devices are used to anchor the k of the EA to a sufficiently low value
during shutdowns, emergencies, etc. This is performed with the help of a series of
blocks of CB4 , conveniently located throughout the Core. This material is very
effective : about 20 kg of CB4 diffused uniformly throughout the core produce a
reactivity change ∆ k = – 0.04. There are three types of such devices: (1) ordinary
scram, performed with an appropriate, fast-moving mechanical device, (2)
emergency scram, based on the design of the ALMR “ultimate shut-off” in which
many small spheres of CB 4 are dropped by gravity inside an evacuated tube which
descends to the Core, and (3) the Molten Lead Activated Scram (MLAS), associated
with the siphon overflow triggered by the excessive expansion of the Lead and
94
consequent level increase in the vessel. As already amply discussed, this trigger
activates also the RVACS to convey the extra heat to the surrounding air and blocks
the proton beam from entering in the core region, filling with Lead the emergency
beam dump volume (EBDV).
The conceptual design of the MLAS is shown in Figure 4.13. If the molten Lead
is penetrating through the siphon, RVACS dedicated volume etc., a small fraction
fills the long thin tube descending down to well below the core region. At this depth
the pressure of the liquid will be of the order of 30 atm, which is amply sufficient to
push upwards the CB 4 blocks well inside the core. A second tube is used to exhaust
the neutral gas (Helium) which is normally filling the tubes. The CB4 blocks, in
presence of Lead, will be held firmly in place by the buoyancy of the liquid.
A lead purification unit is needed to remove impurities from the liquid and to
ensure that the required additives against corrosion are effective. The detailed
parameter list of this device is for the moment largely unknown, pending the results
of the corrosion studies (see paragraph 4.3). Some way as to heat-up the Lead
whenever appropriate is also necessary.
The heat exchangers are relatively conventional, except that they must be
designed in order to introduce a small pressure drop across the primary circuit in
order not to hamper natural convective cooling. At this stage we have assumed that
the pressure drop is about 1/3 of the one across the main Core. We have verified
that this choice is not critical to the performance of the convective cooling. We have
indicated that the primary coolant should not contain an appreciable amount of
Bismuth because of activation problems. This precaution does not apply of course to
the secondary loop which can be filled with a Lead-Bismuth eutectic mixture. The
Pb-Bi eutectic mixture has a boiling point in the vicinity of 125 oC and it has been
chosen to avoid freezing of the coolant in the transmission line.
The EFR design has foreseen a convection driven cooling loop which performs a
function similar to the RVACS. If considered necessary it could be added also to our
design, although it is introducing a duplication which may be redundant. It could be
considered as an alternative to the RVACS system. In the EFR design the decay heat
is extracted by six additional heat exchangers of 15 MW each which reject excess heat
directly in the environment. These Direct C ooling Systems (DCS) consist each of a
(Lead-Bismuth eutectic mixture) filled loops. These loops extract heat from the hot
pool of the primary molten metal by immersed Pb/Pb-Bi heat exchangers and reject
the heat to the environment with Pb-Bi/air heat exchangers located well above the
pool level. One of these DRC units relies exclusively on natural convection heat
95
transfer and natural draught on the air side. The other is normally operated with
forced flow. Each loop is equipped with an electromagnetic pump and two fans in
parallel on the air side. These active loops possess passive heat removal, if pumps
and fans are off to about 2/3 of that of the active flow mode. A special Pb-Bi heat
exchanger freezing protection insures that the temperature in individual pipes
cannot fall below 140 oC.
A large number of monitoring devices are required to follow the radiation
monitoring, neutronics, the hydraulics (speed and temperatures) and the potential
corrosions due to molten Lead.
4.11 - Conclusions In this section, we have presented the conceptual design of
an EA with a power rating (1500 MWth, 675 MWe) that is of direct relevance to the
modules presently considered by nuclear industry to meet the needs of utilities. Such
a machine represents in our view a real breakthrough in the prospects of nuclear
energy in setting the highest standards for safe and economical operation, coupled
with realistic solutions for waste disposal and non-proliferation issues.
The machine is always subcritical. There are no control bars and in normal
operation, the level of power is controlled entirely by the accelerator beam via a
feed-back loop. The separation between the accelerator vacuum and the active
medium (a "frequently asked question") appears entirely solved by a specially
designed window that would be routinely changed once a year. Even if the window
broke, which is unlikely, there would be no serious consequence and the EA would
be brought to a safe halt, even without human intervention.
Conspicuous in our design is the absence of coolant pumps: the heat is
evacuated by convection alone and transferred to the outside world through heat
exchangers via a secondary cooling loop. Convection cooling is a unique feature for
such a large power, and is only made possible by the use of molten Lead as coolant.
The absence of pumps has advantages from the safety and maintenance point of view
(no moving parts). In fact the whole vessel could be sealed during the long interval
(five years) between refuelling as the owner utility has no valid reason to intervene
inside. Obviously this offers an extra means of monitoring, by the controlling bodies
of non-diversion of fissile material. The economical aspect is also important.
Suppressing the pumping system is a substantial simplification in construction as
well as a sizeable economy in capital costs.
96
The burn-up of the fuel is a key parameter in the economic performance of the
EA. The EA achieves an average burn-up of 100 GW-day/t, whilst maintaining
during that time a practically constant gain at the nominal value of G=120,
corresponding to k = 0.98 with no external control devices. This is possible because
one can compensate the loss of reactivity due to FF accumulation by starting the EA
with less 233U than the amount which would correspond to breeding equilibrium.
Such a burn-up is matched to the radiation damage and the pressure build-up of
fission product gases of the fuel pins. The average power density has been set to the
conservative value of 55 W/g which is one half the value considered in Fast
Breeders. This necessitates of course having a larger fuel load (for the nominal
power of 1500 MWth one requires a 27. 3 tons load of mixed fuel oxide) which has
no serious consequence since the fuel is inexpensive. On the other hand, the low
burn-up rate translates into a rather long time between refuelling (5 years). This long
time between access to the fuel has the important consequence of minimising the
radiation dose absorbed by workers. There is no need to have a permanent crew on
site devoted to fuel changes and this could probably be the task of travelling crews of
specialists, conceivably under some kind of international supervision to insure no
possibility of fuel diversion.
A machine designed today should put strong emphasis on safety issues. This
has been a prime consideration during our design. First of all, the machine is safely
subcritical, since any reactivity excursion leading to an increase in power output, will
be immediately corrected by a strong negative temperature effect. The main
difference with a Sodium based FB here is the absence of a positive void coefficient
which could cause the latter to become prompt critical. Then, in the unlikely case of
an accident that would not be corrected by human intervention or electronic
feedbacks, passive measure would be implemented relying on basic properties such
as thermal expansion of Lead, gravity, natural convection in molten Lead, circulation
of air, and radiation. The result would be to bring the machine quickly to a halt and
safely bleed the radioactive decay heat to the environment. At no point could a
temperature increase occur that would cause the core to melt or otherwise lead to a
radioactive release in the environment.
Molten Lead has in our view considerable advantages over Sodium, and its
choice has been essential to us, not only in the physical principle of a Fast Neutron
EA, but also for the inherent safety features which we have just discussed. Objections
against the use of Lead have often been raised in the past on the grounds of its
supposedly corrosive action on steel. We believe that up to the 550 °C - 600 °C
region, on which we have based the present model, there is enough experience (or
97
reasonable extension of known facts) to plan safely on using a known material such
as HT-9 for fuel cladding. However, we believe it would be desirable in the future to
go to higher temperatures (800 °C), for processes such as Hydrogen production or in
order to increase the efficiency of electricity production. For that temperature range,
R&D would be needed.
98
Table 4.1 - Main parameters of the Energy Amplifier
Gross Thermal Power/unit
Primary Electric Power
Type of plant
Coolant
Sub-criticality factor k, (nominal)
Doppler Reactivity Coefficient, (∆k/∆T)
Void coefficient (coolant) ∆k/(∆ρ/ρ)
Nominal energetic Gain
Accelerator re-circulated Power
Fraction Electric Power recirculated in Accel.
Control Bars
Scram systems(3)
Seismic Platform
Main Vessel
Gross height
Diameter
Material
Walls thickness
Weight (excluding cover plug)
Double Liner
Proton Beam and Spallation Target
Accelerator type
Number of beams
Accelerator overall efficiency33
Kinetic energy
Nominal current
Nominal beam Power
Maximum current
Spallation Target material
Beam radius at spallation target
Beam window
Max. power density in window
Max. Temp. increase in window
Window expected lifetime
Fuel Core
33Beam
power/Mains Load
1500
625
Pool
Molten Lead
0.98
– 1.37 × 10-5
+ 0.010
120
30
0.0465
none
CB4 rods
yes
30
6m
HT-9
70
2000
yes
MW
MW
MW
m
m
mm
ton
Cyclotron
1
43%
1.0
GeV
12.5
mA
12.5
MW
20
mA
Molten Lead
7.5
cm
Tungsten, 3.0 (1.5) mm
113
W/cm2
137
°C
≥1
year
99
Initial fuel mixture
Initial fuel mass
Cladding material
Specific power
Power density
Average Fuel Temperature
Maximum Clad Temperature
Dwelling time (eq. @ full power)
Average Burn-up
Breeder Core
Initial fuel mixture
Initial fuel mass
Cladding material
U233 stockpile at discharge
Power density at end cycle
Primary cooling system
Approximate weight of the coolant
Pumping method
Height convection column
Convection generated primary pressure
Heat exchangers
Decay heat removal
Inlet temperature, Core
Outlet temperature, Core
Coolant Flow in Core
Coolant speed in Core, average
Decay Heat Passive Cooling (RVACS)
Riser channel gap width
Downcomer channel gap width
Trigger Temperature
EA Coolant max Temperature rise
Time to max.Temperature rise
Outlet air Temperature (@ max. temp.)
Outlet air Speed (@ max. temp.)
Air flow Rate (@ max. temp.)
Extracted Heat (@ max. temp.)
ThO2 +0.1233UO2
28.41
ton
low act. HT-9
52.8
W/g
523.
W/cm3
908
°C
707
°C
5.0
years
100.0
GW d/t
ThO2
5.6
low act. HT-9
242.7
3.0
10,000
Nat. Convection
25
0.637
4 × 375
RVACS
400
600
53.6
1.5
500
110
17.5
273
13.4
52.8
8.57
Table 4.2 - Main Properties of Molten Sodium and Lead.
18
57
600
83.5
11.2
302
14.2
56.1
9.65
ton
kg
W/g
ton
m
bar
MW
°C
°C
ton/s
m/s
cm
cm
700 ˚C
64.5 ˚C
9.5 hours
334.3 ˚C
15.2 m/s
60 m 3/s
10.84 MW
100
Melting Temperature
Boiling Temperature
Values at 600 oC
Vapour pressure
Density
Heat capacity ( by mass)
Heat capacity (by volume)
Volumic dilatation coeff. (× 104)
Therm. conductivity
Heat transfer coeff (× 104)
Dynamic viscosity (× 10-3)
Surface tension (× 10-3)
Electric conductivity (e.m. pumps)
Sodium
Lead
98
880
328
1743
oC
24.13
0.81
1.30
1.053
3.1938
62.24
3.6
0.206
146
5 × 10-4
10.33
0.15
1.5495
1.3935
16.45
2.3
1.55
431
9.4 × 10-7
Torr
gr/cm 3
J/gr oC
J/cm3 oC
oC-1
W/m oC
W/m2 oC
N s/m2
N/m
Ωm
oC
Table 4.3 - Main parameters of the final Beam Transport to the Vessel
Beam pipe material
Beam pipe shape
Beam pipe length
Beam pipe external diameter
Beam pipe thickness
Window material
Window shape
Window external diameter
Window thickness (edge, centre)
Beam radius at spallation target
Values for 1 GeV, 10 mA beam
Lead coolant nominal speed
Heat deposition in the lead
Max. Temperature increase of Lead
Heat deposition in the window
Max. Temperature increase of window
Max. power density in window
Max. thermal window stress34 (britt, duct)
HT9
cylindrical
~ 30
20
3
Tungsten
hemispherical
20
3.0, 1.5
7.5
cm
mm
cm
5.0
6.97
107
95
137
113
48.2, 82.2
m/s
MW
˚C
kW
˚C
W/cm2
MPa
Table 4.4 - Main design parameters of the Fuel-Breeder Assemblies
34Tensile
strength of Tungsten at 550 ˚C: 380 MPa
m
cm
mm
101
Pins
Outer diameter
Cladding thickness
Wrapper wire thickness
Cladding material
Active length
Void length (total)
Void outer diameter
Void Cladding thickness
Max. clad Temperature
Average Power/met. fuel
Max. Radiation Damage
Sub-Assemblies
Configuration
No hexagonal rounds
No of pins
Total length
Flat to Flat
Pitch between pins
No units-fuel(IC+OC)
No units-breeder
35Inner
FFTF
EFR
Monjou
F-EA
5.84
0.38
1.42
HT-9
91 (+?)
162
5.84
0.38
700
100
8.2; 11.537
0.52; 0.637
1.75
many
100 (+24)
120
8.2
0.52
6.5
0.47
1.75
SUS316
93 (+65)
8.2
0.35
≈ 120
6.5
0.47
675
121
≈ 100
FFTF
EFR
Monjou
Hexag.
Hexag.
Hexag.
8
217
4.7
120
7.26
192
10
331,16937
4.8
188
9.95
387
78
HT-9
150
180
5.0
0.35
692
60
≈ 34
cm
cm
mm
mm
°C
W/g
dpa/y
F-EA
Hexag.
(IC) 35
10
331
Hexag.
(OC)36
11
397
5.3
234
8.25
Core
Core and Breeder
37The two values correspond to the fuel and breeder respectively.
36Outer
mm
mm
mm
12.43
11.38
120
42
m
mm
mm
102
Table 4.5 - Typical neutron capture inventory of a EA.
Zone-Wise
Core
Blanket
Plenum
Diffuser
Beam Tube + Window
Main Vessel
Leakage
Fraction
0.8879
0.0456
0.0277
0.0309
0.0005
0.0073
0.0012
Material-Wise
Fraction
Fuel (Th + U)
Breeder (Th)
Lead of which
Diffuser
Plenum
Core
Blanket
Lead Total
Structures of which
Cladding
Window
Main Vessel
Structures Total
Leakage
0.8493
0.0427
percentage
(48.75 %)
(12.11 %)
(37.13 %)
(2.01 %)
Abs. Fraction
0.0305175
0.00758086
0.02324338
0.00125826
0.0626
percentage
(83.28 %)
(1.03 %)
(15.69 %)
Abs. Fraction
0.03780912
0.00046762
0.00712326
0.0454
0.0012
103
Figure Captions.
Figure 4.1a General layout of the Energy Amplifier unit.
Figure 4.1b The energy producing unit, side view.
Figure 4.2
Saturation vapour pressure and evaporation rate against vacuum for
molten Lead.
Figure 4.3
Solubility of different metals in molten Lead.
Figure 4.4
Layout of the beam window.
Figure 4.5
Contour Map of the Energy Deposit of a 1 GeV Proton into the F-EA
Target.
Figure 4.6
Temperature profiles of the beam window and the surrounding Lead.
Figure 4.7
The Emergency Beam Dump Volume (EBDV).
Figure 4.8
Pin layout.
Figure 4.9
General layout of a fuel sub-assembly.
Figure 4.10a Power density in the pins as a function of pitch.
Figure 4.10b Power density in the pins as a function of coolant speed.
Figure 4.11 Decay heat generation and heat removal rates during a scram event.
Figure 4.12 Evolution of the vessel temperature during a scram event.
Figure 4.13 Conceptual Design of MLAS.
