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The possibility of breeding 233U from thorium was demonstrated by the MSRE experiment [49]. The MSBR [50] project has produced a rather detailed design for a large molten salt reactor, with interesting breeding possibilities. As an alternative to the solid fuel UPu breeders we have studied the potential of the ThU cycle with MSR reactors. The first fissile loads of the 1 GWe MSR are made of industrial plutonium obtained from spent PWR fuel reprocessing. Due to the mediocre neutronic properties of this plutonium, our simulations show that 4tons/GWe are needed to ensure criticality.[11] The initial plutonium load is replaced by 233U. Every year, all 5 year old available plutonium is used for new MSRs. This is not sufficient to ensure the required rate of increase. The complement is obtained from the excess 233U produced in the operating MSRs, used to start new Th — U reactors. Only 1 ton/GWe of U is needed to ensure criticality of an MSR. The doubling time is 25 years with a 10 day cycling time of the salt. The chemical treatment amounts to extracting fission products and protactinium. 233U is reinjected into the salt after protactinium decay.
Figure 2.9 is similar to figure 2.7 for the UPu cycle, and shows the evolution of the reactor park. We have distinguished ThPu and Th233U
Figure 2.10. Evolution of the 233U stockpile in the case of deployment of a ThU molten salt breeder park. 
reactors according to their initial loads. The lifetime of the reactors was assumed to be 40 years, which explains the decrease of the ‘ThPu’ reactors after 2070.
Figure 2.10 shows the evolution of the 233U stockpile outside the reactors. The plutonium stockpile is not displayed since all the plutonium produced is, after 5 years of cooling, used for new ThPu reactors. As for the UPu cycle, the amount of available 233U measures the flexibility of the system which could be used for fission product transmutation and/or smaller production units. It is interesting to note that the final stockpile of 233U is only 16000 tons, to be compared with the much larger stockpile of 80 000 tons of Pu displayed in figure 2.4. However, due to the difference of inventories (1 ton versus 4 tons), the number of new reactors which could be fed with these stockpiles is the same, namely 16 000 GWe. This illustrates the fact that the value of q (2.9 for Pu versus 2.3 for 233U) is not the only relevant quantity to evaluate breeding potentials. In the case of MSRs, the ability to remove the fission products continuously is another determining factor.
Even if catastrophic criticality excursions are prevented by a judicious choice of the different reactivity coefficients, combined with efficient active measures, possible serious accidents, such as that of Three Mile Island, may be caused by a defective extraction of the residual heat produced in the fuel by the radioactivity of the fission fragments after reactor shutdown. Immediately after shutdown the residual heat amounts to 7% of the heat produced at full power. This means that a 1 GWe reactor (3 GWth) produces 200 MWth of residual heat after shutdown. This value drops to 16MWth after 1 day and 9 MWth after 5 days [37]. In principle, if the coolant is still present and the circulating system active, this residual heat is easily disposed of. However, both loss of coolant (LOCA) and a cooling fluid circulation system failure are possible and their probabilities depend on the type of reactor. Since subcritical assemblies of hybrid reactors are not different, in this respect, from critical assemblies, we discuss the properties of the most representative reactor types, as far as heat extraction is concerned.
Analogue Monte Carlo. One particle is followed event by event. This is the standard way to transport particles as shown in figure 5.1. This method is correct if the number of histories is large enough.
Nonanalogue Monte Carlo. Only interesting particles are followed: each time a particle is an interesting one, it is multiplied into Q particles with a weight
1 IQ. This method decreases the statistical error, but could introduce a bias in the results.
Fission probabilities have important implications both on the neutron production of the pnucleus reaction and on the production of nuclear waste. Figure 6.3 compares experimental fission crosssections for the highly fissile 235U to calculations using the Bertini code with or without
Neutron Momentum (MeV/c) Neutron Momentum (MeV/c) Figure 6.2. Comparison of experimental neutron energy spectra following the reaction p + 7Li with spectra calculated using the Bertini and ISABEL INC codes [90]. Light dots: Bertini; solid line: ISABEL; thick dots: data. 
