Because of structural constraints, the flux in critical reactors cannot be too arbitrarily high.

We first discuss the maximum neutron flux which could be achieved in either a fast or a thermal reactor. This is an important quantity since the lifetime of a nucleus in a neutron flux is ‘o-a, independent of the nucleus concentration. The maximum heat density which can be extracted provides the maximum value of the product Xf’. At present, values of 500 W/cm3 are design values for liquid metal cooled reactors. This leads to a value of £f’ = 500/ef = 1.5 x 1013 fissions/cm3/s. Very high values of the flux can be obtained if Xf is very small. However, Xf cannot be arbitrarily small since the reactor has to be critical, thus kx = ^{Xf/[Xf(1 + a) + Sc]} > 1 where Xc is the macroscopic capture cross-section of components other than the fissile part. Thus one should have Xf/Xc > 1/(v — 1 — a)~ 1. As an example of a thermal system, we consider pipes containing a molten salt immersed in a heavy water tank. The lower limit of Xc is given by that of heavy water, Xc = 0.000 044. With a fission cross-section of 500 barns this corresponds to a fissile nucleus density of 0.8 x 1017/cm3. The maximum maximorum of the neutron flux in a thermal reactor is thus 3.4 x 1017. Of course, due to the components of the salt and of the pipes, such a value will probably never be reached. However, fluxes ten times smaller have been considered, for example, by Bowman [2]. For such high flux the lifetime of fissile nuclei would be extremely short: 5 hours for a 1017 n/cm2/s flux. The inventory in fissile material of the reactor would also be extremely small: for a density of fissile nuclei of 3.0 x 1017/cm3, corresponding to a flux of 1017 n/cm2/s, the total fissile mass necessary to produce 3 GW would be only 700 g! The total volume of the reactor would be 6 m3.

For fast reactors we consider a fissile species diluted in molten lead with Xc = 3 x 10 4 cm—1 and thus a maximum maximorum flux of 5.0 x 1016 n/cm2/s. For such a flux the lifetime of the fissile species would be around 3 hours. The minimum inventory for a 3 GW reactor would be 350 kg. This shows that thermal reactors have a higher potential for small inventories and fast burn-up. Of course the actual implementation of these potentialities could be very difficult. In fact, the more or less fissile nature of the fuel for thermal neutrons has a deep influence on the incineration rate achievable. This can be seen in the following more quantitative, although schematic, analysis.

We consider a homogeneous infinite reactor with only two components:

1. the fuel, characterized by its atomic density nfuel, absorption cross-section ^, and its neutron multiplication coefficient kfuel > 1, and

2. the coolant, characterized by its atomic density ncool, and its absorption

cool)

cross-section aa.

The aggregate reactor is characterized by its atomic density nreac = nfuel + ncool, its absorption cross-section

nfuel (fuel) . ncool (cool)

—- aa 4——— aa 7

nreac nreac

and an effective multiplication coefficient

We define the atomic fraction of the fuel x = n^l/n^c. The criticality condition kreac = 1 allows us to write x as

Aside from the criticality condition it seems reasonable to assume that the fission density is limited to a specific value w. Thus

with

(fuel) a(fuel)

a — af

(fuel)

In the case of fissile mixtures (kfuel > 1), it appears that the main difference between fast and thermal reactors lies in the ratio aafuel)/aacool). There is a clear advantage to using coolants with small absorption cross-sections. As examples, for heavy water ncoolaicool) = 4 x 10-5 for thermal reactors, and ncoolaicool) = 3 x 10-4 for lead and fast spectra. Fuel absorption cross­sections for thermal neutrons exceed 500 barns while they lie around 2 barns only for fast neutrons. It follows that, for fissile mixtures, incineration rates with thermal neutrons could, in principle, be three orders of magnitude larger than those with fast neutrons.

The situation is different for non-fissile (minor actinides, for example) mixtures. In this case the major difference between incineration of thermal

and fast neutrons is that of the corresponding fuel multiplication factors. The subcritical nature of the MA fuel with thermal neutrons implies the use of an ADSR to perform the incineration. Dilution of the fuel would thus be counterproductive, since it would decrease the reactor multiplication coefficient kreac below kfuel, and thus require higher accelerator current to keep the neutron flux constant. The incineration rate reduces to the first term of the right-hand side of equation (3.99), i. e.

w

Ainc =—— (3.100)

nreac

which means that it depends, essentially, on the fission density. Indeed, because of the condensed nature of the components of all practical reactor designs, it is not possible to play very much on the value of nreac. For example, for water, the atomic density is 1023/cm3, while for lead it is 0.3 x 1023/cm3 and for uranium 0.6 x 1023/cm3.