104
;
@
À
;À@À@;@À; ;À@
;À@
Vapour pressure
Evaporation rate
Ni
Mn
Al
Cr
Fe
Mo
Evacuated Volume
Window (inner surface)
Lead at the window surface
;
@
À
;À@;À@;À@;À@
;À@;À@;À@
;;
@@
ÀÀ
@
À
;
;;
@@
ÀÀ
@@À@;
ÀÀ
;;
@@
ÀÀ
;;
@@ ;;
ÀÀ
;;
ÀÀ
@@
DT = 250 ¡C
DT = 200 ¡C
DT = 150 ¡C
DT = 250 ¡C
DT = 200 ¡C
DT = 150 ¡C
Decay heat generation rate
Heat removal rate (T0 = 700 ¡C)
Heat removal rate (T0 = 600 ¡C)
Heat removal rate (T0 = 500 ¡C)
T0 = 700 ¡C
T0 = 600 ¡C
T0 = 500 ¡C
B4C rod pushed upwards
by the Lead pressure
105
5. — Computer simulated operation.
5.1 - Simulation methods. Many classic programmes [34] exist which can
calculate the neutronic behaviour of a sub-critical system. However such
programmes have major limitations, namely (i) they operate on a given concentration
of isotopes, while in our Amplifier the concentration of elements varies dynamically
during burn-up or (ii) they are based on multi-group calculation methods and
therefore take only approximately into account the narrow resonances in the Lead
Moderator and in the Fuel. Finally the proton initiated cascade involves many
reactions (spallation etc.) which have important effects on the composition of
materials, especially at discharge. Therefore, appropriate Montecarlo methods have
been developed in which the full evolution with time of the Amplifier is simulated.
The high energy cascade has been simulated with the help of the programme
FLUKA [50] which is known to give a very realistic representation of the many
processes in the energy interval of interest. The spallation neutron yield predicted by
FLUKA has been compared with experimental data collected at CERN, where a
proton beam of different kinetic energies in the interval of interest has been made to
interact with Lead targets of different dimensions [3]. The neutron flux emitted has
been measured after thermalization in water. The results show an excellent
agreement between the experimental results and the predictions of FLUKA [62]. The
agreement is typically better than a few percent.
The FLUKA cascade development is, however, still insufficiently accurate to
emulate the complex neutronic behaviour below a few MeV. A second programme
has been written, based on the ENDF-6 cross sections [30], which follows with
Montecarlo technique the fate of neutrons in the Amplifier and the corresponding
evolution of the local composition of the fuel elements. The volume of the Amplifier
is segmented in a large number of separate regions with independently evolving
concentrations and an accurate model of the geometry has been used. The validity of
our calculations has been cross-verified with more classic programmes [34]. However
all programmes rely on the same cross section data.
While the basic Nuclear Data used in the calculations on the 238U/ 239Pu cycle
have been repeatedly checked and improved over the years, some uncertainties have
persisted on the cross section data required to predict the Thorium based cycle.
Fortunately a rather precise integral experiment has been carried out in the PSI zero-
106
power reactor facility, PROTEUS [63]. These results indicate that the breeding
characteristics of heterogeneous 232Th-containing fast reactor cores are predictable to
an accuracy comparable to that of 238U-containing systems. Measured and calculated
spectra appear in general agreement with calculations based on cross section data
[30]. We believe that the underlying physics information is sufficiently well known
and verified to predict the behaviour of the EA.
Neutrons spend a considerable fraction of their life span in molten Lead. Lead
cross sections have been well measured, but very little experience exists to date on
the behaviour of neutrons in a Lead Moderator/Reflector. An experiment in which a
spallation neutron source is imbedded in a large Lead block is in progress at CERN
in order to compare predictions and experimental data [6].
The Montecarlo simulation starts with a proton beam of specified geometry and
a given initial composition of elements in the Amplifier. The geometry of the EA is
realistically represented. Various geometrical components are segmented in smaller
units that we denominate as “pixels”, in order to be able to record the differences in
composition as a function of the location during burn-up. In the case of mixing
liquids, like for instance the molten Lead, a common concentration table is used. The
continuous proton beam is replaced with a limited number of protons which enter
the EA at a specified event rate f p = 1/tp . The fate of these protons is initially
determined by FLUKA in a phase in which a number of spallation neutrons are
generated. These neutrons are subsequently followed inside the EA to their final
destiny by our dedicated programme. Each particle is given a “weight” w in order to
scale up the event rate to the number of protons actually introduced by the
Accelerator, namely w = i tp /e, where obviously i is the proton current and e its
elementary charge. Wherever available, a set of 35 possible reaction channels [30],
which include inelastic processes like n-n’, n-2n, n-p, n-α and so on, are used to
construct the development of the cascade. Secondary neutrons produced by these
reactions become the source of additional cascades.
As a consequence of the cascade produced by each proton, the chemical
composition of the target pixels is significantly affected. We therefore change the
composition of each relevant pixel according to the nature of the interaction,
replacing the initial nucleus with the fragments of the reaction and, in the case of
fission, with the appropriate fission fragments, but with a weight w, namely as if all
the protons over the time tp had produced the same reaction. Clearly this
approximation will vanish over a large number of events. Spallation products
generated by FLUKA are also included.
107
After the full cascade of a given proton has been followed to its finish line and
all pixel concentrations have been changed accordingly, concentrations of all pixels
are evolved over the time interval tp with the help of a full Bateman formalism, in
preparation for the next proton shot. In particular the complete decay chain for each
element is followed up to the stable elements with the corresponding concentrations
in the pixels of the relevant new elements, whenever appropriate. The decay
schemes for all known elements, including all possible branching ratios is provided
by an appropriate database [31].
Typically the programme will operate with some 1200 different nuclear species
(mostly fission and spallation fragments) and up to 256 different pixels of a variety of
shapes and sizes. The computing speed on an ALPHA computer is of 50 neutron
histories/sec. About one week of computer time is needed in order to obtain
adequate statistics on a typical burn-up of 100 GW × day/t, corresponding to about 3
× 106 neutron histories.
The Montecarlo technique and the evolutive nature of the programme permits
to introduce quite realistic simulations of the operation of the EA. For instance it is
possible to adjust the beam current in order to ensure a specified power output or to
simulate power variations and transients. The relevant parameters of the neutronics,
(multiplication coefficient, k, neutron spectrum, fission fragment poisoning,
fuel/breeder ratio and so on) are in this way accurately followed over a specified
burn-up. Periodically, the fuel pin location may be shuffled to improve
uniformization of burning. At the end of the calculation, the complete list of
elements in the various parts of the Amplifier is provided and used to study
reprocessing and refuelling. The refuelling can also be simulated, introducing
appropriate changes in the pixel concentrations. The asymptotic concentrations after
many refuelling and the overall performance of the device can be realistically
simulated. The activation of the various parts of the EA can be accurately studied.
We have verified that the values of the main parameters of a sub-critical device
obtained with our programme are in excellent agreement with the results of more
classic programmes [34]. In particular the value of the multiplication coefficient k in
the two methods typically agree to better than a fraction of a percent.
5.2 - Simulation of the standard operating conditions. We consider first the
simulation of an initial load of fuel made of 232Th-oxide with an initial concentration
of pure 233U-oxide, chosen to ensure the wanted initial value of the multiplication
108
coefficient ko. The initial choice of the multiplication parameter is set high enough in
order to make the best possible use of the current of the Accelerator, but low enough
as to avoid that the machine in some circumstance may become critical. The main
parameters of the EA are the ones listed in Table 4.1. Note that a real life situation
may be slightly different since the Uranium fuel bred, for instance starting with spent
fuel from a PWR (see paragraph 5.3) or coming from a previous cycle, will contain
also some other isotopes, like 232U, 234U, etc. As amply discussed in paragraph 2.8,
they are not such as to modify the general features of the results, which become more
transparent by our simplifying assumption.
In order to simulate as closely as possible the real operating conditions of the
EA, the programme can, during execution, change the current of the accelerator in
order to ensure a constant power output. This is done introducing a sort of “software
feedback” in which the beam current is adjusted for instance every 100 incident
protons in such a way as to maintain constant the output power. The typical
computer run covers of the order of some 2000 days of operation or a burn-up in
excess of 100 GW × day/t. The integrated burn-up versus simulated time of
operation is shown in Figure 5.1. The proton beam feed-back is the only control
mechanism and control rods are absent.
In Figure 5.2a we display the accelerator current chosen by the programme as a
function of the burn-up in order to produce a constant power of 1500 MW
(Figure 5.2b). The variations of the current reflect the variation of the gain G (Figure
5.3), which in turn is primarily determined by the value of the multiplication
coefficient k (Figure 5.4). The other two most relevant quantities are the (atomic)
concentration of 233U, normalised to 232Th, averaged over the core (Figure 5.5) and
the 233Pa (breeding) concentration, normalised to 233 U (Figure 5.6). As is well
known, this last concentration is closely proportional to the power density. By
inspection of these figures, during burn-up we can distinguish two phases.
A first, relatively short initial phase in which a fraction of the initial 233U is
burnt and the breeding process based on the 233Pa is setting on. During this period
the multiplication coefficient, and hence the gain, is dropping typically by ∆k= – 0.01.
This is normally handled by modulating the proton beam current automatically
through the feed-back control system. Since the regime value of k = 0.98 has been set
(see Table 4.1) the initial value of k at the cold initial start-up will be correspondingly
higher, namely about ko = 0.99. In real life and provided such a number would be
considered as too high, one can during this initial phase introduce for instance some
small amounts of neutron absorbing, “burnable poison” materials which are quickly
109
transmuted and keep the value of k within the specified range. Alternatively the
fuelling can be done in phases, installing inside the core a small fraction of fuel
elements only after an initial period (≈ 10 GW × day/t) with the help of the refuelling
machine. Note that storage space is provided inside the vessel for such elements.
This initial phase is followed by a regime phase in which the 233U and the other
isotopes tend exponentially to the breeding equilibrium and in which the Fission
Fragments (FF) captures 38 grow roughly linearly with burn-up (Figure 5.7) and their
effect on k is almost compensated by the increase in concentration of 233U tending to
the breeding equilibrium (Figure 2.5). One can adjust such a compensation
numerology in such a way as to achieve an almost perfect cancellation over a long
burn-up with a remarkably constant value of k and hence of the gain. But towards
the end of the chosen burn-up the exponential growth of the 233U concentration
flattens out, while the FF growth remains essentially linear, thus causing a drop of
the gain and a corresponding increase of the proton beam current required to
maintain a constant power output. The maximum available current is set by the
parameters of Table 4.1 and hence it determines the ultimate burn-up of the system
without refuelling. This effect can be attenuated with more elaborate multiple
refuelling schemes. In analogy to standard techniques of PWRs fresh batches of fuel
are periodically introduced. Such schemes do not seem necessary in our case, since
the single burn-up is long enough to reach the expected limit of the fuel elements due
to radiation damage and gas pressure build-up.
The burn-up is not constant over the volume of the Core. Even if periodic,
partial refuelling is not necessary, it may seem appropriate to shuffle the fuel
elements locations every maybe ≈ 20 GW × day/t, namely about once a year, in order
to uniformise the burn-up of the fuel load. This procedure can be performed without
extracting fuel elements from the tank, using the fuel storage facility as a buffer
location. If performed fast enough (for instance ≤ 10 days) as not to let a major
fraction of the 233Pa decay, it produces negligible effects on k. We have simulated
this with our programme and found no real benefit for instance in extending the
burn-up of the fuel. Consequently at this stage, we have concluded that this
represents an additional complication with little or no advantage and we have
therefore not applied this procedure to our simulations.
The relative power density distribution over the Core for unit fuel mass is
shown in Table 5.1. Its radial (r) dependence is roughly linear, as expected because
38
Of course only those elements for which cross sections are known are accounted for. We believe
that the correction for the other elements is not very large.
110
of the value of k (see Figure 2.3b). The (z,r)-dependence is easily parametrized using
as a universal parameter r 2 + z 2 the distance from the approximate centre of the
source (r = z = 0). This is why the z-dependence flattens out at larger radii. Likewise
the concentration of 233Pa in the various pixels of the core is directly proportional to
the power density distribution. We have verified that the power distribution does
not change appreciably during burn-up in the specified range, namely ≤ 100 GW ×
day/t.
Similar distributions can be generated for the Breeder. The concentration of
bred 233U rises approximately linearly with time. As already pointed out, such a
Breeder is necessary since although the relative concentration of 233U is growing with
burn-up, its stockpile is in fact reduced because of the significant fraction of 232Th
which is burnt. The stockpiles of 233U are shown in Figure 5.8. The total amount of
233U is at the end of the burn-up slightly larger than at start-up. Note that the full
amount of 233 Pa during fuel cool down will also transform itself into 233 U .
Consequently, there is enough fissile material to start a new cycle at a convenient
value of ko.
The concentration of the main Actinides as a function of the burn-up is given in
Figure 5.8. They are in good qualitative agreement with the simpler analytical
calculations of Section 2.
The simulation programme has been used to explore successive fuel cycles. The
simulated procedure is the following. After 100 GW × day/t the fuel is extracted
from the Amplifier and chemically reprocessed. Uranium and Thorium isotopes are
extracted and after a cool-down period of some 200 days to let primarily the 233Pa
decay into 233U, these are used to manufacture new fuel elements, topped up with
additional Thorium. Although some 12% of the 232Th has been burnt, the stockpile
of 233U in the fuel has only slightly changed. We have reloaded in the EA exactly the
initial concentration of 233U. Since the separation is chemical, the new Uranium fuel
will be made of several isotopes. The tiny quantities of 231 Pa (4.68 kg), of 237Np
(400 g) and of Plutonium [238 Pu (62 g) and 239 Pu (4.6 g)] are separated out and
inserted again in the EA for an indefinite period of time until they are essentially
incinerated.
The initial multiplication factor ko of the renewed fuel is extremely close to the
initial one and persists to be so over several fuel cycles, in agreement with the
analytic description of Section 2.
111
Finally we have simulated the effects of power variations. As is well known,
any major change of power requires that the 233 Pa can adjust itself to the new
conditions. If the power output is suddenly increased (decreased) the value of k
decreases (increases) with the characteristic decay time of the 233Pa (39 days). It has
been verified that the magnitude of this effect is in good agreement with the
predictions of Section 2.
5.3 - Start-up Fuel cycle with “dirty” Plutonium. There are many ways to initiate
the sub-critical operation of an EA. The most naive approach, but most impractical
would consist in starting with a pure ThO2 fuel. This method is most inefficient,
since initially the multiplication factor k is hopelessly low and the power of the
accelerator will be correspondingly huge. Fortunately large amounts of readily fissile
material exist in the form of enriched 235U or of “waste” trans-uranic elements from
ordinary PWRs and either of them can be used as initial substitute for the 233U.
We propose to use for the first fill a mixture of ThO2 spiked with about 14% of
“dirty Plutonium” from the discharge from a PWR, normally destined to Geologic
Storage. Our scheme permits to start-up the EA at the nominal power and gain right
from the beginning and smoothly evolve from the initial to the regime conditions
essentially in one fuel cycle. At the end of the first cycle, most of the 239Pu is burnt,
converted with a high efficiency into 233 U. The higher actinides can then either
follow their initial destiny of geologic storage, with a significant reduction in toxicity
and reduced military proliferation risk or can be continuously incinerated in the
successive cycles until they ultimately fission inside the EA.
The simulation programme has been used in order to simulate the burn up of
the initial mixture of “dirty” Plutonium and of Thorium. The fuel is — as previously
— made of mixed oxides. The concentrations at start-up and at the discharge are
given in Table 5.2. Americium and Neptunium can be freely added to the mixture
with little effects on the over-all performance. The concentration of Plutonium is
chosen such as to produce a reasonable value of initial ko. During operation, a large
amount of breeding interactions occur in 232Th with rapid production of 233U, while
the Plutonium isotopes are progressively burnt. We are witnessing a genuine
transformation of Plutonium into 233U (Figure 5.9).
The multiplication coefficient k (Figure 2.9) and therefore the EA gain is now the
resultant of mutual interplay amongst three main processes, namely (1)
disappearance of the Plutonium and higher Actinides (2) the formation of 233U and
112
(3) the emergence of captures due to FFs. It is a fortunate circumstance that these
three effects combined produce a value of the multiplication coefficient k which is
almost constant, in spite of the large changes in concentrations, although not as
constant as in the case of an EA operated with Th-U mixture. Note also that the fast
drop of k during the early life of the cycle, due in the case of the Th-U mixture to the
formation of the 233Pa is essentially absent in our case, since the initial operation is
dominated by the Plutonium. The variations of k are now sufficiently large to justify
some compensatory measure, justified by the exceptional nature of the initial EA fuel
generation and start-up. The easiest way is to play with the refuelling machine and
introduce the fuel assemblies progressively in the EA.
