Neutron transport problems with nonlinear temperature feedback

We investigate k-eigenvalue neutron transport problems with the effect of nonlinear temperature feedback based on a homogenous model problem. Cross sections are assumed to be linearly dependent on temperature, which is calculated by a heat transfer equation considering both convection and conduction. The effect of thermal expansion on cross sections is considered. The coupled system is solved using the standard method of power (or source) iteration. The spectral radius of the linearized system is obtained using Fourier analysis, and stability conditions in terms of physical parameters are given. Numerical results based on typical physical parameters for PWRs and fast reactors are presented to verify the theoretical result. The main novelty of the work is that the theoretical result is an explicit function of physical parameters such as the temperature coefficients of cross sections, the effects of heat convection and conduction, and thermal expansion. Although the result is obtained based on the oversimplified problems, it can offer insights into how the physical parameters would affect the convergence and stability of the coupled multiphysics system, and it can also be useful for code validation