Let us first introduce a definition of transmutation rates of individual MA nuclides fueled in a reactor core. The calculation method of the transmutation rate relative to the nuclides is as follows. First, conventional burn-up calculations are carried out and burn-up-dependent flux in each region is calculated, which is used in the second step calculation. In the second step, we consider only the relevant MA in each region and perform burn-up calculations using the flux obtained in the first step.

In this second step of calculation, nuclide k is produced from the original nuclide

l. There are many passes of reactions of transmutation of the initial nuclide (shown by N) and the production of N as is shown in Fig. 17.6. We can calculate the production rate of nuclide k at time T from the initial nuclide l as

Pik = N (T)/Ni (0) (17.1)

where Ni(0) is number density of nuclide l at time 0 and Nk (T) is number density of nuclide k at time T, assuming nuclide l is present alone at t = 0. Using Nk(T), the overall fission (see Fig. 17.6) relative to the initial nuclide l is calculated as

(17.2)

where of(t) is fission cross section of nuclide k at time t, ф(ґ) is neutron flux at time t, and £ is summation over all nuclides k resulting from initial nuclide l; this

includes all the fissions from the initial nuclide l. Furthermore, the production of other MA nuclides except the initial nuclide l can be calculated by

oma1 = NN l (0)

к e MA, k=l

The Pu and U production from nuclide і is given by

PUl = Ni (0) Рік (17.4)

к e U, Pu

The production of MA nuclide l from Pu and U is given by

PUMl = NN к (0)Pki (17.5)

к e U, Pu

The production of MA nuclide l from other MA is given by

MAMl = NN к (0)Pki (17.6)

к e MA, k=l

Using Eqs. (17.2), (17.3), (17.4), (17.5), and (17.6), the net transmutation of nuclide l is calculated by

TR1 = OF1 + OMA1 + PU1 — PUM1 — MAM1 (17.7)

In Fig. 17.6, the individual parameters OMA1, PU1, PUM1, MAM1, and OF1 are shown. PUM1 and MAM1 denote the productions of the relevant MA nuclide from fuel (Pu, U) and other MA nuclides, respectively. Thus, there are minus signs in these parameters in Eq. (17.7), whereas other parameters show the elimination of the relevant MA nuclide, so the signs are positive.

When we consider the total MA transmutation for all MA nuclides, the second and the fifth terms cancel each other, so the whole transmutation is given by

TR = TR1 = ^ (OF1 + PU1 — PUM1) (17.8)

1 e MA 1 e MA

Therefore, we can define the MA transmutation of MA nuclide 1 by

TR1 = OF1 + PU1 — PUM1 (17.9)

Thus, the transmutation rate is composed of two terms: the first is the amount of incineration rate by fission and the second is the net transmutation rate to fuel (U and Pu). The first fission rates of individual nuclides contain the direct fission of the relevant nuclide plus the fission of other nuclides transmuted by decays or neutron reactions as “overall fission” [OF1 in Eq. (17.9)] (Fig. 17.7). It was found that the indirect fission contribution by Pu and 9Pu is remarkably large for

nuclides 239Np and 241Am. The net production rates of U and Pu are calculated from the difference between the production rates of U and Pu from the relevant MA nuclide and the MA production from the initial U and Pu. Figure 17.7 shows the overall fission rate of 237Np in a thermal advanced pressurized water reactor (APWR) and two fast reactors, a MOX-fueled sodium-cooled fast reactor and a metal-fueled lead-cooled fast reactor [8]. In the thermal reactor, the overall fission rate is about 5 % in one cycle and is very small compared with the fast reactors. In fast reactors, the direct fission of Np is rather large, and the Pu fission contribution is also large. The 239Pu fission contribution is small for fast reactors.

We are developing a calculation code system based on the foregoing method and are planning to apply the system to MA transmutation core design. In the core design we consider a homogeneous MA loading core, and a heterogeneous MA loading core, in which MA is loaded in special assemblies with moderators.