Page 257 - Dynamics and Control of Nuclear Reactors

258 APPENDIX C Basic reactor physics

where
V¼Total volume of core.
F¼Energy produced per fission (3.225 10 11 Watt s/fission).

If we assume that all the terms on the right-hand side of Eq. (C.3) are constant, except
neutron density, n, the reactor power is directly proportional to the neutron density or
the neutron flux.
P/n / ϕ (C.4)
This relationship is important because in the neutronics equations we can replace the
neutron density with actual reactor power within a multiplication factor.

C.4 Nuclear fission
The nuclei of U-235, U-233, Pu-239 and Pu-241 can undergo fission by low-energy
neutrons. Such materials are called fissile materials. Isotopes such as U-238 and
Th-232 can undergo fission with fast neutrons and are said to be fissionable (as
opposed to fissile) and are referred to as fertile materials. Note that U-238 and
Th-232 can be converted to Pu-239 and U-233, respectively, by absorption of neu-
trons and final decay into the respective fissile isotopes. The reactions are as follows
1
92 U 238 + 0 n ! 92 U 239 ! 93 Np 239 + 1 β 0
# (C.5)
93 Pu 239 + 1 β 0
The half-life for U-239 is 23 min and for Np-238 is 2.3 days
1
90 Th 232 + 0 n ! 90 Th 233 ! 91 Pa 233 + 1 β 0
# (C.6)
92 U 233 + 1 β 0
The half-life for Th-233 is 22 min and it decays to Protactinium (Pa-233). Pa-233 has
a half-life of 27 days and has a quite large neutron absorption cross section (around
7.5% as large as the U-233 fission cross section). Therefore, Pa-233 is a significant
neutron absorber and its presence diminishes potential U-233 production. The resi-
dence of Pa-233 in an operating reactor core results in a significant loss in U-233
production.
Numerous fission fragments are released during the fission reaction. These are
classified according to the percent of fission yield. Fission yield is the percentage
of a given isotope atoms in the total of all fission fragments. The reactions are as
follows:
235 1 236 A1 A2 1
92 U + n ! 92 U ∗ ! z1 F + z2 F + υ n + Energy
0
0
where υ¼number of neutrons produced in the fission reaction (2 or 3).