preequilibrium treatment. It is seen that, in this case, the preequilibrium treatment does not influence the results very much. This is a consequence of the very high fission probability. For neutron energies below 100 MeV, all INC calculations become unsatisfactory. This reflects a deficiency of the INC codes in reproducing reaction crosssections below that energy. Figure 6.4 compares experimental fission crosssections for the poorly fissile 208Pb with calculations using the Bertini and the ISABEL INC codes
Figure 6.3. Comparison of experimental neutron induced fission crosssections of 235U with calculations based on the Bertini INC with or without preequilibrium [90]. Solid line: standard preequilibrium MPM calculation [109]. Dashed line: no preequilibrium step. Dotted line: hybrid MPM. See Prael [90] for details. 
with or without preequilibrium treatment, and for different level densities. Here the interest of the preequilibrium treatment is far from obvious. The standard level density is that of Igniatyuk [101] and gives the best results. The Julich level density [84] includes the effects of shells on level densities but not the washing out of these effects with temperature. It clearly underestimates the level density. In any case, as stated earlier, it seems clear that progress has to be made in the fission treatment.
Equation (9.23) shows that full extraction can only be obtained for an infinitely large organic solvent current. Improved extraction can be obtained
with a cascade arrangement, such as that shown in figure 9.4. For the two — stage system shown in figure 9.4 the value of the fractional recovery becomes, for y2 = 0,
(9.24)
which is larger than the value given by equation (9.23). Generalizing to N stages, assuming that yN = 0 and defining = DIe/If we obtain the
equation for y0:
N — 1
У0 = DxnJ2 fl. (9.25)
i = 0
Mass conservation implies
IFx0 = IFxN + IE У0 (9.26)
which allows us to write
eN 1
У0 = Dx0 flN + 1 _ 1 (9.27)
One sees that for large N and P > 1 the efficiency tends towards one. For
P < 1,p! P for N! 1.
The preceding calculation assumes that yN = 0. This condition can easily be dropped and one gets an overall recovery of the extractable component
Note that, because of the definition of p = IEy0//Fx0, the term depending on yN is partly trivial since it gives a finite contribution even when there is no transfer from the aqueous to the organic phase (P = 0). If it is the extraction efficiency that is of interest, it might be more informative to use
IE yN yN
7—— = P — P —
IF x0 Dx0
N
For yN = 0, p = reff. When yN = 0, the extraction efficiency decreases, which seems natural since the final value xN = yN _ 1 /D has a finite minimum value yN/D.
Figure 9.5. Extraction of a component from an aqueous phase into an organic solvent followed by redissolution of the component into an aqueous phase (stripping). 
We have also assumed that the value of D does not depend on the stage number. This is only true for rather dilute solutions, as we have seen above. When this is not the case we refer to the discussion in reference [138].[48]
It is important that the treatment is completely symmetric with respect to the nature of the phases. Thus it is possible to transfer a component from an organic phase to an aqueous phase. This makes recovering the expensive organic solvent possible, as shown in figure 9.5.
The large lead volume allows fuel cooling by natural convection. To this aim, the mass of lead is as big as 10000 tons contained in a vessel 30 m high. Natural convection is initiated by the mass difference between the hot lead at the output of the core and the colder lead at the output of the heat exchangers. The height of the lead column determines the flow velocity. The 30 m height is needed for a flow velocity sufficient to extract the operating heat. Thanks to natural convection no primary tubing, as a potential cause of serious problems in the case of leaks, is needed. Because of the large lead mass, the thermal inertia is very large, minimizing the effects of sudden variations of the accelerator beam intensity.
