We use the developments of section 3.3 to express кж. This expression involves averaging cross-sections over the reactor’s neutron spectrum, as seen in equation (3.74). The average cross-sections depend strongly on the neutron spectrum, which itself depends on the composition of the fuel and on the reactor geometry. To illustrate these influences, table 11.6 compares important cross-sections obtained in three cases:

1. the Superphenix fuel composition (U-Pu) and geometry (sodium coolant)

2. a lead-cooled reactor (50% lead in volume) with minor actinide oxide fuel

3. a lead-cooled reactor (50% lead in volume) with minor actinide metal fuel.

In case 1, it is assumed that the presence of MA does not affect the energy distribution of the neutron flux. In cases 2 and 3 the neutron flux is obtained from the Monte Carlo calculation with the initial MA load. The initial composition of the MA fuel was 237Np(12.5%), 241Am(50%), 243Am(25%), 244Cm(12.5%), as given by Spiro et al. [44]. These values were obtained assuming multirecycling of the plutonium in PWRs and extraction of the remaining minor actinides at each reprocessing stage.

The neutron spectra are harder and harder for cases 1, 2 and 3. The presence of sodium in case 1, and oxygen in both cases 1 and 2, is responsible

for the softening of the spectra. It is also found that the nature of the fissile and fertile components has a strong influence on the hardness of the neutron spectrum. The strong absorption cross-sections of minor actinides at low neutron energies lead to flux depression at low energies and therefore to hard spectra. Table 11.7 shows the values of кж obtained in the three cases considered as well as that obtained for a PWR-type neutron spectrum and, for comparison, that obtained for industrial metallic plutonium (238Pu(2.5%), 239Pu(60.8%), 240Pu(24.9%), 241Pu(11.7%)). It is seen, as expected from the values of D shown in table 3.10, that thermal spectra are at a strong disadvantage for the incineration of minor actinides. The

low value of кж for the Superphenix spectrum is due to the presence of a large low energy component of the neutron spectrum, which tends to significantly increase the values of the capture cross-sections.

The case considered here is that of deep disposal in a clay layer through which a well is drilled. To have a starting point, let us assume that the flow through the well is 10 m3 per day and thus that a = 4 x 10~4. Let us note that here, too, the scenario is extravagant, as it consists of looking for water where there is none. The point of this approach is to define a safety frame for the project.

Storage is conceived as modular; each module includes a number of cavities (or cells) inside which a limited number of packages are placed. By design also, all pieces of work are meant to be independent of each other, in particular hydraulically. This is obtained by module spacing. Pumping through a drilling done either directly through a handling gallery serving several cells, or through the geologic medium very close to a cell, would allow hydraulic solicitation of the neighbouring zone, i. e. a fraction of the storage. The worst case corresponds to drilling through the handling gallery, impacting a module equivalent to 2000 metric tons of IF. The computation has been done taking the man-made barrier into consideration, this time the purpose being to evaluate its efficiency. The radionuclides are assumed to be transferred through the clay stopper placed at each cell opening. We give a simplified procedure for two particularly interesting cases and the result of the full computation for a set of radioelements.

In the context of fission reactors, the properties of nuclei heavier than thorium are of paramount importance. In particular a distinction is made between fissile and fertile nuclei. This distinction is based on the response of these nuclei to the absorption of a slow neutron: while fissile nuclei have a high probability of fissioning after such absorption, as shown in figure 3.1, fertile nuclei do not, although they have significant fission cross-sections for neutrons with energy in the MeV range, as shown in figure 3.2.

Neutron capture by fertile nuclei eventually leads to the production of a fissile species, usually following beta decay. The best known examples of fissile nuclei are U, U and Pu. Typical fissile nucleus production processes following neutron capture by fertile species are:

Figure 3.3 shows that the capture cross-sections, above the resonance region, decrease sharply with energy.

As a rule, heavy nuclei with an even number of neutrons are fertile while those with an odd number of neutrons are fissile. This is the result of the even/odd effect on neutron binding energies as well as of the

fact that fission barrier heights lie between odd and even neutron binding energies.

