A TIME-DEPENDENT COLLISION PROBABILITY METHOD FOR ONE-DIMENSIONAL SPACE-TIME NUCLEAR-REACTOR KINETICS

A time-dependent collision probability method has been developed for t he solution of neutron transport and nuclear reactor kinetics problems in one-dimensional slab geometry. The time-dependent collision probab ilities permit the solution of time-dependent neutron transport proble ms involving general source distributions over an indefinite time peri od and an infinite number of collision generations. The method is base d on the analytic integration of the time-dependent integral transport kernel involving purely real cross sections. The neutron time-of-flig ht and causality considerations lead to a number of complex formulas i nvolving exponential and exponential integral functions. Occasional co nflicts between the regular grid in time and space and the causality c onsiderations lead to some formulas that are inexact, it is shown that these inexact formulas are terms of the third order in the time-step length, and thus the method has overall second-order accuracy in time. The method has been used to solve two types of neutron transport prob lems. The first, a pulsed, planar fixed-source problem, yielded a flux solution with a root-mean-square relative difference of 0.94% from a benchmark analytic solution. The second problem solved was a pair of m ultigroup nuclear reactor kinetics problems. While the kinetics result s were not conclusive, they suggest that diffusion theory may yield re sults that underestimate the amplitude and deposited energy of certain reactor transients.