Because of the “external” contribution of the Plutonium, the burn-up of this fuel
load can be extended well beyond the one of the normal cycles and a value in the
vicinity of 150 ÷ 200 GW × day/t is appropriate. In order to reach such a long burnup, it may be necessary to exchange the fuel assemblies during operation, in order to
uniformise the radiation damage on the pins. As already mentioned this operation is
easily performed in a short time.
5.4 - Neutron Spectra and Estimates of the Radiation Damage. Neutron flux
distribution can be easily calculated by the Montecarlo programme by adding the
path length inside each “pixel”. Its energy dependence is easily obtained by binning
the accumulated path length according to energy. The results have been cross
checked by a less accurate method in which a standard multi-group (reactor-like)
calculation has been performed on the structure. The latter method does not take
into complete account the sub-critical nature of the device, like for instance spallation
neutrons. Since it is not an evolutionary programme, it does not take into account
the variations of the chemical composition during burn-up. As anticipated, the high
energy component of the spectrum due to the high energy beam is quickly
attenuated by the (n,n’) inelastic collisions in Lead (Figure 5.10). By the time the
neutrons reach the closest structural element of the Fuel the spectrum has softened to
the point of becoming similar to the one of Liquid Metal Fast Reactors 39 (LMFBRs)
for which a considerable experience exists already. For instance the flux ≥ 100 keV (≥
1.0 MeV) is in both cases 55% (10%) of the whole flux. Neutron damage for LMFBRs
[64] has been studied in the past theoretically and experimentally, and a large
experience up to high fluences has been accumulated. Testing and development of
39
SuperPhénix (inner core).
113
materials for such reactors has arrived at fluences well within the range of the
present design (see section 4.5).
Neutron irradiation in structural materials is an important design parameter
and it determines their rate of replacement. The main physical and mechanical
effects of the irradiation of metals are summarised in Table 5.3 [65]. In the case of
fast neutrons, for fluences ∫φdt ≤ 1022 cm -2 changes are usually undetectable.
Structural modifications start to appear at larger fluences, eventually approaching
saturation for very large irradiation. Effects on metals are relevant to our case and
they are generally smaller at higher temperatures since recovery (annealing) of the
Frenkel defects produced by irradiation is facilitated. After irradiation one generally
observes an increase of the yield strength and, to a smaller extent, of the ultimate
tensile strength. Hence, irradiation results in a decrease in ductility and an increase
in the temperature characterising the transition from ductile to brittle fracture (NDT).
This is an important effect in nuclear power systems.
There are several mechanisms by which irradiation may cause modifications
besides direct heating. We shall mention two of them, namely creation of defects in
the lattice and gas production. Particles of significant energy traversing the material
collide both with electrons and nuclei, which in turn recoil inside the lattice
generating lattice defects. The magnitude of the corresponding effects on properties
such as elasticity, can be described in terms of an empirical parameter, the number of
displaced atoms (DPA). Such DPA depends in turn on the total energy spent to
cause displacements, Ea , and the (average) energy required to displace an atom from
its lattice position, Ed :
E
DPA ∝ a
(1)
2Ed
The denominator Ed is a purely empirical but universal parameter of the material
and of which a wide range of values are available in the literature [66] [67]. The
energy Ea depends on the spectrum and nature of the incident radiation and on the
energy partition between electronic excitations and atomic recoils. We have used in
our computer simulations the module HEATR of the nuclear data processing code
system NJOY [68]. The partition function used was given by Robinson [69] based on
the electronic screening theory of Lindhard [70]. HEATR calculates the damage
energy production cross section, σEa (barn-keV). An estimate of the number of
displacements per second in the metal is given by:
dpa σEa
=
S
φ ⋅10 −21
2E
d
s
η
where η ≈ 0.8 is the collision efficiency factor and φ the particle flux (cm-2s-1).
(2)
114
Helium, hydrogen and other light gases are produced in structural materials by
nuclear reactions process with α, p, T and so on in the final state. In the case of fast
neutrons (n,α) and (n,p) reactions have significant cross sections. In conditions of
large fluence, these locally generated gases may be in sufficient amount as to have a
pronounced effect on the mechanical and dimensional properties of components, like
for instance:
- The radiation induced swelling due to vacancy agglomeration (voids), in
which the internally produced gas acts as a nucleating agent for voids,
promoting their growth and stabilising them once they are formed.
- The high temperature embrittlement due to inert gas bubbles.
- The low temperature embrittlement due to defect clusters-vacancy or
interstitial clusters.
- The "in-pile-creep" producing dimensional changes like swelling.
Swelling and "in-pile-creep" may cause some dimensional changes of the core
components which may even affect the dynamics of the energy amplification.
We consider next in more detail the radiation damage in two main structural
components namely (1) the beam window and (2) structure and cladding of the Fuel
Core. Note that molten Lead is not a “structural material” and it is continuously
recirculated from a very large mass. Paradoxically, radiation damage in the highest
flux by the highest energy particles can be neglected, evidently with the exception of
the beam window! Molten Lead acts as a “filter”, moderating the most radiation
damaging components of the spallation spectrum.
The rate of radiation damage in the beam window is comparable to the one in
high-yield spallation sources under design and construction (see for instance SINQ
[71]). The most severe effect is produced by the incoming proton beam. Effects due
to the secondary neutrons produced by the cascade are small in comparison with the
high energy charged particles. According to Eq. (2), the damage rate is given by:
σEa
dpa
= 3.18 × 10 −6
S
I(mA)
Ed 2
s
D
η
where D is the beam diameter. Production yields of He and H can be obtained from
cross sections and incident flux (current density):
appm
−3 σ
=
7.95
×
10
P
I(mA)
D2
s
Parameters for a proton energy of 800 MeV and several relevant materials are given
in Table 5.4. Since cross sections change only very slowly with energy, these values
are applicable to a wide interval of proton energies and in particular to our design.
115
The relevant parameters after 7000 hours at the nominal (see section 4.4) peak current
density of 113 µA/cm2 are about 200 dpa, 13150 He (appm), and 116,350 H (appm).
With these numbers, because of embrittlement and swelling, in order to guarantee
safety, the window should be replaced after about one year [53]. The periodic
replacement of the proton window can be easily accomplished as a routine
maintenance task.
It is however evident that some experimental work is required in order to
ensure safe conditions of operation of this relatively new component which is the
beam window. In particular we remark that the peak beam current density is
inversely proportional to the square of the beam diameter. If required by these
additional investigations, the beam size could be enlarged without major
consequences in the rest of the system.
The irradiation effects on the Fuel Core region have been already mentioned.
They must not limit the maximum burn-up due to FFs poisoning which has been set
to be of the order of 100 GW × day/t. This corresponds to an integrated neutron
fluence through the cladding of ∫ φ dt = 3.3 × 1023 n/cm2, averaged over the core.
The most exposed pins will accumulate about twice such a fluence. Two structural
components deserve consideration namely (1) the Fuel itself, a mixture of ceramic
oxides and (2) the steel cladding of the fuel pins and other structural materials
holding the pins together.
If Thorium is mixed with Uranium using Thorium-Uranium oxides, the
irradiation experience available for these components indicates a small incidence on
fuel swelling. However, more data needs to be collected to attain a high degree of
confidence for long-term performance [53].
It is expected that our cladding material will experience conditions similar to
those of an LMFBR at 600 ÷ 700 °C and neutron fluences above 0.1 MeV of about 1023
cm-2 . As already mentioned we must consider four major effects: (1) radiation
hardening, (2) irradiation creep, (3) embrittlement and (4) swelling. Different alloys
have been proposed and studied as cladding in these neutron environments: (i)
stainless steels (304, 316, 321, 347, Incoloy 800); (ii) Nickel based alloys (Inconel 600,
Inconel X750, Hastelloy X, Inconel 718, Inconel 625). Type 316 is the reference
material for many LMFBR in-core cladding and structural applications.
In the design of the EA there are the added requirements of corrosion in molten
Lead (see paragraph 4.3) and the necessity of keeping the activation stockpile to a
minimum at long times. For these reasons we prefer to use instead low-activation
116
HT-9 steel [72]. Ferritic steels (e.g. HT-9) have demonstrated a high swelling
resistance, a good stress-corrosion resistance, and a particularly high temperature
strength which could increase significantly the fuel element lifetime. The rates of
displacements and gas production in different material zones of interest are given in
Table 5.5. Combining these with the data of ref. [72] it is expected a swell fraction of
≈ 1 % and a shift in the temperature characterising the transition from ductile to
brittle fracture (DBTT) of about 30 °C at design fluence. Under these conditions, our
design lifetime of approximately 5 years corresponds to an acceptable radiation
damage level for the fuel cladding.
5.5 - Temperature distributions and coolant Flow. The temperatures reached by the
different elements of the core are important parameters related with the safety of the
EA. In particular, a safe operation requires the cladding and fuel temperatures to be
well below the structural limits of the constituent materials.
The lead temperature distribution along any cooling pin channel can be
estimated on the basis of the pin axial power density distribution. The internal
temperature of the pin cladding can be calculated adding to the lead temperature the
temperature increases from the lead to the outer part of the cladding and from there
to the inner part. The fuel temperature is then obtained by adding to the internal
cladding temperature the increment inside the fuel.
For the EA the linear power density axial distribution (q’) can be expressed as:
q©(z) = q©max 1 − b(z − zmid )2
(q©≡ W / m)
(1)
[
]
where z is the axial coordinate, q’max is the maximum linear power density, reached
in the middle of the pin (z = z’mid ), and b is a parameter given by the power
distribution shape. Both q’ and b are function of the pin radial position in the core.
The temperature distribution of lead can be calculated by using the expression
dT(z)
q' (z)
(2)
=
dz
f a v ρ Cp
where T is the lead temperature and fa , v, ρ and Cp are the lead flow area, velocity,
density and specific heat respectively. In the approximation in which these quantities
are kept constant (as an averaged values) the lead axial temperature through the
channel distribution is given by
q©max
3
b 3
b
T Lead (z) = T Lead,in +
z − ( z − zmid ) − zmid
(3)
3
3
f a v ρ Cp
117
The heat flow between the cladding and the lead surface is described by the
Newton law of convection
q©©(z)
T out clad (z) = T Lead (z) +
h
where q’’ is the surface power density distribution and h is the local heat transfer
coefficient which can be calculated as a function of the Nusselt number
0.827
v ρ Cp de
Nu.kL
Nu = 4.82 + 0.0185×
; h=
de
kL
de is the effective diameter, defined in section 4.7, and k L is the lead thermal
conductivity. By using for the surface power density (q’’) the same z behaviour for
the linear power density, the temperature increase between the lead and the outer
surface of the cladding can be obtained,
q©max
b 3
b
3
T out clad (z) = T Lead, in +
z − ( z − zmid ) − zmid
fa v ρ Cp
3
3
+
[
q©©max 1 − b( z − zmid )
2
(4)
]
h
A similar calculation allows to get the temperature difference between the outer
and inner parts of the cladding, which depends on the HT-9 thermal conductivity kc
and the cladding thickness e, according to the following expression
e
2
Tinn clad (z) = T out clad (z) + q©©max 1 − b( z − zmid )
kc
[
]
The temperature increase inside the fuel, without considering the axial pin heat
transfer, can be written as a function of the radius and the fuel length:
q' ' ' (z) 2
Tinn fuel (r, z) = Tout fuel (z) +
r1 − r 2
r2 ≤ r ≤ r1
4kThO2
(
where q©©©(z) = W ρThO2 (W / m 3 ) .
T out fuel (z) = Tinn clad (z) +
)
[
q©©max
2
1 − b( z − zmid )
kThO2
]
r being the radial position and r1, r 2 the fuel pellet radius and the inner void radius
respectively. kThO2 is the temperature averaged Thorium oxide thermal conductivity.
The calculations were performed with a simulation programme [73]. The
results, which are in excellent agreement with the full thermal-hydraulic code
COBRA [55], give a maximum cladding and fuel temperature of 707 °C and 2250 °C,
well below 1470 °C and 3220 °C, which are the HT-9 and ThO2 melting temperatures
respectively.
118
As described in section 4.7 the EA cooling is achieved by convective pumping.
The pressure difference generated in the lead loop is sufficient to extract the heat
from the core. For a fixed ∆T in the core, a variable pitch value is used in order to
adjust the coolant speed through the core to the pin power density. In practice,
however, the pitch value is quantified and there is a residual radial dependence of
∆T. This effect is particularly important if the breeder is to be included in the same
coolant loop and if its pitch value is not drastically different from that of the fuel,
since its power density is very low. A simple method of cancelling this residual
dependence is to decrease the pressure at the entry of the bundles such as to get the
same ∆T than for the hottest channel, for which the pressure decrease is set to zero.
For the other channels this extra pressure drop increases when the power density
decreases. This implies a tuning of the coolant flow rate as a function of the bundle
radial position.
The calculations were done by a simulation programme using the expressions
already described in section 4.7. The results, pressure drop inserted and lead velocity
distribution, are shown in Figures 5.11a and b. Finally, the speed map at the exit of
the core has been used as input in a simulation of the coolant flow. As observed in
Figure 5.12, the speed gently homogenises along the path through the lead column.
The convection start-up has been simulated using a computational model based
on the following expression
∂v
lf ρ
= ∆PColumn + ∆PCore − ∑ ∆Pi
∂t
where l f , is the fuel length, ∆PColumn , ∆PCore are the pressure induced by the lead in the
column and in the core and ∆Pi are the pressure terms losses due to friction and
changes in flow area, as defined in section 4.7
The lead outlet core temperature T out has been obtained as:
q
T out = Tin +
ρ f a vCp
where Tin is the lead inlet core temperature.
The equation was solved by time steps and for each time ∆PColumn and ∆PCore
have been estimated by averaging, with the appropriate weights, the temperatures of
the lead in the column and in the core with the temperatures of the lead leaving and
entering the core respectively. In the model the time of heating the fuel has been
neglected and the heat transmission to lead was supposed instantaneous.
119
The results show that it is possible to reach the operating power conditions in a
few minutes without overheating the Lead leaving the core beyond the nominal
operating temperatures (Table 5.6). For start-up times below 2 minutes the lead is
overheated, for instance by about ≈ 20 °C if the start-up is done in 1 minute or by ≈
100 °C if it is done in 30 s. Also, after an instantaneous shut down and without
considering the residual heating, the inertia of the coolant is such as to maintain the
lead speed in ≈ 8% of its steady state value after 5 minutes, and ≈ 3% after 15
minutes.
5.6 - Safety and Control of Fast Transients. The safety of multiplying systems
depends to a large extent on fast transients caused by accidental reactivity insertions.
To study the power changes in accelerator driven systems a kinetic model dealing
with fast transients as a function of reactivity insertion, Doppler feedback and the
intensity of an external neutron source, was developed and programmed.
A kinetic model is given by the diffusion equation, in one energy group. This
equation relates the change in time of the neutron density with the physical constants
of the system, specially the reactivity, and has to consider the prompt and delayed
neutron production rates [74]:
(1)
N 6
∂N 1 − β
=
− 1 + ∑ λ i Ci + S(t)
∂ t 1 − ρ ($) β Λ i =1
(2)
∂ Ci
βi
N
=
− λ i Ci
∂ t 1 − ρ ($)β Λ
where N is the neutron density, β i , β are the delayed neutron fraction of the i-th
delayed precursor group and the total delayed neutron fraction respectively, λ i and
Ci are the decay constant and the concentration of the i-th delayed precursor group
respectively, ρ ($) is the total reactivity, expressed in dollars, Λ is the averaged
prompt-neutron lifetime and S(t) is the external source term.