Passive safety. In the improbable case where the lead temperature would exceed by more than 100 °C the normal operating value (for example if the
Thermal insulating wall Plenum region
Fuel region
Spallation region
Figure 12.2. Detail of the CERN system [76]. Note the heat evacuation by natural convection. The molten lead is contained in a kind of Dewar vessel. In the case of significant increase (around 100 °C) of the lead temperature it will overflow into the beam tube and into the space separating the inner and outer walls of the Dewar, thus allowing residual heat evacuation by air convection. The large structure above the Dewar helps air cooling.
primary heat exchangers break down while the beam stays in) the lead overflows into the beam tube, stopping neutron production in the fuel zone. At the same time, the molten lead flows into the void which normally isolates the molten lead pool from air. Thermal contact with air ensures extraction of the residual heat produced by radioactive decay of the irradiated fuel.
Finally the lead overflow positions a neutron absorber which brings the multiplication factor down to 0.9. The system may then stay in a safe state as long as necessary. Note that the core is placed in a deep well and is protected by a lead thickness of 20 m.
Fuel reprocessing [138]. In the original proposal, based on the ThU cycle, fuel reprocessing was either Thorex for oxide fuels [153], or pyropro cessing for metallic fuels as developed at Argonne National Laboratory [22].
The purpose of creating an underground laboratory is, on one hand, to verify the characteristics of the CallovoOxfordian formation, at the scale of the proposed installation, and, on the other hand, to subject it to a number of solicitations to verify its robustness.
Current programmes are aimed at completing the geologic and hydrodynamic characterization of the site. As a first step, the homogeneity and continuity of the formation will be verified, and it will be checked for the absence of faults likely to create hydraulic shorts within the Callovo — Oxfordian formation. Subsequently, the local hydrogeologic regimes will be analysed, along with their possible evolution, using network drillings that register ground water behaviour during the operations, in particular during the drilling of the underground laboratory access shafts.
Migration data have also been used in the safety computations; they influence diffusion and the delay coefficients. In both cases, measurements were done on samples at the centimetre scale. Determinations done in situ, or from larger sized samples, are necessary to verify the validity of the values obtained. Another important issue is access to water. The chemical form of different species depends on water chemistry, of the processes regulating it in a natural environment. One of the difficulties is the reliable determination of the characteristics of a given water as it is very difficult to extract the water from small samples. The underground laboratory provides direct access; sampling and measurement devices can help in a better determination of this chemistry. Another aspect that can be studied in an underground laboratory is geomechanics, first to ascertain that construction can be undertaken safely, but also to study damaged zones on the walls of the construction susceptible to form hydraulic shorts.
Exogenous materials would also be placed in the disposal, among which is the waste itself. Various interactions that they might cause must also be studied in situ, in particular the effects due to thermal release as well as materials ageing. The experimental programme being prepared is geared to the study of the various mechanisms that come into play and of the behaviour of the various materials components.
The modelling and simulation approach, and the 3D representations, must be studied; this holds also for any possible evolution in the conception of the constructions.
A set of means are thus available to demonstrate the safety of disposal installations; a large research effort is required, implying numerous teams.
Although, at the beginning of nuclear energy deployment, many different reactor systems were proposed and more or less tested, only a few of them became standard in the Western hemisphere: lightwater reactors like the PWR (pressurized water reactor) or BWR (boiling water reactor), heavy — water reactors of the CANDU (Canadian deuterium uranium) type and, finally, the sodium cooled fastneutron reactors (LMR: liquid metal reactor). It was clear from the beginning that breeder reactors like the LMR were necessary for a sustainable development of nuclear power. However, the experience with the LMR is far from conclusive, especially since the universally used sodium coolant seems to lead to too strong safety constraints on the building and operation of the reactors. Furthermore, lightwater reactors are plagued by the problem of radioactive waste which, to date, has not found a consensual solution. The waste problem added to the fear of catastrophic accidents (Chernobyl syndrome) explains the large societal opposition to nuclear power observed in many countries. To some extent one may think that nuclear energy will come to a dead end. This is an unfortunate situation when the rising concern about the greenhouse effect pleads for a severe reduction in the use of fossil fuels. The development of safer and less polluting means of producing energy from nuclear fission is, thus, of great relevance.