Aside from fission and capture cross-sections, the values of q are very important in order to assess the potentialities of the nuclei to sustain a chain reaction. Variations of q with neutron energy are shown for some nuclei in figure 3.4. The figure shows that 233U has a particularly high value of q at low neutron energies, while, at high energies, 239Pu takes the lead. Indeed, only 233U has allowed breeding in a thermal neutron reactor, the Molten Salt Reactor Experiment at ORNL [49]. Here the breeding rate was barely 5% per year and was only obtained with an online extraction of the neutron capturing 233Pa. Breeding is obtained much more readily with fast neutron reactors using 239Pu as fuel, a rate of 18% per year having been reached with Superphenix.

In order to stress the main trends of the evolution of the nuclear fuel we consider a model where only three types of nucleus are present:

1. the fertile nuclei (cap);

2. the fissile nuclei (fis);

3. the fission products (fp).

The fuel is replenished in fertile nuclei at a rate S(t). Absorption cross­sections are denoted o(a), and fission cross-section o(f). The evolution of the nuclei is given by the system

where nfp is the number of fission products’ pairs.

In order to discuss the dominant features of the fuel evolution we shall make the simplifying assumption that the number of fertile nuclei is kept constant. This assumption is approximately valid as long as the characteristic
evolution time of the fissile part is much shorter than that of the fertile part, i. e. f » 4^.[23] Then

dncap Q

dt

and the number of fissile nuclei obtained is^

‘cap4lp[1 — exp( —4fisV)] + nfis(0)44 exp( —4fe’t)}.

(3.133)

The term ncap ^ cap [1 — exp(-fVt)] expresses the rise of nf. s(t) due to the conversion of fertile nuclei into fissile ones. The term nfis (0)4^ exp(—f!’t) corresponds to the disappearance, by fission, of the fissile nuclei present at the initial time. It appears that nfis(t) tends towards an equilibrium value nfis4u) = ncap4ap/f at large times. If nfis(Q) < 4^ the number of fissile nuclei will increase with time, so that the reactor is of the breeder type. Inversely, if nfis (Q) > 4fsqu) the reactor will be an incinerator. It is important to note that a hybrid reactor can always be a breeder, in contrast to critical reactors.

The evolution of the number of fission products is given by

(a

. (a) cap

tncap4cap’ T ncap Ta"

4&

+ nfis(Q)[1 — exp( —4fisV)]. (3.134)

Here the first term corresponds to the linear consumption of fertile nuclei, the second term to the building up of the fissile nuclei from the fertile ones, and the last term to the disappearance of the initial load of fissile nuclei. For large times, the first term dominates.

Knowing the evolution of the concentrations one gets the evolution of the multiplication factor*

where P(t) is the number of neutrons lost in structural materials, control rods or escaping the reactor. In critical reactors the condition k = 1 is kept via modulation of P(t). For hybrid reactors the value of k is allowed to evolve within prescribed limits around a nominal value provided it remains sufficiently smaller than unity. This may be obtained by periodical regeneration of the fuel as well as by defining working conditions between two regeneration events that minimize the variations of kM. These conditions are implemented differently in systems using liquid fuels and in those using solid fuels.

We have already mentioned that cells may have different importances (see section 5.4.1). These importances are defined with the IMP card. The aim of increasing cell importance is to increase the number of histories, i. e. to reduce the statistical error. Going from one cell with importance 1 to a cell with importance 2 will multiply tracks (i. e. the number of neutrons) by 2, halving the weight of each track. Conversely, going from a cell of importance 2 to a cell of importance 1 will halve the number of tracks, doubling the weight of each particle. A zero importance cell means that no transport is done. By default, cell importances are zero. Thus, before doing a calculation, you have to specify the importance of each cell. One way is to do it along with the cell definition; in the previous example, the cell part is just:

c

c Cell cards c

10-1 imp:n=1 $ the inner sphere

20-23-41 imp:n=1 $ the cylinder without the sphere 3 0 #2 #1 imp:n=0 $ exterior

In cells 1 and 2, neutron importance (‘:n’) is 1 whereas the exterior (cell 3) where neutrons are not followed has a null importance.

