Nonlinear Stability and Limit Cycles in Xenon-Induced Reactor Oscillations

Pressurized water reactors (PWR) have become the mainstay of nuclear energy in the past decades. Considered both reliable and safe, they constitute the large majority of all Western nuclear power plants. It is known that large cores, in terms of neutron migration length, are subject to oscillatory and spatial instabilities when operated at high power levels. Such instabilities usually arise due to delayed negative feedbacks of fission products, mainly by the formation of iodine and xenon, which may yield spatial and temporal oscillations.

Such oscillatory and spatial instabilities in PWRs have been studied previously. While the control procedures of present-day PWRs are well established, they may not suit new generation core designs, which include larger core sizes and higher power levels. Such designs may be vulnerable to instabilities driven by higher spatial and temporal modes, for which current reactors are susceptible. It is hence important to study the behavior and characteristics of unstable oscillatory modes in PWRs, and to analyze their dependence on the physical parameters that govern the dynamics in power reactors.

In this paper we applied methods of stability analysis, both linear and nonlinear, in order to achieve better understanding of xenon-induced oscillations` mechanisms and thresholds. The dynamics are described by a spatio-temporal nonlinear model, which includes feedback processes of xenon absorption, as well as fuel and coolant temperature changes. It is shown through linear stability analysis that the homogeneous steady state solutions are unstable to Hopf bifurcation for various values of neutron flux. Moreover, under non-uniform perturbations, there exists a range of wavenumbers for which a reactor might be unstable through periodic oscillations. Finally, using the formalism of nonlinear stability analysis and multiple time scales method, an amplitude equation is derived, allowing the identification of asymptotic oscillatory bound behavior in unstable regions by the formation of limit cycles.

In current power reactors, xenon oscillations are typically avoided by either using advanced control systems or by limiting the reactor operation to stable regions in terms of the physical parameters such as the flux and power. However, since the nonlinear processes are not well understood, large safety margins are required. Using the amplitude equation derived throughout this work, one may identify regions of instability in which the dynamics is bounded by a finite-amplitude limit cycle. Such regions should not be excluded for safe reactor operation. Thus, this method may be used to broaden both the safety margins and the operational limits which are required for the suppression of xenon oscillations and safe reactor operation.