Characteristics of Entry into the Xenon Oscillations Regime in a Reactor with Feedback on the Coolant Temperature

Abstract

The simplest approximations (one-dimensional reactor, single-group diffusion model of neutron transfer) are used to study the characteristics of xenon oscillations in a reactor with negative feedback on the coolant temperature. It is shown that in this case, in contrast to the situation where the predominant feedback is on the neutron fl ux density, the emergence into the xenon instability regime will manifest in the form of perturbations of the reactor power and energy release simultaneously. In addition, the deformations of the energy-release fi eld grow with increasing neutron fl ux and physical dimensions of the reactor.Theoretically, in the absence of external control the principal harmonic of the energy-release fi eld is least stable against xenon oscillations, while the higher-order harmonics are less subject to them [1]. An important circumstance is that this result was obtained for negative feedback on the neutron fl ux density. We shall consider a different situation where feedback is determined by the coolant temperature, which is a characteristic situation when, for example, high-enrichment uranium is used.We shall use a qualitative physical model similar to that in [1]. We shall study a planar reactor surrounded by an ideal refl ector; the neutron fl ux will be described in a single-group diffusion approximation, neglecting the delay in the emission of delayed neutrons and the lag in the manifestation of feedback. This model corresponds to the system of equations:where the generally accepted notation is used, and for brevity the arguments of the indicated functions are omitted. With the exception of k(z), we shall assume the parameters appearing in the equations to be constants. Let us consider a stationary state of the reactor with the neutron fl ux being independent of the spatial coordinate: Φ(z, t) = Φ 0 . In this case, the concentration of iodine and xenon also becomes constant I(z, t) = I 0 and X(z, t) = I 0 , which can