For a sub-critical device, fed by a spallation neutron source, the source term
may be expressed as [75]:
ρ n
(3)
S(t) = − 0 sp
Λ
where ρ0 < 0 is the total reactivity in the steady state and nsp is the number of
spallation neutrons density per source proton. At the steady state the external source
term is kept constant. Establishing the k0, effective multiplication factor, at this steady
state, the nsp value is expressed as:
120
1
N0
1 − ρ0 ($) β
N
S(t) = (1 − k0 ) 0
Λ
Here N0 is the neutron density at the steady state.
nsp =
The coupled equations (1) and (2) are solved by a numerical method described
later. The general features of the program include time dependence of the total
reactivity, prompt neutron generation time and time size step, and a maximum of six
delayed neutron precursors groups. In addition, the total stored energy is also
calculated by integrating the reactor power from t = 0 to the time of interest.
The total reactivity of the sub critical device is then a sum of four terms:
ρ (t) = ρ0 + ρext (t) + ρ Doppler (t) + ρ Mod. density (t)
(4)
0
α ($ / C)
ρ Doppler =
× P(t) × t
cp
ρ Mod. density = α ' ($ / g cm −3 ) × ( Dens.(T mod. (t)) − Densmod.,0 )
where ρext (t) is the external reactivity inserted, simulating an accident. It is time
dependent, usually represented by a linear or quadratic ramp; ρ Doppler is the reactivity
decrease due to the fuel temperature increase ( α < 0) and P(t) is the power density.
The reference fuel temperature is the one at the steady state. This effect is very fast, it
is therefore the main stability feedback of an external reactivity insertion accident
which would rise at high speed. The rapid fuel answer is due to the direct
relationship between the power density change with the reactivity increase and the
fuel temperature variation; ρ Mod. density is the reactivity decrease ( α ' < 0) due to the
moderator density change, which is a moderator temperature function. This negative
reactivity evolves at a lower speed because of the thermal inertia of the moderator.
Hence, this effect is less important than the one mentioned above.
The last equations, necessary to complete the cycle, are the power density and
neutron density relationships, and the temperature changes due to a power density
variation. The first one is given as
ε Σ f N(t)v
P(t) (W / g) =
Fuel density
where ε = 3.044·10-11 Joule (190 MeV/fission), v is the averaged neutron speed. Once
the averaged power density at the steady state is known (P0) and also the neutron
density (N0) is fixed, it is not necessary to calculate the neutron group constants
( Σ f ,v )
N(t)
(5)
P(t) = P0
N0
121
The reactivity reduction by the Doppler coefficient is calculated as a heat generation
coefficient [74]. Let ρ0 represent the initial reactivity increase resulting from a step
change. If α (= − dρ dT ) is the negative of the temperature coefficient of reactivity,
i.e., α is a positive quantity, the reactivity resulting from a temperature increase T is
given by
ρ = ρ0 − α T
Suppose the time scale of the power excursion is such that the heat loss from the
system is insignificant. The increase in thermal energy E will then be related to T by
E = CT
where C is the heat capacity, i.e., mass × specific heat, of the system. Hence,
α
ρ = ρ0 − E = ρ0 − γ E,
(6)
C
where γ = α C = − dρ dE is the negative of the energy coefficient of reactivity. The
reactor power P is equal to the time rate of energy change, i.e., dE dt; it is obtained
by differentiating equation (6) with respect to time, so that
dE
1 dρ
P=
=−
.
dt
γ dt
It follows, therefore, that
dρ
= − γ P.
dt
(7)
The coupled equations (1) and (2) were integrated by discrete time steps. It is
important to note that the time step has to be of the same order of magnitude as the
prompt-neutron average lifetime. Three types of unprotected reactivity accidents
have been considered.
- A slow reactivity ramp insertion: the reactivity increases at a rate of 170 $/s for
a period of 15 ms (this corresponds to a control rod withdrawal speed of 0.55
cm/ms in the case of a reactor). After this time the reactivity is kept constant.
- A fast reactivity ramp insertion: the reactivity increases at a rate of 250 $/s for
a period of 15 ms (0.81 cm/ms).
- A thermal run-off of the accelerator, due to a variation in the proton beam
intensity. The new source term is:
I
S' (t) = S(t) new
I0
where I0 is the nominal beam intensity and I new is the accidental new proton
current, increased by a factor 2.
The analysis of this problem allows a comparison with transient calculations
obtained for a critical reactor (Figure 5.13). It gives a first indication of the mitigating
effect of using a sub critical accelerator driven system. The parameters used for the
122
Energy Amplifier transient study, extracted from references [76] [77], are indicated in
Table 5.7.
Figures 5.14(a-d) show the power, fuel average temperature and reactivity
change in a critical reactor (lead cooled) and in the Fast Energy Amplifier subjected
to a slow reactivity insertion. The important reactivity effects all occur within one
second.
- The power excursion curve which corresponds to a critical reactor oscillates
and has two distinct peaks in a short time interval. Super prompt criticality
produces these peaks (Figure 5.14b). The power rises rapidly during the
period of super prompt criticality and reaches its peak, 100 times nominal
after 7 ms, at the time when the Doppler effect reduces the reactivity to values
below super prompt limit. However, the fuel average temperature continues
to rise rapidly during 15 ms (due to the thermal inertia of the fuel), until the
Doppler counter-reactivity has fully established itself. By this time, the
average temperature of the fuel has increased by 50 % ( T fuel ≈ 1250 0C ),
assuming that the heat loss from the fuel is insignificant during the power
excursion. The integrated power, after 20 ms, measured from the start of the
ramp is ≈ 0.8 full power seconds.
- In the case of the Fast Energy Amplifier operated at k = 0.98, the power
increases only by 42 % after 15 ms and after 20 ms the power decreases almost
proportionally with the neutron source strength. If on the other hand the
neutron source is maintained (the accelerator is not shut-off), the power
remains almost constant in this time range. The total energy released during
the excursion is much less than for a critical reactor (0.025 full power seconds
after 20 ms). The average temperature of the fuel rises gradually but at a
much lower rate. After 20 ms, the fuel average temperature has increased by
8%. Note, that in this case the Doppler reactivity feedback is almost
negligible and very much delayed (appears only after 23 ms). The long time
constant of the response implies that the heat loss from the fuel cannot be
neglected anymore. In fact, there is sufficient time (of the order of a few
seconds, as estimated by the convection studies described in section 5.5) for
the natural convection mechanism to safely adapt itself to the new operating
conditions without occurring any fuel damage.
The next examples illustrated in Figures 5.15(a-d) and 5.16(a-d) deal with a fast
reactivity ramp insertion and a thermal run-off of the accelerator, respectively.
Compared to the previous case, the power peak values are higher. The power and
temperature changes are faster, and so is the response (fuel Doppler reactivity
123
feedback). The integrated power, i.e. the total energy released during the excursion,
is slightly larger.
An interesting result of this analysis is the fact that the Fast Energy Amplifier
responds much more benignly to a sudden reactivity insertion than a critical reactor.
Indeed, no power excursions leading to high power levels are possible for positive
reactivity additions which are of the order of the sub criticality and similarly for a
thermal run-off of the accelerator. More importantly, even if the spallation source is
still active (the accelerator is not shut-off), the relative slow power changes induced
could be passively controlled by means of natural convection alone (massive coolant
response) thus avoiding any meltdown of the sub-critical core.
5.7- Compositions at Discharge. The evolution programme computes the full
composition of the elements of the EA during operation. The composition at
discharge is therefore directly obtained, with the proviso however that the beam is
made of discrete pulses separated in time. Appropriate corrections have to be
introduced if short-lived components, with lifetime shorter than the proton repetition
rate (typically 5×103÷3×10 4 s) have to be exactly estimated. In the case of the Fuel
discharge also an appropriated, averaged mixture of elements substitutes the actual
fine structure of the fuel pins and of the lead coolant. Therefore, the discharge
composition will include also the small amount of new elements produced in the
closely surrounding Lead.
The discharge composition of the Fuel after 110 GW × day/t corresponding to
approximately 5 years in the standard operating conditions are listed in Table 5.8.
We have listed only those elements which have a 1/e lifetime longer than 10 days
and an amount larger then 100 mg. The relative scarcity of trans-uranic elements
reflects the conditions of the first Fuel cycle. The evolution of the Actinides with fuel
cycle has been amply discussed in section 2.9 to which we refer for further details.
The FF mass composition is substantially different from the one of an ordinary PWR
for two main reasons, namely (1) the fission yields for 233 U and 235 U are quite
different and (2) incineration of some of the FFs is quite strong for thermal spectrum
and it is quite small in our case. We have listed in Table 5.8 the ratio of mass yields
for the same thermal energy produced by the EA and a PWR after 33 GW day/t and
initial enrichment of the 235 U to 3.3%. Some of the elements show a ratio very
different from 1.
124
The activation of the Fuel cladding material (HT-9) leads mainly to about 0.2 kg
of 54Mn (1.24 y), 1.72 kg of 55Fe (3.95 y), 0.234 kg of 185W (108.6 d) and 2.52 kg of
187Re (6.30× 1010y), the last two elements due to the very small content of just 162.6
kg of W in the steel alloy. Other radioactive elements like 60Co, 51Cr, 59Fe, etc. are
present in traces at the level of ≤ 1 g.
The Lead coolant within the core volume accumulates over 5 years of operation
about 20.3 kg of rather inoffensive 205Pb (2.2 × 107 y), K-capture at 0.065 MeV, no γ
i.e. ν-emission), some 45 g of 202Pb (7.5 × 104 y) and very small traces of 194Hg (751.9
y), 204Tl (5.47 y),208Bi (5.32 × 105 y) and 210 Po (200 d). The very small amount of
194Hg is in contrast with the much larger production rate of the same isotope in the
Spallation target (see next paragraph). Its absence evidences the sharp confinement of
the spallation processes in the target region, away from the fuel core. Radioactive
isotopes in the coolant are rapidly mixed in the bulk of the coolant, about 10 4 tons,
leading to very small relative concentrations40, in many instances measured in units
of parts per billion. The fate of these impurities is to a major extent unpredictable
and specific experiments are required.
The discharge from the Breeder has to a major extent the same general features
as the one from the Fuel, with the exception of the much smaller number of FFs and
the smaller neutron flux.
The Lead coolant surrounding the Core and Breeder volumes, with the
exception of the spallation region which will be discussed separately, is relatively
unaffected by the neutron flux (paragraph 4.2). Two unstable Lead isotopes are
present, the long lived 205 Pb with 43.71 kg and the short lived (4.7 h) 209Pb with
traces at the level of 1 g. Its modest activation is related to the lower energy and flux
in the region immediately surrounding the core. Even smaller is the activation of the
containment vessel, dominated by 55Fe (3.95 y) and 59Fe (64.35 d), with 400 g and 1 g
respectively.
The Actinide composition is also radically different from the one, for instance,
of a PWR and its consequences need some consideration. The main differences are:
(1) the presence of several Protactinium isotopes. At the design power level, the
stockpiles of 233Pa is of 53.25 kg in the Core and of 5.60 kg in the Breeder. This
relatively short lived element is the source of a substantial amount of decay
40
1 kg of dissolved material corresponds to 0.1 ppm in relative mass. Many radioactive impurities
which amount typically to ≈ 1 g, once diluted in the bulk of the coolant, represent a concentration of
10-10 by weight in the coolant.
125
heat, 2.99 MW (2.70 MW in the Fuel Core) immediately after shut-off and
decaying with the characteristic 1/e time of 38.99 days. Since the 233 P a
concentration is proportional to the power produced during steady operation,
its decay heat represents a constant fraction of this last quantity, initially 0.2 %
of the design power. In view of its relatively long decay constant, the
contribution of 233Pa is comparable to the decay heat produced by the FFs and it
must be taken into account (Figure 5.17). The breeding transformation is
accompanied by intense γ-emission. More specifically we have calculated the
time dependence of the γ-spectra produced by Actinides of Table 5.8. In Figure
5.18 we give the time dependence of the γ-activity of the Fuel weighted
proportionally to energy over the spectrum, namely the number of 1 MeV
equivalent γ’s produced per second. As one can see, the dominant contribution
comes from 233Pa, at least during the early times. A corresponding cooling time
of about one year is strongly recommended, which also insures that the major
fraction of 233Pa has decayed into useful 233U. With these provisos, the presence
of 233Pa should not introduce additional, specific problems. Other Protactinium
Isotopes are some 4.47 kg (including the 0.15 kg in the Breeder) of the long-lived
231Pa (4.74 × 104 y), amply discussed in paragraphs 2.8 ÷ 2.10 and traces (≤ 1 g)
of the short-lived 232Pa (1.89 d) and 234Pa (9.69 h). The long-lived isotope 231Pa
primarily produced by fast neutrons through the (n,2n) reaction on the main
element 232Th followed by β-decay, constitutes a considerable source of radiotoxicity and it must be incinerated, re-injecting it inside the subsequent Fuel
Loads, as discussed in paragraph 2.10. Fortunately the cross section for neutron
capture, leading to 232U is quite large and equilibrium between production and
decay is reached already at the end of the first cycle. This means that a net
stockpile of the order of 5 kg of 231Pa will persist during the whole lifetime of
the EA plant as balance between production and incineration.
(2)The presence of a specific composition of Uranium isotopes, evolving toward an
asymptotic distribution. A relative novelty is the presence of a substantial
amount (1.46 kg) of the long lived isotope 232 U (99.6 y) produced by fast
neutrons and the (n,2n) reaction on the main fissile material 233U. As in the
case of 231Pa, the concentration of 232U reaches practically its asymptotic limit
already at the end of the first fuel cycle. As already pointed out, the presence of
such an isotope, which has a decay chain prolific of high energy γ-rays is a major
inconvenience if some of the Uranium fuel were to be diverted to military
applications. The γ-ray activity of the Fuel is of primary importance also during
reprocessing and new fuel preparation. We show in Figure 5.18 the number of 1
MeV equivalent γ’s produced per second by the discharge fuel of an EA and
126
compared with the one of an ordinary PWR. This last curve has been normalised
to the same electric energy produced in the EA. As one can see, after the cooling
down period of about one year needed to transform the 233Pa, the γ-doses of the spent
fuel of an EA are not substantially different than the one of an ordinary PWR.
(3)The isotopic composition of the Uranium is a rapidly decreasing function of the
atomic number. There is essentially no 238 U produced, since the previous
element, 237 U is short lived (9.76 d) and it β-decays into 237Np, which is the
main gateway to the trans-uranic elements.
(4) A remarkable scarcity of trans-Uranic elements. Concentrations are fuel cycle
dependent and values of Table 5.8. refer to the most favourable case of the first
fuel cycle. The main production mechanism is neutron capture of the long-lived
237Np producing 238Np, which then quickly (3.06 d) decays into 238Pu (127 y).
The family of Plutonium isotopes with A ≥ 239 becomes accessible by
successive neutron captures. Even asymptotically, as shown in detail in
paragraph 2.9, concentrations decrease rapidly with growing A, because of the
competing fission channel at each step. Asymptotic concentrations are also
many orders of magnitude lower than for instance in the case of a Uranium
driven Reactor. Seven neutrons are needed for instance to transform 232Th into
239Pu, while a single neutron capture can achieve the same result starting from
238U.
Amongst the unstable elements which require special consideration in the Table
5.8, there is a significant amount (14.5 g) of 14C (8286 y) produced by n-capture
reaction on the isotope 17O, present in small amounts (1.84 kg) in the natural Oxygen
of the ThO 2 and UO2 in the Fuel and in the Breeder. The production of this isotope is
however of importance since it is one of the main contributors to the radio-toxicity
emitted in the environment during reprocessing. It is difficult to separate out such a
small amount of Carbon with the methods proposed to reprocess the Fuel (see
paragraph 6.2). The relevant neutron capture cross section for the process 17O(n,α)
(averaged over the Fuel spectrum) has the relatively large value of 23.3 mbarn. An
additional source of 14 C in the EA, not included in Table 5.8 could be due to the
presence of N2 impurities in the fuel, typically of the order of 10 ppm by weight (0.3
kg). The cross section for the relevant process 14N(n,p) is of the order of 2 mbarn and
its contribution for the integrated neutron fluence ∫Φdt = 3.3 × 1023 n/cm2 is then
only 0.198 grams. Note that the total amount of chemical Carbon produced in the
Fuel is 0.587 kg, mostly of 13C. It is expected to be almost completely oxidised at the
127
fuel operating temperatures and therefore be mostly in the form of CO2 at the time of
reprocessing.
