Approximate Solution and Application of the Survival Probability Diffusion Equation

Abstract

While stochastic neutron transport theories have been developed in rigorous detail, many applications have historically been investigated using the point-kinetics formulation. In this work we develop a space-dependent model using the diffusion approximation to the Pál-Bell probability generating function equation, resulting in a nonlinear analog of the conventional time-dependent neutron diffusion equation. We investigate a variety of approximate solutions for the time- and space-dependent survival probability in one-dimensional symmetric, one-speed, isotropic, delayed neutron precursor-free systems, and compare them to counterpart point-kinetics results. Following the theoretical developments, we apply the new results in the context of a criticality accident scenario, from which the importance of spatial effects is revealed.