EXTENSION OF XENON OSCILLATIONS SAFETY MARGINS USING WEAKLY NONLINEAR STABILITY ANALYSIS

¹ Physics Department, Ben-Gurion University of the Negev, P.O. Box 653, 84105 Beer-Sheva, Israel
² Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990, Israel
³ Nuclear Research Centre – Negev, P.O. Box 9001, 84190 Beer-Sheva, Israel
⁴ Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI 48109, USA

nirkastin@gmail.com
ehud@bgu.ac.il
assafkolin@gmail.com
kinast@nrcn.gov.il

Published online: 22 February 2021

Abstract

Weakly nonlinear stability analysis is applied to study xenon oscillations in nuclear reactors using the approach of multiple time-scales method. This approach allows to characterize the dynamics of the system beyond the Hopf instability point. It provides important insight on the characteristics of the oscillations, namely if they diverge with time, or converge into a bounded limit cycle. Detailed derivation of the amplitude equation is presented. This equation is used to identify parameter ranges of bounded periodic oscillations, which may be allowed for safe operation. The influence of neutron generation time and the power feedback coefficients on the amplitude of limit cycles, as well as on convergence times, is discussed. The described method may be used to extend the safety margins required to prevent xenon unstable oscillations in reactor cores.