5.8 - Spallation Products.
The spallation process produces a large amount of
fragments. These fragments, which are generated primarily by high energy particles,
have been properly taken into account in the FLUKA part of the simulation
programme. The mass spectrum of the spallation fragments is strongly energy
dependent. At low proton energies (≤ 40 MeV), the mass (A,Z) spectrum is peaked
close to the father nucleus. At intermediate energies (≈ 400 MeV) a splitting similar
to fission occurs, in which two fragments of roughly similar mass are formed. At very
high energies, the spallation spectrum changes again and all (A,Z) are produced in a
roughly flat distribution. This complex phenomenology is only approximately
represented by FLUKA and the mass yield could be uncertain to up to a factor two.
In order to evidence them the spallation target region, namely the Lead volume
to which the core is concentric has been considered as a different material. In our
design however the whole coolant is mixed during operation. Hence in reality
spallation products will diffuse inside the whole EA volume.
As shown in Figure 5.18, the overall γ-activity of the spallation products is many
orders of magnitude smaller than the one of the Fuel. Still it is sizeable and it must
be considered carefully. We give in Table 5.9 the list of unstable elements with
lifetime larger than 10 days. As already mentioned this corresponds to very small
concentrations (1 g = 0.1 ppb) and therefore it is difficult to predict what will be their
actual fate without additional experiments.
Qualitatively we can say that several elements will come out in the form of gas
or vapours and accumulate in the (inert) gas inside the vessel41. This is definitely the
case of (1) some Tritium and the noble gases 39Ar (389 y), 42Ar (47.6 y),81Kr (3.3 × 106
y), 85Kr (15.5 y),127Xe (52.6 d), which are produced at the modest total rate of about
few g/year, (2) traces (≤ 1 g) of some elements which have a significant vapour
tension at the operating temperature of the EA, namely 36 Cl (4.3 × 10 6 y), 73As
(116 d), 125Sb( 4.0 y), 125I (86 d), 134Cs (2.98 y) and the main elements which are 15.25
g of 202Tl (17.68 d), 386 g of 204Tl (5.5 y), 415.9 g of 194Hg (751.9 y) and 6.2 g of 203Hg
(67 d).
41
Note that the quoted values for the masses are the values at discharge after 5 years of continuous
operation. If continuously extracted, the total amount of the short-lived elements is correspondingly
larger.
128
Others will remain in solution inside the coolant. There is a large number of
elements which will form with Lead inter-metallic compounds. Some elements will
combine chemically with Lead (S, Se and Te) and remain dissolved. We note that
210Po (200 d) belongs to the same series but its precise chemistry is unknown. There
are several elements which will remain metallic but have a large solubility in Lead
and therefore should be retained. Finally some elements have a very high melting
point and presumably will also remain trapped inside the coolant.
During operation some of the spallation products may be “incinerated” by the
neutron bombardment. The programme records the secondary interactions of all the
materials of the spallation target and therefore the effect is taken into account in
Table 5.9. The effects of these secondary interactions are negligibly small, since the
concentrations are insufficient to produce a sizeable interaction probability.
129
Table 5.1- Power density distribution, in units of averaged power, over the Core.
Data are for an average power density ρ = 52.76 W/g of mixed fuel oxide.
Radial (Bottom)← ← Segmentation along fuel pins →
↓Segm.↓
1
2
3
4
5
6
7
8
→(Top) Average
9
10
over pin
Fuel section
5
1.42 1.74 2.15 2.43 2.62 2.62 2.41 2.10 1.70 1.40
6
1.28 1.58 1.88 2.18 2.35 2.33 2.14 1.88 1.54 1.24
7
1.20 1.47 1.77 1.99 2.12 2.11 1.99 1.74 1.45 1.16
8
1.12 1.36 1.66 1.84 1.97 1.97 1.86 1.63 1.35 1.10
9
1.05 1.29 1.52 1.71 1.79 1.81 1.70 1.54 1.28 1.02
10
0.97 1.20 1.45 1.58 1.67 1.69 1.57 1.43 1.18 0.96
11
0.91 1.12 1.32 1.47 1.53 1.54 1.46 1.30 1.10 0.90
12
0.82 1.01 1.19 1.33 1.40 1.42 1.32 1.20 1.01 0.82
13
0.74 0.91 1.07 1.19 1.26 1.25 1.20 1.08 0.91 0.74
14
0.66 0.82 0.97 1.07 1.11 1.12 1.06 0.95 0.80 0.66
15
0.60 0.71 0.83 0.92 0.95 0.96 0.92 0.84 0.69 0.58
16
0.51 0.60 0.70 0.77 0.81 0.80 0.78 0.70 0.59 0.50
17
0.44 0.49 0.56 0.62 0.65 0.66 0.63 0.57 0.49 0.42
18
0.38 0.40 0.46 0.50 0.52 0.52 0.51 0.46 0.40 0.37
Breeder section: Power proportional to burn-up. Values for 100 GW × day/t
19
0.07 0.07 0.09 0.10 0.11 0.11 0.09 0.09 0.07 0.07
20
0.07 0.08 0.07 0.08 0.09 0.09 0.09 0.08 0.07 0.07
2.06
1.84
1.70
1.59
1.47
1.37
1.27
1.15
1.04
0.92
0.80
0.68
0.55
0.45
0.09
0.08
Table 5.2 - (Dirty) Plutonium into 233 U conversion: stockpiles at start-up and at
discharge. The Plutonium isotopic concentrations correspond to the discharge after
33 GW × day/t of a standard PWR with initial 235U enrichment to 3.3%.
Nuclide
238Pu
Mass at start-up
(kg)
242Pu
67.98
1636.0
671.6
314.9
109.9
All Plutonium’s
2800.38
239Pu
240Pu
241Pu
233U
0.0
Mass at discharge
(kg)
39.49
323.0
527.0
78.3
105.4
Difference(kg)
-28.49
-1313.0
-144.6
-236.6
-4.5
1073.1
-1727.19
1809
+1809
130
Table 5.3 - General effects of neutron irradiation on metals
Irradiation increases
Length (growth)
Volume (swelling)
Yield strength (usually)
Ultimate tensile strength
NDT temperature
Hardness
Creep rate
Irradiation decreases
Ductility
Stress-rupture strength
Density
Fracture toughness
Thermal conductivity
Yield strength
Corrosion resistance
Strain hardening rate
Table 5.4 - Parameters relevant to a proton energy of 800 MeV (extracted from
reference [71])
Material
63
Al
Steel
Cu
Mo
W
( σEa ) [barn-keV]
300
330
900
1430
Ed [eV]
σ He [barn]
σ H [barn]
40
0.21
0.86
40
30
58
65
0.32
0.40
0.58
0.58
2.52
2.58
4.00
5.13
Table 5.5 - Displacements and gas production rates in the Energy Amplifier
Region
Fluence/y
Inner
1.1x
Core
1023
Outer Core
Breeder
Plenum
Main Vessel
6.5x1022
2.3x1022
2.5x1022
9.7x1019
dpa/y
He [appm]/y
H [appm]/y
25
2.0
40
15
3.5
2.5
0.001
1.5
0.2
0.1
--
27
3
1
--
131
Table 5.6 - Simulation of convection start-up and shut-down (hottest fuel channel)
Steady conditions:
q st
Tinst
st
T out
102 W/g
400°C
649 °C
v st
2.02 m/s
Start-up42:Power Density, quadratic for (0 < t < at1*),exponential for at1 < t <
t1,; constant = q st for 1< t
T max
649 + 439 e–0.051t1
T max
≈ 649
10 < t1 < 120
t1 > 120
Time in which the Lead Tmax is reached, in seconds:
t ( T max )
0.43 t1
t ( T max )
≈ t1
10 < t1 < 120
t1 > 120
Shut-down: Power Density for t < 0, q = q st ; for t > 0, q = q st
v(t) (m/s)
T out (t) (°C)
42Steady
*
v st
(1+ 0.2t 0.725 )
st
(T out
−Tinst )
st
T out (t) = Tin +
(1+ 0.4t 0.76 )
v (t) =
conditions reached at t = t1, in seconds
The results are for a = 0.35 but they do not change significantly for other values giving a smooth time
dependence.
132
Table 5.7 - Main kinetic parameters used for the Energy Amplifier transient study
Prompt neutron lifetime:
Λ=
Doppler effect coefficient:
∆k
∆T fuel
1 ∆k
∆ρ
= 2
∆T fuel k0 ∆T fuel
Moderator density change coefficient:
∆k
∆Dens lead
1 ∆k
∆ρ
=
∆Dens lead k02 ∆Dens lead
Denslead ( kg / m 3 )
∆ρ
∆ρ ∆Dens
=
∆T lead ∆Dens lead ∆T lead
2.9 × 10 −8 s
−1.380 × 10 −5 °C −1
−1.44 × 10 −5 °C −1
9.68 × 10 −7 m 3 kg −1
1.01 × 10 −6 m 3 kg −1
11149.7442 −1.3594615 ×Tlead ( 0C)
Tlead ∈ [ 400 °C, 900 °C]
−1.37 × 10 −6 °C −1
133
Table 5.8 - Discharge of Core Volume at the end of the First Fuel Cycle.
EA/
PWR
—
1/e Lifetime
14C
Mass
(kg)
0.0145
8286.
y
102Rh
49V
0.0003
—
1.339
y
107Pd
1.926
51Cr
0.0078
—
40.06
d
111Ag
0.0063 0.152
53Mn
54Mn
0.004
0.2019
—
—
0.540E+07 y
1.237 y
55Fe
59Fe
123Sn
125Sn
126Sn
0.1047 2.645
0.0149 1.435
4.236 1.734
1.717
0.0033
—
—
3.948
64.35
y
d
60Co
0.0006
—
7.622
y
124Sb
125Sb
126Sb
0.0084 1.087
1.127 0.889
0.0026 2.253
70Zn
0.006
—
0.723E+15 y
79Se
0.9983
1.916
0.94E+06 y
85Kr
21.64
10.160
86Rb
87Rb
0.0088
46.52
4.261
2.157
89Sr
90Sr
2.402
74.76
1.127
1.578
73.07
41.62
d
y
88Y
91Y
0.0006
3.313
—
0.991
154.2
84.61
d
d
93Zr
95Zr
88.34
3.537
1.387
0.623
15.55
y
26.94 d
0.687E+11 y
0.221E+07 y
92.57 d
94Nb
95Nb
0.0011
2.026
—
0.649
0.293E+05 y
50.57 d
97Tc
98Tc
99Tc
0.0003
0.0014
56.08
—
—
0.827
0.376E+07 y
0.607E+07 y
0.305E+06 y
103Ru
106Ru
0.708
1.147
0.176
0.074
56.77
1.480
d
y
Mass EA/
(kg)
PWR
0.0007 —
0.096
1/e Lifetime
299.3
d
0.939E+07 y
10.77
d
186.8 d
13.94 d
0.144E+06 y
87.05
3.988
18.02
d
y
d
129I
131I
27.28
1.722
0.2924 0.458
0.227E+08 y
11.63 d
134Cs
135Cs
136Cs
137Cs
6.062
115.9
0.1134
118.5
2.982 y
0.332E+07 y
19.03 d
43.52 y
0.546
4.505
2.103
1.109
140Ba
0.8585 0.470
137La
138La
0.0135
0.0040
—
—
18.44
d
0.867E+05 y
0.151E+12 y
139Ce
141Ce
144Ce
0.0023 —
2.5330 0.575
17.300 0.515
199.0
47.00
1.129
d
d
y
143Pr
0.9254 0.547
19.62
d
147Nd
0.2539 0.401
15.88
d
146Pm
147Pm
0.0010 —
15.410 1.315
7.996
3.793
y
y
147Sm
151Sm
12.010 2.551
4.7700 0.568
0.153E+12 y
130.1 y
134
Table 5.8(cont.) - Discharge of Core Volume at the end of the First Fuel Cycle.
Mass
(kg)
EA/
PWR
156Eu
0.0324
0.6074
0.4376
0.0046
12.843
0.164
0.290
0.012
160Tb
0.0028
0.300
152Eu
154Eu
155Eu
185W
187Re
0.2344
2.5220
—
—
1/e
Lifetime
19.58 y
12.43 y
6.767 y
21.96 d
104.5
108.6
d
Mass
(kg)
EA/
PWR
1/e
Lifetime
751.9 y
67.40 d
0.0026
203Hg 0.0001
—
—
204Tl
0.0049
—
202Pb
205Pb
0.0455
20.300
—
—
0.759E+05 y
0.221E+08 y
208Bi
0.0011
—
0.532E+06 y
210Po
0.0055
—
194Hg
5.466
y
d
0.629E+11
y
200.1
d
Table 5.8(cont.). - Actinides of Core Volume at the end of the First Fuel Cycle.
Element
228Th
230Th
232Th
234Th
Mass
(kg)
0.0213
0.2352
20850.044
0.0059
1/e Lifetime
Element
2.766 y
0.1090E+06 y
0.2032E+11 y
34.85 d
232U
233U
234U
235U
236U
231Pa
233Pa
4.3120
53.2500
0.4737E+05 y
38.99 d
44Initially
1/e Lifetime
99.63 y
0.2302E+06 y
0.3543E+06 y
0.1018E+10 y
0.3387E+08 y
237Np
0.2889
0.3094E+07 y
238Pu
0.0712
0.0003
126.9 y
0.3486E+05 y
239Pu
43Initially
Mass
(kg)
1.4270
2463.0043
260.40
24.0800
2.7860
24,230 kg. Difference due to burn-up
2635 kg. Difference (172 kg) to be compensated by the Breeder
135
Table 5.9 - Products at Discharge produced in the Spallation Target Volume.
Mass
(g)
1.435
1/e
Vapour
Lifetime [boil. T]
3H
17.83 y Gaseous
[-252°C]
35S
0.009
126.5 d Gaseous
[445 °C]
36Cl
0.204
0.435E+6 y Bound +)
[- 34°C]
39Ar
0.336
389.0 y Gaseous
42Ar
0.336
47.57 y Gaseous
[-186°C]
45Ca
0.007
236.9 d Intermet
0.2 Torr
49V
0.072
1.339 y Solid
[3409°C]
53Mn
0.387
0.540E+7 y Solid(*)
10-5 Torr
59Fe
0.049
64.35 d Solid(*)
60Fe
0.586
0.216E+7 y Solid(*)
[2862°C]
56Co
0.029
111.7 d Solid(*)
57Co
0.065
1.077 y Solid(*)
58Co
0.002
102.4 d Solid(*)
60Co
1.084
7.622 y Solid(*)
[2928°C]
59Ni
0.253
0.109E+6 y Solid(*)
63 Ni
2.134
144.7 y Solid(*)
[2914°C]
65Zn
0.004
353.2 d Volatile
70Zn
2.424
0.723E+15y Volatile
40 Torr
68Ge
0.032
1.073 y Solid
71Ge
0.079
16.53 d Solid
[2834°C]
73As
0.329
116.1 d Gaseous
[615 °C]
75Se
0.184
173.2 d Intermet
79Se
2.03
0.939E+6 y Intermet
[685 °C]
81Kr
5.777
0.331E+6 y Gaseous
85Kr
4.326
15.55 y Gaseous
[-153 °C]
+) Lead Cloride, PbCl2, b.p. 950 °C
Mass
(g)
0.036
0.181
1/e
Lifetime
124.6 d
26.94 d
Vapour
[boil. T]
83Rb
Gaseous
86Rb
Gaseous
[688 °C]
85Sr
0.264
93.76 d Intermet
89Sr
0.21
73.07 d Intermet
90Sr
3.88
41.62 y Intermet
0.40 Torr
88Y
0.247
154.2 d Solid
91Y
0.318
84.61 d Solid
[3338°C]
88Zr
0.581
120.6 d Solid(*)
93Zr
6.426
0.221E+7 y Solid(*)
95Zr
0.46
92.57 d Solid(*)
[4409°C]
91Nb
4.139
983.3 y Solid
92Nb
0.496
0.501E+8 y Solid
94Nb
1.13
0.293E+5 y Solid
95Nb
1.187
50.57 d Solid
[4744°C]
93Mo
4.726
5784. y Solid
[4639°C]
97Tc
1.896
0.376E+7 y Solid
99Tc
8.333
0.305E+6 y Solid
[4265°C]
103Ru 0.182
56.77 d Solid
106Ru 1.069
1.480 y Solid
[4150°C]
101Rh
4.32
4.772 y Solid
102Rh
0.244
299.3 d Solid
[3697°C]
107Pd
5.207
0.939E+7 y Solid
[2964°C]
105 Ag
0.108
59.71 d Solid ?
