Neutron fission chain behavior for modern 235U multiplicity data

Abstract

The use of modern analog Monte Carlo software to perform space-time kinetics and probability of extinction (POE) calculations in support of nuclear design and safety studies can be hampered by appreciable execution times and code crashes attributable to lengthy finite and divergent prompt-neutron fission chains. To estimate chain behavior for modern 235U fission-multiplicity data and constant reactivity conditions, static point POE discrete-step stochastic models of unrestricted and restricted prompt-neutron fission chains are developed and solved analytically. These models are used in a simple expression which gives the estimated chain length LMAX required to calculate a POE to a prescribed accuracy. The analytical procedure entails solving a quintic polynomial, the roots of which are POE candidates. Methods including Galois theory are used to analyze the POE quintic. Analytical techniques are used to show that only a single POE exists for any state of criticality. Ingenious mathematics from the late 1800's, as updated in the early 1990's by King, are used to obtain the algebraic roots. The analytical models give valuable insights into fission chain behavior, and should be of use in providing chain control guidance for mainstream analog Monte Carlo code simulations of nuclear systems.