Material

Now, we know how to define empty geometries. Materials that fill the cells are entered in the Data cards. A material is defined with an ‘M’ followed by a number (without blank), a cross-section reference and a proportion. Let us see an example on our simple geometry test:

First simple geometry c

c Cell cards c

1 1 -18.75 -1 $ the inner sphere

2 2 -1.0 -2 3 -4 1 $ the cylinder without the sphere

3 0 #2 #1 $ exterior

c

c Surface cards c

1 SO 5 $ centred sphere with R=5 cm

2 CZ 20 $ infinite cylinder with R=20 cm

3 PZ -20 $ bottom plane intersecting the cylinder.

4 PZ 20 $ top plane intersecting the cylinder.

c Materials

M1 92235.60c 1 $ 235U

M2 1001.60c 2 8016.60c 1 $ H2O

We have placed in cell 1 (the sphere) material 1 of density 18.75 g/cm3 (the ‘-’ sign means that it is a mass density in g/cm3). Material 1 is pure 235U (note that the cross-section code is ZZAAA. id for a nucleus of atomic number ZZ and mass number AAA; id refers to the version of cross-section used and the type (continuous or discrete). The complete list of cross-section codes is found in appendix G of the MCNP reference manual). The cylinder is filled with water (density 1 g/cm3); the water is composed of two nuclei of hydrogen (code 1001.60c) and one of oxygen (8016.60c).

If you try to view the geometry as previously explained, you will see that non-empty cells are now in colour.

In association with the Material data cards, it is possible to use so-called MT cards for some materials (moderators) in order to specify that an S(a, 0) treatment must be supplied for low-energy neutrons (En < 4 eV). This treat­ment replaces the free-gas treatment below 4 eV (the most significant effects are below 2eV). For example for material 2 (water) in the previous example one can write:

M2 1001.60c 2 8016.60c 1 $ H2O

MT2 LWTR.07

This treatment does not exist for all materials.

From the above discussion it appears that most simulation codes account reasonably well for neutron multiplicities. However, the traditional approach which associates the Bertini INC and the Dresner evaporation for the high — energy part of the cascade, and the MCNP or MORSE codes for neutrons below 20MeV, has serious failures, especially for the prediction of the neutron energy spectra and the residual nucleus mass and charge distribu­tions. Significant improvements are obtained when either the ISABEL or the Cugnon codes are used, especially in combination with the relatively new GSI evaporation code. The extension of the MCNP type calculations up to 150 MeV, which is being carried out at Los Alamos and Bruyeres le Chatel, is also a very significant improvement. In this respect a large amount of work, both experimental and calculational, has to be done for

the completion of the evaluated data files for neutrons and protons between 20 and 150 MeV.

It is well known that uranium hexafluoride is used in its gaseous state in isotopic separation plants. This property can be used in the vaporization separation of fluorides. The melting and boiling temperatures of stable actinide fluorides are given in table 9.2.

It is seen that UF6, NpF6 and PuF6 are stable and gaseous at low temperature. They can be produced by fluorination of the tetrafluorides. Gas (helium) purging can then allow their extraction from the molten salt mixture. However, PuF6 is thermodynamically unstable and dissociates readily to PuF4 + F2 at the high temperature of the molten salts. In practice, the extraction by fluorination of UF6 has been demonstrated and that of NpF6 is thought to be possible. The selective extraction of UF6 from other heavy-metal fluorides (Np, Pu, Zr) uses the fact that these form a stable complex with NaF at 400 °C while UF6 does not. Inversely, the separation of UF6 from lighter fluorides uses adsorption of UF6 on NaF at 100 °C. Finally, UF6 is desorbed from NaF at 400 °C.

In the event of a massive use of nuclear power it is clear that any production system should be fuel breeding. Hybrid systems have very good characteris­tics in this respect. They would allow switching from a plutonium economy to a much less polluting thorium one. They could, in principle, allow the implementation of intrinsically safe reactors. They are also an attractive option for nuclear waste incineration, including minor actinides which would be difficult fuels for critical reactors. In their molten salt version they could allow fast plutonium incineration.

Numerous issues have to be studied: reliability, safety, cost effectiveness, etc. High-intensity accelerators have to be built. A first demonstration proto­type of several tens of MW could be built within 5 to 7 years.[60] An industrial realization would, probably, require at least 20 years.

Hybrid systems require non-conventional technologies for the neutron multiplying assembly: molten salts, molten lead, natural convection, Th-U cycle. In principle such technologies could be used with critical reactors. The neutron surplus obtained from spallation is relatively small, especially for fast systems. The main asset of hybrid systems is their subcriticality which would allow building of reactors with deterministic safety and the use of fuels with unfavourable safety characteristics when used in critical reactors. They give a unique opportunity to improve the social acceptability of fission energy. In particular, given the well known problems of the sodium cooled fast reactors, they are a credible alternative if breeding conditions are to be reached, a must for any large extension of nuclear energy production.