5 10-6 To
109 Cd
1.627
1.833 y Volatile
200 Torr
113Sn
0.427
166.4 d Solid(*)
123Sn
0.206
186.8 d Solid(*)
126Sn
0.622
0.144E+6 y Solid(*)
3 10-8 To
(*) Dissolved in the Molten Lead
136
Table 5.9(cont.) - Products at Discharge produced in the Spallation Target Volume.
124Sb
125Sb
121Te
Mass
(g)
0.043
0.404
0.008
1/e
Lifetime
87.05 d
3.988 y
[1585°C]
24.26 d
Vapour
[boil. T]
Volatile
Volatile
0.5 Torr
Intermet
173Lu
172Hf
175Hf
Mass
(g)
0.908
0.288
0.029
-)
85.90 d Gaseous
[184°C]
127Xe
0.37
52.63 d Gaseous
[-108°C]
131Cs
0.003
14.01 d Gaseous
134Cs
0.282
2.982 y Gaseous
[671°C]
131Ba
0.001
17.06 d Intermet
133Ba
0.396
15.21 y Intermet
2 10-2 To
137La
2.653
0.867E+5 y Solid
[3464°C]
139Ce
0.722
199.0 d Solid
141Ce
0.002
47.00 d Solid
[3443°C]
143Pm
1.1
1.050 y Solid
145Pm
0.419
25.59 y Solid
146Pm
0.205
7.996 y Solid
[3520°C]
145Sm
1.064
1.347 y Intermet
146Sm
0.406
0.148E+9 y Intermet
151Sm
2.492
130.1 y Intermet
2 10-4 To
149Eu
0.001
134.6 d Intermet
150Eu
0.76
51.77 y Intermet
154Eu
0.932
12.43 y Intermet
8 10-3 To
151Gd
0.05
179.3 d Solid
[3273°C]
160Tb
0.214
104.5 d Solid
[3230°C]
159Dy
0.021
208.8 d Solid
[2587°C]
-) Lead Telluride, PbTe, m.p. 917 °C
125I
0.014
182Ta
2.467
1.025
181W
1.621
183Re
187Re
3.267
1.829
185Os
8.957
189Ir
3.362
179Ta
1.515
196.2
193Pt 307.4
188Pt
190Pt
195Au
109.5
194Hg
415.9
6.252
203Hg
202Tl
204Tl
202Pb
205Pb
15.25
386
2071
11960
208Bi
4.299
69.79
14.63
210Po
0.995
205Bi
207Bi
1/e
Vapour
Lifetime [boil. T]
1.981 y Solid
[3402°C]
2.704 y Solid
101.2 d Solid
[4603°C]
2.588 y Solid
165.5 d Solid
[5458°C]
175.3 d Solid
[5555°C]
101.2 d Solid
0.629E+11y Solid
[5596°C]
135.3 d Solid
[5012°C]
19.09 d Solid
[4428°C]
14.75 d Solid
0.94E+12 y Solid
72.30 y Solid
[3827°C]
269.1 d Solid
[2857°C]
751.9 y Gaseous
67.40 d Gaseous
[357°C]
17.68 d Volatile ?
5.466 y Volatile ?
6 10-2 To
0.759E+5 y Dissolved
0.221E+8 y Dissolved
30 Torr
22.14 d Eutectic
45.62 y Eutectic
0.532E+6 y Eutectic
200.1 d Volatile
(boils at 254 °C )
137
Figure Captions.
Figure 5.1
Integrated burn-up versus simulated time of operation for an initial
233U filling and pre-set regime at k ≈ 0.98. Related parameters of the EA
are given in Table 4.1.
Figure 5.2a Accelerator current chosen by the programme as a function of the burnup in order to produce a constant power of 1500 MW. Related
parameters of the EA are given in Table 4.1.
Figure 5.2b Resulting EA power output as a function of burn-up with appropriate
variation of accelerator.
Figure 5.3
Energetic gain G of the EA as a function of the burn-up.
conditions as Figure 5.1.
Same
Figure 5.4
Multiplication coefficient k of the EA as a function of the burn-up: (a)
linear time scale, (b) logarithmic time scale. Same conditions as Figure
5.1.
Figure 5.5
Atomic concentration of 233U, normalised to 232Th, averaged over the
core (Breeding Ratio) as a function of the burn-up. Same conditions as
Figure 5.1.
Figure 5.6
Atomic concentration of 233Pa, normalised to 233U, averaged over the
core as a function of the burn-up. Same conditions as Figure 5.1.
Figure 5.7
Fraction of all neutrons captured by Fission Fragment products, as a
function of the burn-up. Same conditions as Figure 5.1.
Figure 5.8
Concentration of the main Actinides as a function of the burn-up. Same
conditions as Figure 5.1.
Figure 5.9
Stockpile of Plutonium and Americium isotopes as a function of the
burn-up, for an initial fuel made of “dirty” Plutonium (see Table 5.2)
and native Thorium. The concentration of produced 233U is also shown.
Figure 5.10 Neutron flux spectrum in the different material regions of the F-EA. The
breeder and the Fuel have similar distributions with fine resolution due
to the resonant structure of the material cross sections.
138
Figure 5.11a Pressure drop inserted as a function of the radial position. As a
reference the total pressure drop due to the Lead column is also
displayed.
Figure 5.11b Lead velocity distribution as a function of the radial position.
Figure 5.12 Velocity map of Lead in the column above the Core.
Figure 5.13 LMFBR power excursion benchmark (as defined in a comparative
NEACRP exercise) assuming a rod ejection accident.
Figure 5.14 Comparison of power excursions in a critical reactor (lead cooled) with
the Fast Energy Amplifier for an accidental reactivity insertion of 170
$/s for 15 ms.
Figure 5.15 Comparison of power excursions in a critical reactor (lead cooled) with
the Fast Energy Amplifier for an accidental reactivity insertion of 255
$/s for 15 ms.
Figure 5.16 Power excursion and reactivity behaviour during a beam run-off in the
Fast Energy Amplifier.
Figure 5.17 Effect of 233 Pa on the decay heat of the Fast Energy Amplifier.
Figure 5.18 Time Evolution of the γ-activity of the fuel after discharge of the EA.
The number of γ−rays is normalized according to their energy in MeV.
The curve for the PWR has been calculated for the same energy
delivered and a burn-up of 33 GW × day/t.
Energy Amplifier Output
Accelerator Input
Parabolic Fit
Th-232
U-233
U-234
Pa-233
U-235
Pa-231
U-236
U-232
Th-230
Np-237
Pu-238
U-233
Pu-240
Pu-239
Pu-241
Pu-238
Am-243
Am-241
Normalized Spectra
Breeder
Spall. target
Iron Vessel
Fuel
Fuel
Lead diffuser
Spallation
region
Fuel region
pitch = 12.43 mm
Fuel region
pitch = 11.38
Pressure due to convection pumping
Breeder
region
Spallation
region
Fuel region
pitch = 12.43 mm
Fuel region
pitch = 11.38
Breeder
region
10 m above core
5 m above core
core outlet
20 m above core
25 m above core
1 = Beam on
2 = Beam off
Critical reactor
1
1 $ subcritical
1
2 $ subcritical
3 $ subcritical
1
2
2
2
Keff -1 Critical reactor
Doppler
EA
Critical reactor
Doppler Critical
(Beam ON)
reactor
Keff -1 EA
(Beam OFF)
Critical reactor
(Beam ON)
(Beam OFF)
Critical reactor
(Beam ON) (Beam OFF)
Fast Energy Amplifier
(keff = 0.98)
Fast Energy Amplifier
(keff = 0.98)
K
-1 Critical reactor
Doppler
EA
Critical reactor
Doppler
K
(Beam ON)
Fast Energy Amplifier
(keff = 0.98)
Critical reactor
-1 EA
(Beam OFF)
Critical reactor
Critical reactor
(Beam ON)
(Beam OFF)
Fast Energy Amplifier
(keff = 0.98)
(Beam OFF)
(Beam ON)
Fast Energy Amplifier
(keff = 0.98)
(Beam ON)
Keff -1
(Beam OFF)
(Beam ON)
(Beam ON)
(Beam OFF)
(Beam OFF)
Total decay heat
Fission fragments decay heat
233Pa decay heat
Fission Fragments
(PWR & EA)
Pa-233
(EA)
All Actinides (EA )
U-232
(EA)
Spallation Target
products (EA )
All Actinides
(PWR)
139
6. — Closing the Fuel Cycle.
6.1 - General Considerations. There are significant, conceptual differences
between what one means by "reprocessing" in the case of a PWR and an EA. In the
case of a PWR, the primary purpose of reprocessing — if one excludes recovery of
Plutonium for military applications — is the one of preparing for a more orderly,
definitive repository of the radio-toxic products, separating for instance Actinides
from FFs. Many conceptual designs have been proposed for the purpose of further
healing the strong radio-toxicity of such individual products with nuclear
transformations with the help of neutrons from Accelerators and Reactors. We shall
mention as our reference case the project CAPRA [23] in which one intends to reduce
the radio-toxicity of the Plutonium from spent fuels by about a factor 30 with the
help of Fast-Breeders similar to SuperPhénix. In addition to producing a large
amount of electric energy, one such device could process Plutonium and eventually
Americium produced by about five ordinary PWRs.
In the case of the EA, at "replacement" time the fuel itself (Actinides) is still
perfectly sound and it could continue to burn much further if it were not for the
neutron absorption due to the accumulated FFs. Hence after a "reprocessing", which
is in fact basically a "FF separation and disposal", the fuel can and should be used
again. This is a fundamental difference with a PWR, where spent fuel is hardly more
than waste material and for which reprocessing is arguable. In the case of an EA, fuel
reprocessing could be better described as fuel regeneration . The purpose of such a
procedure is
(1) to remove the poisoning FFs;
(2) to add the fraction of the Thorium fuel which has been burnt;
(3) to re-establish mechanical solidity to the fuel and the cladding which has
been affected by the strong neutron flux.
In nuclear power generation, radioactive materials must be isolated at all times
from the environment with an appropriate, multiple containment. The residual
radio-toxicity is defined as the toxicity of products extracted from such a closed
environment. Since the bulk of the Actinides are recycled inside the core for further
use, the relevant toxicity is basically the one which is spilled out during the fuel
regeneration process and the one of the elements which are deliberately removed,
like for instance the one of the FFs which are not incinerated and of the sleeves which
contain the fuel which are not reused. This is in contrast with an ordinary PWR — at
140
least if no incineration is performed — in which the totality of the radio-toxicity of
the spent fuel constitutes “Waste” and it must be isolated from the environment by a
Geologic Repository over millions of years.
6.2 - Strategy for the Spent Fuel. The main requirement of the reprocessing of the
fuel from the EA is the one of generating a new fuel free of FFs. Therefore
reprocessing is inevitable in our conception of the EA. In practice one must separate
the Fuel into two different stock piles, the first destined to the next fuel load and the
remainder which is usually called the high activity stream (HLW). The bulk of the
Actinides are to be recycled into new fuel and they belong to the former stockpile.
There is no need to worry about their long lasting consequences, since they will be
burnt in the successive, cycles. The latter stockpile will contain all fission fragments
and activity in the cladding plus the tiny fraction f of Actinides which is not
separated by the reprocessing. They represent a considerable radio-toxicity, which
will be handled either with natural decay or with active incineration of some specific
radio-nuclides. Figure. 6.1 gives the ingestive radio-toxicity [31] of such a high
activity stream assuming f = 1.0×10-4 (the choice of such a value will be clearer later
on). The total radio-toxicity of a PWR initially loaded with 3.3% enriched Uranium
and without reprocessing is also shown for comparison. Data are given for the fuel
discharge after the first fill and for asymptotic fuel composition. The two
distributions are very similar, since the fuel remaining radio-toxicity at long times is
dominated by the 233U contamination which is the same for all fillings. After a large
drop over the first ≈ 500 years due to the decay of medium lifetime FFs (90Sr-90Y,
137Cs), the ingestive radio-toxicity stabilises to a roughly constant level, dominated
by the truly long lived FFs (129 I, 99 Tc, 126Sn 135Cs, 93 Zr and 79 Se) and to a lower
extent by the residual fraction f of Actinides. After such a cooling-off time the
residual radio-toxicity is comparable to the one of the 232Th in the EA and about 5 ×
10-5 times smaller than the one of a throw-away PWR of equivalent yield. The αactivity is very modest since it is dominated by the leaked fraction f of Actinides.
Inspection of Figure 6.1 suggests that the HLW should be stored for about 500 ÷
700 years in what we call the “Secular Repository”. Beyond such period, the
residual radio-toxicity is considerably reduced as shown in Figure 6.2. The specific
FFs contributing to radio-toxicity after 1000 years are listed in Table 6.1. It is possible
to consider at this point the surviving radiation as Class A (10 CFR 61) for surface
storage material even if the waste material will remain buried and provided it is
diluted in ≥ 1000 m3/(GWe × year).
141
It is possible to further reduce the activity of the residual waste by extracting
some or all the sensitive elements of Table 6.1 and “incinerating” them with neutrons
in the EA. A more detailed paper on incineration is in preparation [78] and an
experiment is in preparation at CERN [6], since most of the relevant cross sections are
poorly known. Here we shall limit our considerations to the ones on general
strategy. Three possible further steps are possible:
1) Technetium and Iodine are chemically extracted and incinerated. The first is
a pure 99Tc isotope and the second besides 129I contains about 33% of stable
isotopes which are kept in the incineration stream. The total mass to be
incinerated is about 19 kg/(GW e × year), which is modest. The ingestive
radio-toxicity of the remainder after 1000 years is reduced from 63.4 kSv to
16.2 kSv and the Class A dilution volume from 1194 m 3/(GWe × year) to 68
m 3/(GWe × year).
2) Procedure as point 1) but also Caesium is chemically extracted. The amount
of Caesium is much larger, ≈ 100 kg/(GWe × year). In addition isotopic
separation is necessary in order to separate the 34 kg/(GWe × year) of 135Cs
from the very radio-toxic ( 3.92 × 10 6 Sv) but shorter lived 137Cs. This may be
difficult, although a feasibility study has been carried out [79]. After
incineration of 135 Cs, the ingestive radio-toxicity after 1000 years of the
remainder is reduced to 6.3 kSv and the Class A dilution volume to 29
m 3/(GWe × year).
3) Procedure as point 2) but also Zirconium and Tin are chemically extracted.
Both elements require isotopic separation. One of the other isotopes of Tin is
radioactive and slightly toxic. In this way the only known long lived isotope
left in the discharge is 79 Se (0.3 kg) which represents 0.745 kSv and the
ridiculously small Class A dilution volume of 0.6 m3/(GWe × year).
These procedures (Figure 6.3) will ensure that the radio-toxicity of the FFs in the
“Secular Repository” is exhausted in less than 1000 years, which is a sufficiently short
time to be absolutely confident that current technologies of vitrification and of
containment can make the storage totally safe.
In addition to the FFs, in the High Level Stream there will be leaks of Actinides
due to the imperfections of the reprocessing. These radio-nuclides are more
worrisome since some of them are important α-emitters. The radio-toxicity and the
α-activity in Ci for leaked fractions f = 10-4 and f = 2 × 10-6 are displayed in Figure 6.4
and in Figure 6.5 respectively. The radio-toxicity has two maxima or “bumps”, the
first roughly for time span of the secular repository and a second for very long times,
namely 105 ÷ 10 6 years. The second maximum is due to 233U and its descendants.
