The reactor kinetics equations derived in Section 1-3.2 are labeled “point” kinetics since the neutron density, n, was considered only as a function of time. Actually, n should be written as n(x, y,/,t) to emphasize its spatial dependence Similarly, the density of delayed-neutron emitters should be written C,(x, y,z, t), and each of the fission-product concentrations should be written as func­tions of x, y,z, t. The spatial dependence of the neutron flux depends on many’ factors, such as fuel loading, primary — coolant-sy’stem structure, and reactor-vessel penetrations It also depends on the past history of the individual fuel elements

Since the neutron flux in the fuel determines the heat generated, it follows that knowledge of the spatial distribu­tion of the flux is necessary if the reactor is to be used safely and efficiently as a heat source. Instrumentation systems must be included to provide this knowledge to the operator.

If the neutron flux is not constant throughout the reactor, then the kinetics of the chain reaction is not the same in all parts of the reactor The preceding section shows that many reactivity effects are flux-dependent For example, if a reactor is operating with the neutron flux less in one region of the reactor than in another region, then the equilibrium concentrations of the fission-product poisons in the two regions will not be the same, nor (if the reactor has run this way for any length of time) will the fuel burnup be the same in the two regions

Nonuniform spatial distribution of neutron flux can lead to self-induced oscillations of the flux level, the so-called xenon instability or flux tilt The oscillations result from the fact that regions with different neutron-flux levels have different equilibrium 13,Xe concentrations (Fq. 116) If the flux is increased in a region where it has been low, then the increased flux reduces the 13SXe concentration (since more is removed by neutron capture) and, thereby, the poisoning The reduction in 1 35Xe is not offset immediately by 135| decay since the 13SI concentra­tion has been set by the previous (lower) flux level The net result is that the flux tends to keep on increasing On the other hand, m regions where the flux has been high, a decrease in flux tends to increase the 135Xe (fewer art removed by neutron capture), again with no immediate compensation by decreased 135I The tendency of the increasing flux to keep on increasing and the decreasing flux to keep on decreasing is eventually reversed by the 13SI decay’—the peaking of the xenon poisoning shown m Fig 18 The net result is an oscillation in 1 35Xe poisoning between the regions of the reactor with a period given by

2 it

Period of xenon oscillation = 77717 (1 29)

[Xi(Ax + ахФ) l*

where A| = disintegration constant of 135 I (2 9 X 10 s/sec) Ax = disintegration constant of 1 3sXe (2 1 X 10 5/ sec)

ax — microscopic thermal-neutron cross section of 1 3 5 Xe

ф = thermal-neutron flux

If the flux is 5 X 1013 neutrons cm 2 see 1 , the period of the oscillation is 23 hr, somewhat longer than either the 1 3 51 half-life (6 7 hr) or the 1 3 5 Xe half-life (9 2 hr). As the flux is lowered, the period of the xenon oscillation

approaches 70 hr, at 1014 neutrons cm 2 sec 1 , it is about 17 hr.

The possibility of such flux oscillations must be taken into account in designing the reactoi control system ‘1 Im­possibility of high and low regions of heat generation can introduce potential hazards if there is a natural mechanism that makes the high higher and the low lowet Instrumenta­tion must be provided to sense the onset of an such oscillations.