In this context, in recent years, a great deal of interest has been displayed, worldwide, in accelerator driven subcritical nuclear reactors (ADSR or ADS), also called subcritical or hybrid reactors, to produce energy and transmute radioactive wastes in a, possibly, cleaner and safer way than at present. Pioneers in this revival have been Furukawa [1], Bowman [2] and Rubbia [3]. Similar ideas were first proposed more than 50 years ago [616]. At that time they were not carried through, not so much because of technical difficulties but for lack of economic incentive. It is true, also, that while building reliable GeV accelerators achieving intensities of several tens of milli — amperes was by no means considered to be a trivial matter, efficient critical reactors were available, and were thus thought to be the simplest and most natural way to harness nuclear fission. It was, however, acknowledged that accelerator driven nuclear devices might offer interesting transmutation possibilities. For example, without a large enough concentration of 235U in natural uranium, the only way to exploit fission energy would have been the use of such subcritical systems.[1]
Highenergy accelerators appear to be a promising way to incinerate heavy actinides [17, 18]. It has also been acknowledged that a thorium — based fuel cycle would considerably limit the amount of transuranic wastes produced. The implementation of such a cycle would be made easier with subcritical reactors, due to the improved neutron economy of such systems as compared with classical critical reactors [13]. Hybrid reactors appear to be a credible alternative to fast breeder and fusion reactors.
In chapter 2 we examine the general question of world energy needs and possible supplies. In chapter 3 we give an elementary reminder of reactor theory. Chapter 5 is devoted to the description of commonly used reactor simulation codes. In chapter 6 we describe the basic physics of hybrid reactors, including an account of the experimental and computational state of the arts of spallation reactions. In chapter 7 we discuss safety questions specific to ADSRs. In chapter 8 we examine the evolution of hybrid reactor fuel as a function of time. This evolution determines the most important constraints on the neutronics of hybrid reactors. Chapter 9 describes the main fuel reprocessing techniques, since these condition the possibility of implementing a durable nuclear energy production. Chapter 10 shows how the existence of a spatially confined neutron source influences the size of the reactor. Chapter 11 examines the possible use of hybrid reactors in the nuclear waste issue. Chapter 12 gives some examples of ‘historic’ projects which used either solid or liquid fuels. Chapter 13 discusses the present state of thoughts for the possible development of ADSRs.
In this book we have, deliberately, chosen to place the emphasis on simple, intuitive, treatments of the different aspects of the physics of hybrid reactors, in order to provide the reader with the possibility of gaining physical insight into these systems. However, the reader should be aware that realistic calculations require the use of complex codes, most frequently of the Monte Carlo type. Nevertheless, it is our experience that starting with simple models helps the understanding of the results of the ‘real’ calculations, and provides intuition of the most fruitful ways to improve systems or discover new ones. As far as possible this review is selfcontained and does not require a priori knowledge of the field. It elaborates on reviews of the subject previously published in Progress in Particle and Nuclear Physics [4] and in Nuclear Instruments and Methods [5].
In many cases it can be seen that critical reactors could do as well as ADSRs. We hope that this book will give the reader the elements needed to form an opinion on the possible usefulness of ADSRs, as well as to have a good basis for starting working on these systems. More generally, students and practitioners in nuclear reactor technology might find useful the more recent developments presented here.
We thank the ISN group, and especially Professor J M Loiseaux, Dr D Heuer, A Nuttin and F Perdu, for contributing to many ideas and much of the material presented here. Professor C Rubbia was the originator of our interest in the subject of hybrid reactors and the main inspiration for our thoughts on the subject. We enjoyed many fruitful interactions with Professors J P Schapira, M Salvatores, M E Brendan and C D Bowmann. Professors D Hilscher, L TassanGot, W Mittig, B Lott and S Leray were kind enough to provide us with originals of their figures. Mrs E Huffer was kind enough to read our manuscript carefully and correct the English. The patience and support of Helene Meplan and Marguerite Nifenecker are gratefully acknowledged.