142
The first bump in the toxicity in the early fillings is due to 232 U and it grows
substantially in the later fillings and in the asymptotic fuel composition because of
the increased presence of 238Pu and its descendants. The α-activity is instead always
determined by the 232 U and its descendants at short times and by 233 U and its
descendants at long times. The total α-activity of Actinides is about 10 5 Ci, for a fuel
mass of the order of 22 tons, which corresponds to an average activity of about 5
mCi/g. Note that the activity of Thorium which is the largest mass is very small and
that if Uranium’s are separated out they will have a specific activity which is about
ten times larger than the bulk of the spent fuel.
6.3 - Fuel reprocessing methods. In our case production of the lighter Neptunium
and Plutonium isotopes is very low and higher actinides are nearly absent. However
the (n,2n) reactions, more probable at high energies, increase the amount of highly
toxic 231Pa and 232U.
The EA requires the recovery of the Uranium (233U). However, it offers the
opportunity of destroying the other Actinides by concentrating them, after each
discharge, in a few dedicated fuel bars (targets) inserted somewhere in the bundles of
ordinary fuel, where an incineration lifetime of years is at hand. The amount of
leaking Actinides in the High activity Waste stream destined to the Secular
repository must be a small fraction f ≤ 10-4 of the produced amount. If incineration of
the long lived FFs is performed to alleviate the radio-toxicity of the stored products
after 500 years, an even higher performance in separating power is advisable, f ≤ 2.0 ×
10-6. The efforts in order to attain such a figure is justified by the considerable benefit
attained by the practical elimination of the “Geologic times Repository”. We remark
that such an incentive has been so far absent.
Two methods have been considered and appear suitable to our application: (1)
aqueous methods, presently in use and (2) the newly developed pyro-electric
method. We shall review both of them in succession.
Aqueous reprocessing methods have proven to be efficient, particularly for the
separation of U and Th (99.5% and higher). The best known example is the THOREX
process, based on solvent extraction through the use of tributyl phosphate (TBP),
which extracts and separates the Thorium and Uranium. Other Actinides can also be
extracted although their concentrations are so low that the extraction efficiency will
be lower.
143
Figure 6.6 describes schematically the overall fuel cycle. The fuel rods should
be stored for cooling at least for one year, to allow the 233Pa to decay to 233U. Fuel
rods are then sheared and chopped. The gaseous fission products will be
accumulated, with in particular attention for the 85Kr and 14CO2 which are destined
to the secular repository. Dissolution should be made with a mixture of nitric acid
(HNO3) and hydrofluoric acid (HF) since ThO2 is a very refractory ceramic material.
The HF concentration should not be higher than 0.1 M and the addition of
aluminium nitrate Al(NO3)3 as reagent could be needed in order to avoid corrosion
of the stainless steel dissolver. Before carrying out the solvent extraction process from
the obtained liquids they should be cleared of the remaining solids. The main
components of the liquid will then be Thorium, Uranium, Fission Products,
Protactinium and other trans-uranic Actinides.
The classic process to carry out the separation of Th and U from fission
fragments is the acid THOREX. It uses TBP 30% v/v diluted with an organic solvent
like dodecane. The partition of U from Th is done by washing the organic phase with
diluted nitric acid. The U stream will also contain the very small amount of Pu and
some contamination of Th and FF. The contamination of the Thorium stream will be
mainly FF. The high active liquid waste stream will mainly contain FF, trans-uranic
Actinides (231 Pa, 237 Np) and some residual contamination of Th and U. Further
cycles for purification of Uranium and Thorium should be applied using TBP as
extractant.
There is little information on the recovery of Pa and it will possibly require
some additional studies. Tests carried out at Oak Ridge have shown [80] that Pa
could be absorbed from solutions with high content of nitric acid by using various
absorbents like unfired Vycor glass, silica gel or Zirconium phosphate. Its extraction
should be done from the high level waste stream. Relative to the other Actinides its
extraction will be less efficient since their concentration in the Highly Radioactive
liquid Waste stream, although it can and should be increased, will nevertheless be
very low.
The performance quoted in Figure 6.6 is above the current values according to
standard experience on the THOREX process [13], [81], but appropriate tuning of the
chemical parameters should allow higher efficiencies. The minimisation and
ultimate disposal of High-Level radioactive Waste (HLW) generated from the
reprocessing of spent fuel (THOREX) is an important part of the global nuclear fuel
recycling strategy proposed in the framework of the Energy Amplifier Concept, as an
alternative to classical disposal methods. The goal is twofold, (i) to recover from the
144
insoluble residue useful metals such us Ru, Rh and Pd; (ii) and to separate
Actinides45 and some of the LLFPs (Long-Lived Fission Products) for their further
use (incineration) or disposal. We believe this can best be achieved with the method
developed in the context of the IFR (Integral Fast Reactor) programme [82], where it
is proposed to separate actinides46 and FPs from HLW by dry process with pyrochemical (or pyro-metallurgical) methods (Figure 6.7). However, the only process
that has reached an industrial scale is, at least for the moment, the PUREX process
(aqueous method) which has already been described in the previous paragraphs. All
the other methods are still in the technical or laboratory development phase.
Figure 6.8 shows the flow diagram of the dry process for partitioning of
Actinides [83]. This process consists of (i) denitration to obtain oxides, (ii)
chlorination to oxide to chlorides, (iii) reductive extraction to reduce Actinides from
molten chlorides in liquid cadmium by using lithium as reductant, and (iv) electrorefining to increase the purity of Actinides recovered. Both denitration and
chlorination steps are pre-treatment processes prior to the application of the pyrometallurgical process.
The principle of the reductive extraction with the subsequent step of electrorefining is schematically drawn in Figure 6.9. The electro-refiner is a steel vessel that
is maintained at 775 K (500 o C ). Liquid LiCl-KCl electrolyte in the electro-refiner
contains about 2 mol% of the Actinide chlorides. The Actinide solution (in liquid
cadmium) is inserted into the electrolyte and connected to the positive pole of a dc
power source (anode). The negative pole of the power source is connected to a
cathode immersed in the same electrolyte. The cathodes are simple steel rods. About
80% of the Actinide metals is electro-transported from the anode to the cathode rods,
where it deposits as nearly pure metal along with a relatively small amount of rare
earth fission products47. All the products are retorted to remove salt (and Cadmium
from the Cadmium electrode). Ingots from the retort are blended to appropriate
composition, and recast into special fuel pins. The fission products, with the
exception of Tritium, Krypton and Xenon, accumulate in the electro-refiner during
processing, and some noble metal fission products are removed with the anode after
each batch of fuel has been processed. The three gases are released into the process
45In
the F-EA, the Actinide residue consists mainly of Thorium, Protactinium, Uranium and a very
small amount of TRUs, whereas in a PWR it is mostly TRUs.
46 We expect this method can be extendedto the extraction of Thorium and Protactinium.
47 In reprocessing F-EA fuel, the complete removal of fission products may not be necessary since
their effect on the neutron economy is much less in a fast neutron spectrum than it is in a thermal
spectrum.
145
cell which has an argon atmosphere. They are recovered at high concentrations by
the cell gas purification system.
Several dozen batches of fuel are processed in a "campaign". At the end of a
campaign, the salt in the electro-refiner is treated by a series of steps to remove active
metal fission products, particulate noble metals, and any oxide or carbide impurities
for incorporation in high-level waste forms. The salt and its associated Actinide
chlorides are returned to the electro-refiner. The Actinide inventory in the electrorefiner amounts to about 20% of the Actinide elements fed; this must be recovered to
achieve more than 99.9% overall Actinide recovery. A non-metal and a metal waste
form will accommodate all of the high-level wastes. The non-metal waste form will
contain Samarium, Europium and Yttrium; the halogens and chalogens; the alkali,
and alkaline earth fission products; and a small amount of excess salt generated in
the process. The Actinide content of that waste form will be exceptionally low (less
than 1 part in 106 of the Actinides in the fuel that is processed). The only significant
long-lived activity in this waste will be Se-79, I-129 and Cs-135: the total alpha
activity should be less than 10 nCi. g-1. Metal wastes from the electro-refiner - noble
metals, cladding hulls and salt filter elements - will be combined with any process
scrap such as broken electrodes and the rare earths from the salt purification process
in the metal waste form. The metal waste form will have a very low Actinide content,
because of the effective Actinide recovery in the pyro-metallurgical process, but its
Actinide level will not be quite as low as that of the non-metal waste form. This
whole process can be made continuous, and thus can take place in a matter of only a
few hours.
Pyro-processing offers a simple, compact means for closure of the fuel cycle,
with anticipated high decontamination factor (> 99.9%), minimal production of highlevel radioactive waste, and significant reductions in fuel cycle costs. In addition,
mainly from the weapons proliferation viewpoint, it offers an advantage over the
PUREX and/or TRUEX methods, in that there is only partial removal of the fission
products. Even though the process is based on the use of a metallic fuel alloy with
nominal composition U-20Pu-10Zr, we believe it can be readily adapted to the EA
fuel cycle without much efforts.
The final content of the HLW stream coming from the EA fuel reprocessing is
mainly FFs, with only traces of Actinides. The volume generated is about 5 m 3 per
ton of fuel. The following step is to concentrate the aqueous raffinate and to transfer
it to an intermediate storage of the reprocessing plant. The volume of the concentrate
will be about 1 m 3/t. of fuel and the usual intermediate storage are tanks of suitable
146
stainless steel such as to minimise the acid waste corrosion. To prevent the highly
active liquid from boiling a redundant cooling system is required. Then, the
concentrate is cooled for a period of about 10 years in order to reduce the heat
generation by more than an order of magnitude before proceeding to waste
solidification. Among the fission fragments, excluding the short lived and stable
elements, there are a few elements which are medium lived (30 years, 90Sr, 90Y, 137Cs,
etc.) and some others (99Tc, 135Cs, 129I, etc.) which are long lived (Table 6.1). Since
Actinides are essentially absent from the HLW concentrates the policy we proposed
to follow is to store in man-watched, secular repositories for several centuries the
medium lived, in order to isolate them from the biosphere and to promote a vigorous
research and development of methods for incinerating the bulk of the long lived FFs.
The EA is an efficient tool to incinerate these wastes at the price of fraction of the
neutron flux [6], but alternatively dedicated burners can be used.
In parallel with the R&D on incinerators, development on solvent extraction
methods of long lived FF, which in some cases may additionally require isotopic
separation, should be promoted, the goal being to virtually eliminate the need for
Geological Repositories.
After the concentrates will be cooled down for the 10 years period and the longlived FF extraction applied for later incineration the wastes will be solidified by using
well known techniques. For instance by calcination and vitrification. The first step
allows to get waste oxides and in the second step glasses are obtained by melting the
waste oxides together with additives such as SiO2 , B2 O 3 , Al2O 3, P2O 5, Na2O, and
CaO. Borosilicate glass is the most studied solidification product but others like
phosphate glass, glass ceramic, etc. are also used. When the solidification process is
finished the wastes are ready for disposal in the appropriate secular repositories.
6.4 - Spallation induced Radio-nuclides. In addition to the radioactive waste
produced in the Fuel and in a minor extent in the Breeder, substantial amounts of
radio-nuclides are produced by the spallation target. As pointed out they divide
roughly into two batches, those which remain inside the molten Lead and those
which are either gases or volatile and which can be found in the neutral filling gas of
the main vessel. These last compounds are collected from the gas and stored in an
appropriate way in order to avoid leaks in the biosphere (paragraph 5.8). The
relative ingestive radio-toxicity of the various components of the Spallation target are
given in Figure 6.10. Following Table 5.9 spallation products at 700 °C can be
broadly divided into three different categories namely (1) gases or vapours in which
147
the contribution of 194Hg (751.9 y, 123 g/(GWe × year)) is largely dominant in size
and duration; (2) volatiles which, after a few years, are essentially dominated by to
204Tl (5.466 y, 114 g/(GW e × year)), (3) inter-metallic combinations (alloys) with the
molten Lead which at short times, shows a leading contribution from 90Sr and, at
longer times by 202Pb (7.59 × 104 y, 614 g/(GWe × year)). The radio-toxicity of the
spallation products is by no mean negligible: at early times it is about 10-3 of the total
radio-toxicity produced. At the end of the Secular repository time for FFs, the effects
of 194Hg exceed all other contributions until about 2,000 years. There is no major
difficulty in extending safely and economically the storage of about 2.3 kg/(GW e ×
year) of Mercury collected as vapours from the top main Vessel up to about 2000
years. Note that at least in the present design, the molten Lead of the Target region is
directly mixed with the big volume (≈ 1000 m 3) which constitute the main coolant.
Therefore at least the elements which remain inside the liquid are largely dispersed.
They will follow the fate of the Lead at the time of final decommissioning of the
installation.
We finally remark the existence of another lead isotope, 205 Pb (2.21 × 10 7y)
which is abundantly produced by neutron capture of 204Pb, namely 3.54 kg/(GWe ×
year) in the target region and 23.15 kg/(GWe × year) in total, and fortunately it is also
rather inoffensive, since it is very long lived and it decays by K-conversion with an
energy release of 51 keV mostly in the form of neutrinos.
6.5 - Radio-toxicity emitted in the Environment. Nuclear power production is
based on the concept that pollutants and toxic materials are retained within the plant
and in total isolation from the biosphere. The limited mass of such products makes it
possible to achieve such a goal. Mining process however cannot retain all products
and a significant amount of radiation is emitted in the biosphere during preparation
of the fuel. Likewise in the reprocessing of the spent fuel some radioactive elements
are currently re-emitted in the biosphere. Finally the ultimate storage of such
materials (geologic repository) have raised some question on the ability of isolating
them from the biosphere for times which largely exceed what can be considered an
experience based retention. The EA concept strongly reduces such environmental
impacts, when compared to the present reactor technology. We examine these points
in turn.
(1)- Mining. Thorium is largely present in the Earth's crust, but in small
concentrations. In addition several minerals exist, which have an excellent
concentration of Thorium and which can be exploited economically. The
148
primary choice is the monazite, which is a phosphate of Cerium and other
lantanides, containing a variable amount of Thorium and Uranium in a solid
mixture. Usually the Thorium concentration is of the order of 10% but some
mineral may reach as much as 20% by weight. Uranium minerals are usually
much less rich, its concentration being in the best cases of the order of 0.2%.
Incidentally one can remark that the solubility of Thorium is 1000 times
smaller than the one of Uranium. Taking into account that Thorium burnt in
the EA has an energetic yield which is 250 times larger than one of natural
Uranium destined to PWRs, we conclude that the relative mining effort is
reduced by a factor of the order 250 × 50 = 12500 times for a given produced
energy. Starting with mineral containing 10% of Thorium by weight we need
to dig only 70 tons of mineral to produce GW e × year. For comparison and
for the same energy produced the standard PWR methodology would require
0.875 106 ton of mineral. In the case of Coal, the mass of fuel (TEC) is 4.24 106
ton.
A pure Thorium mineral out of which the totality of Thorium is extracted will
produce tailings with a negligible radio-toxicity after some sixty years, since
all descendants of 232 Th have short decay lifetimes. Their evolution is
governed by the 5.7 year half-life of 228Ra. Furthermore there will be no risk
associated to Radon, since 220Rn has a half-life of 55.6 seconds and it decays
before escaping the minerals. As pointed out by Schapira [5] the situation in
reality is somewhat more complex, mainly because the monazite, which is the
primary source of Thorium is generally mixed with some Uranium
contamination. Such a contamination is strongly source dependent, as shown
in Table 6.2, taken from Ref. [5]. Assuming somewhat pessimistically that the
Uranium content is about 10% of the one of Thorium and that the long lived
toxicity and Radon contamination are primarily due to Uranium, we
conclude that the radio-toxicity produced at the mine is in the case of an EA
about 250 / (10% = 2500 times smaller than the one of today's PWR for a given
energy produced.