Critical nuclear reactor safety is intimately related to the existence of a ‘safety culture’ in the host country. Indeed, a poorly maintained critical reactor may become dangerous while still remaining operational. Even poorly trained staff may keep such a reactor working in dangerous

conditions. In contrast, an ill maintained accelerator will have its beam inten­sity decrease and eventually vanish. It is clear that any deterioration of the technical skills of the operating staff would rapidly lead to a stopping of the hybrid system. Such feedback might be very useful when one considers the danger of ill maintained and/or ill staffed reactors in some countries of the former USSR.

Will hybrid systems be mostly used for breeding and transmutation or will they have a significant role in energy production? Whatever the answers to these questions, it remains that hybrid system proponents have renewed thinking on the future of energy production by nuclear fission.

In the discussion in chapter 6 it was shown that a minimum energy of the charged incident particles of several hundred MeV/nucleon was required to obtain sufficient neutron production. Such energies cannot be reached with static electric fields. They require high-frequency (HF) acceleration. HF accelerators make use of various arrangements of high-frequency cavities, acceleration gaps and magnetic devices. In traditional linear accelerators,[65] particles cross accelerating cavities and magnetic elements only once during their acceleration. In contrast, in circular accelerators particles cross accelerating cavities and magnetic elements many times. For non-relativistic particles orbiting in a fixed magnetic field, synchronism can be maintained between the particle frequency and the HF frequency, so that particles are almost continuously accelerated. This is the principle of the cyclotron. When the particles become relativistic, keeping the synchronism between particles and HF frequency requires a time- varying magnetic field or radio frequency. This is the case for synchrocyclotrons and synchrotrons. The need for time-varying magnetic fields or radio frequencies implies that particles are bunched in time, preventing quasi-continuous accelera­tion. Using bunched beams implies that the maximum particle intensity greatly exceeds the average intensity. We shall see that intensity limitations come mainly from the particle maximum density which is proportional to the maximum intensity rather than to the average intensity. This is why accelerators presently considered for high intensities are of the continuous type, i. e. linear accelerators and cyclotrons, on which we concentrate henceforth.^

The WEC and IIASA [29] have considered different scenarios for energy production up to 2100. It seems useful to discuss them as examples of possible energy futures. These scenarios belong to three main types depending upon the Gross Domestic Product per capita reached in different geographical aggregates. Table 2.7 shows the parameters chosen by WEC for these scenarios in 2050.

Scenario A corresponds to a fast growth of the GDP per capita in all regions. It assumes a significant reduction of inequality between them. The growth is especially fast in former Soviet Union countries. Scenario C has a rather slow average GDP per capita growth but is, clearly, of the egalitarian type.

Table 2.8 shows the regional energy intensities typical of the three scenarios. For scenarios A and B the energy intensities decrease as a

consequence of the increase in the GDP per capita, as currently observed, and shown in figure 2.5. In particular the lower GDP per capita in former Soviet countries retained in scenario B leads to higher energy intensities for these countries. Scenario C assumes a voluntary decrease of energy intensities, especially in the most developed countries.

Table 2.9 shows the contribution of electricity to the primary energy consumed. This table shows the same features as table 2.8: in scenarios A

and B the share of electricity increases gradually with the GDP per capita. Scenario C assumes a deliberately increased share of electricity. Note that in table 2.9 we refer to subscenarios labelled A2 and C2. Indeed, the WEC and IIASA subdivide their scenarios A and C into three and two sub­scenarios respectively. The main differences between the subscenarios are the energy mixes producing the primary energy. In subscenarios A1, A2 and A3 the relative shares of coal, oil and gas are different. In subscenarios C1 and C2 the relative shares of renewable and nuclear energies are different. These features are displayed in Table 2.10. Note, also, the relative impor­tance of gas in the energy mix of subscenario C1.

From table 2.10 it is seen that only scenarios C might lead to CO2 stabilization within this century. These scenarios require very strong limita­tions on energy consumptions which might be very difficult to implement. Scenario C assumes a voluntary decrease of energy intensities, especially in the most developed countries.

Table 2.11 compares the expected fuel consumptions cumulated from 1990 to 2050 to the reserves estimated in 1990. It is not clear from the

table that scenarios A and B are compatible with oil and gas reserves. Even scenarios C might come close to exhausting these reserves.