The Boltzmann equation can be written in an integral form. This can be done by mathematical manipulations on equation (3.18). Here we give a physical derivation of the integral form based on physical arguments, in the simplifying case where the macroscopic crosssections are time independent, the scattering crosssection is isotropic, the medium homogeneous and the system is stationary in time. Then the flux at position r is due to neutrons created elsewhere, be they scattered neutrons or fission neutrons with the right velocity. The probability that a neutron with velocity v at position r’ reaches position r is
e ^T (v)lr — r’l
r — r’2
The number of neutrons scattered and created at position r 0 is
‘(r, v)(^(?, v! v) + mpf(v)Xf(r’, v’)) dv’.
Thus, the flux at position r reads:
xCSs(r’, v! v) +mpf(v)Xf(r’, v )) dv’ . (3.19)
The possibility of transmuting and incinerating nuclei depends on the neutron cost of these reactions. The simplest case is that of fission products.
Fission product transmutation
The transmutation of fission products requires, obviously, at least one neutron per nucleus. The production rate of the most important LLFPs, 99Tc and 129I, are given in table 3.8. From this table it appears that at least 0.07 neutron per fission would be required to achieve transmutation of these two nuclei. Ideally the most efficient way to transmute fission products is to use neutrons which
Table 3.8. Yields of technetium 99 and iodine 129 per fission of three important nuclei.

would be lost to captures in the structural elements or which would escape the reactor. This is why it has been proposed to capture neutrons in the resonances of fission fragments, whenever these display strong resonances [57]. In this way, it is hoped that neutrons are captured by the fission products before they reach thermal energies where captures in structure materials are significant. We discuss these ideas in the case of a fast reactor using a lead reflector, such as was proposed by Rubbia et al. [76]. 99Tc is characterized by the existence of a strong resonance at ER = 5584meV, with Г = 149.2meV and a0 = 104 barns. We apply equation (3.64):
which we write, after numerical evaluation (o, = 10 barns for lead)
PSurv(x)=exp(" Е gg^’2 (P1 + x X 103 — 1^ (3.141)
where x is the concentration of 99Tc nuclei with respect to lead. We find that 90% of the neutrons are captured for a 99Tc concentration of 6 x 104. In the energy amplifier original design [76], about 6% of the neutrons were captured in the lead. About half of these are captured below 5 eV and could, thus, be captured in the diluted technetium. Since each fission produces 2.5 neutrons, it follows that 7.5 neutrons could be absorbed in technetium per 100 fissions. The volume of lead to consider is that where the neutron flux is high enough, rather than the full volume of the lead pool described in the energy amplifier proposal. The transport length in lead is around 1 m. It is found that the total weight of lead irradiated by a high neutron flux is around 600 tons. The amount of 99Tc which should be dissolved in order to capture 90% of the available neutrons would then be around 180 kg. The number of neutrons captured per year in the 99Tc would be
NTccap) = 8.4 x 1025 (3.142)
assuming a 10 MW beam and a value of ks = 0.98. These captures correspond to a transmuted mass of 14 kg. The halflife of the 99Tc in the neutron flux would be 7.5 years.
These data can be compared with those obtained with critical reactors. Calculations have been made both for fast and PWR reactors [66]. In the case of fast reactors the best results are obtained using moderated assemblies where 99Tc is mixed with a hydrogeneous material like CaH2. In the case of fast reactors, the shortest halflife is 15 years, while it is 21 years in the case of PWR. Thus, it appears that capture by adiabatic resonance crossing, like that discussed above, might be advantageous.
For transmutation, the most important parameter is the neutron flux, since the effective lifetime of a nucleus in a neutron flux is inversely
proportional to the flux value. As an example, a set of nuclei with a crosssection of 1 barn, typical of some fission products, needs 200 years in a 1014 neutron/cm2/s flux to be reduced by a factor of 2. Such numbers explain, partly, why projects such as that of Bowman et al. [2] aimed at a thermal neutron flux as high as 1016/cm2/s.