The simplest space-dependent neutron kinetics model uses the mono­energetic diffusion equation

where D is the diffusion coefficient, ф the neutron flux, the macroscopic absorption cross section, Ly the macroscopic fission cross section, v the number of neutrons produced per fission, and v the average neutron velocity. Energy dependence of the neutron flux and the detection process can be handled using multiple energy groups.

In this book, we are not concerned with methods for calculating space — dependent frequency response functions. Rather, we are interested in the possible influence of spatial effects on experimental results.

Space-dependent effects are important in two significantly different cases. The first is a high-frequency effect that occurs because it takes a finite time for the flux to change from one steady-state distribution to another following a localized perturbation. This type of spatial effect is important only above 10 rad/sec. This is above the frequency range where feedback effects are important and where questions about the suitability of the system for normal operation are encountered.

The other spatial effect is a very-low-frequency phenomenon due to xenon-135. In this case, the flux is always essentially in a steady-state distribu­tion for a given core composition. The spatial effect occurs because the core composition changes with time because of changing xenon-135 concentration. The space dependence can occur because of the effect of the very large thermal absorption cross section of xenon-135 and because the xenon-135 is coupled to the neutron flux mainly through iodine-135. Iodine-135 is produced as a fission product, and it decays to xenon-135 with a 6.7-hr half-life.