The UNSCEAR report [7] has estimated that the level of exposure of
individuals to mining for today's PWRs amounts to about 1.5 man Sv
(GW y)-1 as local and regional component and to 150 man Sv (GW y)-1 as
global component. We remark that according to the same report the
production of electricity from Coal is estimated to result in a global collective
dose of 20 man Sv (GW y)-1. The practice of using coal ashes for production
of concrete will add as much as 20,000 man Sv (GW y)-1. Values relative to
Thorium and its use in the EA for some possible mineral sources are listed in
149
Table 6.2. We conclude that the typical radiation exposure to public with the
EA due to mineral mining for the same energy produced are much smaller
than today’s PWRs and also Coal burning, even if solid ashes are correctly
handled.
The same report estimates the collective dose due to initial Uranium
enrichment and fuel fabrication to as little as 0.003 man Sv (GW y) -1. In the
case of the EA it is expected to be at least 1/4 of such a number, since the
burn-up is four times longer and there is no isotopic separation, The
collective doses are negligible in both cases.
(2) -EA Operation. During the EA operation the fuel and the spallation target
volumes are kept strictly sealed. Indeed also for proliferation protective
measures it is recommended that such volume be opened only in occurrence
with the re-fuelling, namely once every about five years and only by a
specialised team. While the fuel is safely sealed, the Lead coolant produces a
significant amount of radioactive products, some of which remain in the
liquid phase, but others are either gaseous or volatile and are found in the
neutral gas (Helium) with which the main Vessel is filled. These volatile
compounds are summarised in Table 6.3, extracted from Table 5.9. Some of
these are noble gases and Tritium which remain gaseous at room
temperature. Other, mostly Mercury and Thallium can be condensed and
preserved in the solid state. Some other elements will be collected by the
Lead purifier. In view of its small amount involved we believe that the
gaseous elements can be released in the atmosphere. The collective effective
dose per unit energy release is given by the UNSCEAR report [7] and
summarised in Table 6.4. It is assumed that gases are released every 6
months, without cool-down period. A short cool-down will dramatically
reduce the effects of 127Xe (52.63 d) and it is recommended. The total local
and regional doses are 0.42 man Sv (GW y) -1. The global doses, integrated
over 10,000 years, following the convention of Ref. [7] are of 0.18 man Sv
(GW y)-1. Both values are dominated by the effects of Tritium.
The rest of the solid high activity waste from the spallation products
(dominated by Mercury and Thallium) has a substantial ingestive radiotoxicity (Figure 6.10) and it should be carefully accumulated and destined to
the repository.
(3)-Fuel reprocessing has to deal with the very large radioactivity of the spent
fuel. Since the techniques are not different that those generally in use, we can
150
make direct use of the estimated collective doses of Ref. [7] (Table 6.5), taking
into account the differences in stockpile of the radio-nuclides produced (see
Table 5.8). It is however assumed that both 14 C and 85 Kr are extracted
during reprocessing and sent to the repository for cool-down. Separation of
85 Kr can be performed cryogenically according to a well documented
procedure [84]. Also 14C once reduced in the form of CO2 can be extracted on
the same time by the same method.
The total doses to members of the public are summarised in Table 6.6. Total
global dose truncated at 10,000 years is 0.6 man Sv (GW y) -1, namely for the same
energy produced about 0.003 of the one of an ordinary Reactors [7] — without
counting occurred criticality and melt-down accidental releases, avoided by the EA,
(≈ 300 man Sv (GW y)-1 — and about 0.03 of the alternative of Coal burning, even if
solid ashes are correctly handled.
6.6 - Conclusions. Realistic schemes are possible in which the spent Fuel from
the EA is “regenerated” for further uses. Separation of the fuel materials into two
streams is performed, the Actinide stream destined to the fuel fabrication and the
FFs stream which is destined to the Secular repository. After 500 years the radiotoxicity for unit energy produced of the EA is about 20,000 smaller than the one of a
PWR with a “throw-away” cycle. Incineration with the help of neutrons of some of
the critical, long lived radio-nuclides can strongly reduce the radio-toxicity of the
waste beyond 500 years. If sufficiently diluted it could be also let “die away” without
incineration since it can be made to satisfy the requirements for Class A repository.
Note also that at that time the residual ingestive radio-toxicity is comparable with the
one of the Thorium metal burnt in the EA.
An essential element in the clean disposal of the spent fuel is the small leakage
of Actinides (mainly Uranium) into the FFs stream. A level of 100 ppm. or better is
required. We believe that it is within the state of the art, eventually with a few
improvements.
An important source of radio-toxicity are the spallation products due to the
proton beam interacting with the molten Lead target. A specific element of concern
is 194Hg which is the main surviving source of toxicity of the EA in the period of time
between 500 and 2000 years. It can either be preserved far from the biosphere that
long or, alternatively, incinerated, following the fate of the Actinides inside the EA.
Unfortunately the relevant cross sections are only poorly known but they should be
measured soon [6].
151
An experimental test of the feasibility of incineration with neutrons in a Lead
diffuser [6] is in preparation at CERN. Would it be successful it could offer the right
technique in order to eliminate also the modest amount of long lived radio-toxic
elements produced.
Likewise important is the total radioactivity doses to members of the public
due to operation. Total global dose of the EA truncated at 10,000 years is estimated
to be 0.6 man Sv (GW y)-1, namely about 1/330 of the one of an ordinary Reactors for
the same energy produced (200 man Sv (GW y)-1)— without counting occurred
criticality and melt-down accidental releases, avoided by the EA (≈ 300 man Sv
(GW y)-1) — and about 1/33 of the alternative of burning Coal (≈ 20 man Sv (GW y)1), even if solid ashes are correctly handled.
Table 6.1 - Fission fragments‘ activity after 1000 years of cool-down in the Secular
Repository. Values are given for 1 GWe × year.
RadioIsotope
129I
99Tc
126Sn
135Cs
93Zr
79Se
1/e Life
Mass
years
(kg)
Other
Isotopes
(kg)
8.09
16.61
1.187
34.12
26.11
0.30
3.48
—
1.783
66.77
99.11
3.02
2.27E+7
3.05E+5
1.44E+5
3.32E+6
2.21E+6
9.40E+5
Activity Ingestive
@ 1000 y Toxicity
(Ci)
(Sv) × 103
1.43
284.29
33.79
39.32
65.64
2.06
19.58
27.67
3.20
9.87
2.38
0.745
Dilution
Class A
(m 3)
178.47
947.65
9.65
39.32
18.75
0.59
Table 6.2 - Uranium and Thorium content in percent [5] and levels of population
exposure for typical Ores [7].
Source
Italy
Sri Lanka
California
India
UO2
ThO2
Ratio
U/Th
15.64
0.10
6.95
0.29
11.34
14.32
4.22
9.80
1.38
0.007
1.64
0.029
Local
Global
Sv (GW y)-1 Sv (GW y)-1
8.28 × 10-3
4.20× 10 -5
9.84 × 10 -3
1.74 × 10 -4
0.828
4.2 × 10 -3
0.984
0.0174
152
Table 6.3 - Radio-nuclides emitted in the neutral gas inside the Vessel by the
Spallation target and the molten Lead coolant ( ≈ 700 °C).
3H
39Ar
42Ar
81Kr
85Kr
127Xe
Gas at Room Temperature
Mass
1/e
Boils at
(g)
Lifetime
°C
1.435
17.83 y -252
Solid at Room Temperature
Mass
1/e
Boils at
(g)
Lifetime
°C
35S
0.009
126.5 d 445
0.336
0.336
389.0 y
47.57 y
-186
-186
65Zn
5.777
4.326
0.331E+6 y
15.55 y
-153
-153
0.37
(675)48
52.63 d
-108
70Zn
0.004
2.424
353.2 d
0.723E+15y
907
907
73As
0.329
116.1 d
83Rb
86Rb
0.036
0.181
124.6 d
26.94 d
615
615
688
688
109 Cd
1.627
1.833 y
767
125I
0.014
85.90 d
184
124Sb
0.043
0.404
87.05 d
3.988 y
1585
1585
0.003
0.282
14.01 d
2.982 y
671
671
415.9
203Hg 6.252
751.9 y
67.40 d
357
357
17.68 d
5.466 y
1473
1473
200.1 d
254
125Sb
131Cs
134Cs
194Hg
202Tl
204Tl
15.25
386
210Po
48
Total integrated production, without decay over 5 years
0.995
153
Table 6.4 - Normalised, collective effective dose from locally, regionally and globally
dispersed radio-nuclei during operation over a period of 10,000 years.
Normalised
release (Tbq)
3H
14C
39Ar
42Ar
81Kr
85Kr
127Xe
Totals
521
—
0.430
3.268
0.004
63.6
3718.51
Collective dose per unit Normalised collective
release (man SvTbq-1)[7] Dose (man Sv (GW y)-1)
Local &
Local &
Global50
Global
Regional49
Regional
0.0027
0.40
7.4 10-6
7.4 10-6
7.4 10-6
7.4 10-6
7.4 10-6
0.0012
85
5.0 10-4
6.1 10-5
1.8 10-2
2.0 10-5
1.05 10-7
4307
0.418
—
9.4 10-7
7.2 10-6
9.2 10-9
1.4 10-4
8.2 10-3
0.185
—
6.38 10-5
5.91 10-5
2.24 10-5
3.77 10-4
1.16 10-4
0.42
0.186
Table 6.5 - Normalised released dose of airborne and liquid effluents of radionuclides during reprocessing of Fuel. Values have been normalised to current
practices [7].
3H
14C
85Kr
129I
131I
137Cs
90Sr
106Ru
Totals
Process
(kg)
EA/
PWR
Normalised collective
Dose (man Sv (GW y)-1)
Airborne
Liquid
Effluents
Effluents
—
0.0145
21.64
27.28
0.2924
118.5
74.76
1.147
1.0
9.2
10.16
1.722
0.458
1.109
0.11
(7.45)
(0.924)
0.430
1.37 10-4
0.0188
0.0012
—
—
—
1.578
0.074
—
—
0.205
0.207
0.60
1.63
—
1.22
Comments
assumed same as PWR
Retained
Retained
standard practices
“
“
“
“
“
“
“
“
For noble gases, values are taken to be the same as 85Kr.
For noble gases, values are taken to be the same ones as 85Kr, for decay over 10,000 years.
51Periodic (every 6 months) release, without cool-down.
49
50
154
Table 6.6 - Summary of normalised, collective doses to members of the public from
radio-nuclides released from the EA.
Local and regional
Doses
(man Sv (GW y)1)
Global Doses
(man Sv (GW y)-1)
Mining52, Milling, Fuel fabrication
EA operation
Reprocessing (Atmospheric)
Reprocessing (Aquatic)
Miscellanea53
4.2 10-5 ÷ 9.8 10-3
0.42
0.60
1.63
0.1
0.0042 ÷ 0.984
0.188
0.1
0.1
0.05
Totals( variation over mining range)
2.75 ÷ 2.76
0.44 ÷ 1.42
Source
52
The dose range depends on the Uranium content in the Thorium mineral. We have taken extreme
values of Table 6.1.
53 This includes mainly Transportation, Fuel fabrication, Solid Waste disposal. Figures are taken from
Ref. [7].
155
Figure Captions.
Figure 6.1
Evolution of the ingestive radio-toxicity of High Level Waste(HLW)
during Secular Repository period.
Figure 6.2
Evolution of the ingestive radio-toxicity of HLW beyond the "Secular
Repository" period.
Figure 6.3
Evolution of the ingestive radio-toxicity of the FFs for different
incineration procedures.
Figure 6.4
Radio-toxicity of the residual Actinide waste stream for different leak
fractions.
Figure 6.5
α - activity of the residual Actinide waste stream for different leak
fractions.
Figure 6.6
Flow diagram of the partitioning process of spent fuel.
Figure 6.7
High-Level Waste (HLW) reprocessing scheme.
Figure 6.8
Flow diagram of the pyro-metallurgical process for partitioning of the
residual Actinides from HLW.
Figure 6.9
Schematic illustration of the pyro-metallurgical partitioning process.
Figure 6.10 Relative ingestive radio-toxicity of the spallation target products.
156
Ratio =
PWR for same
delivered energy
no reprocess
EA discharge , f = 10 -4
(Asymptotic Fuel composition)
TH-232 in EA
EA discharge, f = 10 -4
(First Fill)
PWR for same
delivered energy
no reprocess
EA discharge , f = 10 -4
(Asymptotic Fuel composition)
TH-232 in EA
EA discharge , f = 10 -4
(First Fill)
PWR for same
delivered energy
no reprocess
TH-232 in EA
All Fission
Fragments
Tc99, I129
and Cs135
removed
Tc99 and
I129 removed
Tc99, I129 ,
Zr93 ,Sn126 and
Se79 removed
Carbon 14
Tc99, I129 ,Cs135
Zr93 ,Sn126 and
Se79 removed
Tc99, I129 ,Cs135
Zr93 ,Sn126 removed
PWR for same
delivered energy
no reprocess
TH-232 in EA
Leaked Fuel in
High Level Stream
f = 10 -4
Leaked Fuel in
High Level Stream
f = 2 x10 -6
Fuel Regeneration
;
@
À
;À@;À@;À@
;À@ ;À@
À
@
;
;À@;À@
;À@
EA discharge , f = 10 -4
(Asymptotic Fuel composition)
Total Spallation
Products
Hg-194
Tl-204
Volatiles
@ 700 ¡C
Inter-Metals @
700 ¡C
Solids @
700 ¡C
Pb-202
Gases & Vapours
@ 700 ¡C
157
Acknowledgements.
We would like to acknowledge the superb and dedicated work of Susan Maio
and F. Saldaña, without whom this paper could not have become a reality. We
would like to thank many of our CERN colleagues for frequent discussions of various
aspects of the project and for their continuing and enthusiastic support. Stress
analysis and hydrodynamic calculations have been performed with the help of M.
Battistin and A. Catinaccio. I. Goulas has helped with programming. M. Cobo,
M. Embid and R. Fernandez have diligently helped during their stay as summer
students at CERN.
We have profited from (too) short, but illuminating visits of E. Greenspan
(Univ. California at Berkeley), V. Orlov (RDIPE, Moscow), H. Branover (Ben Gurion
University, Israel) and K. Mileikowski.
Many experts have helped us in different fields. We would like to thank in
particular: A. Ferrari and P. Sala (University of Milan) for the code FLUKA;
J.P. Schapira and R. Meunier (IN2P3) for their contributions to radio-toxicity and
end-of-cycle aspects; E. Gonzalez and A. Uriarte (CIEMAT, Madrid); R. Caro and
A. Alonso (Consejo de Seguridad Nuclear, Madrid); M. Perlado, J. L. Sanz,
E. Gallego and P.Trueba (Universidad Politecnica, Madrid) and A. Perez-Navarro
(Alfonso X El Sabio) for numerous and extended contributions pertinent to safety,
radiation damage and end of cycle aspects; H. Rief (JRC, Ispra) for contributions to
the question of reactivity insertions; P. Gerontopoulos, J. Magill, M. Matzke,
C. O'Carrol, K. Richter and J. Van Geel (JRC Karlsruhe) for proliferation aspects;
D. Finon and Ph. Menanteau (Institut d'Economie et de Politique de l'Energie,
Grenoble), M. Gigliarelli-Fiumi (INFN, Frascati) and M. A. Rodriguez-Borra
(SERCOBE, Madrid) for the economic and industrial aspects; E. Sartori (NEA), The
International Dosimetry and Computation Group of NRPP (UK); C. Dunford and
S. Ganessan (IAEA) and G. Audi, (CSNSM, Orsay), for their invaluable assistance in
facilitating our access to relevant Data Banks.
The design of the accelerator has been made possible with the help of
Laboratoire du Cyclotron, Centre Antoine Lacassagne. We thank its Director, F.
Demard, and wish to acknowledge J. M. Bergerot, A. Giusto, P. Montalant, J. F. Di
Carlo, V. Rossin. We had helpful discussions with W. Joho, U. Schryber and P. Sigg
(PSI, Zurich) and J. Pamela (CEN, Cadarache). Last but not least, we would like to
acknowledge the continuing support of the CERN Management (in particular of H.
Wenninger), of the Sincrotrone Trieste (in particular G. Viani), and the DGXII of the
European Commission, in particular its Director General, P. Fasella and
H.J. Allgeier, G. C. Caratti and W. Baltz.
158
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