A Semianalytical Analysis of Transient Supercritical Assembly Extinction Probabilities

Stochastic point kinetics neglecting delayed neutrons has been subject to rigorous analysis in the years since its introduction. Many approximate solutions appearing within this context are based upon the “quadratic approximation,” where fission multiplicity is truncated at two. In this technical note we review the quadratic approximation within the context of a stochastic, space-independent, one-energy-group model neglecting delayed neutrons and its generalization to higher-order approximations in transient and stationary systems. This generalization results in the probability of a zero neutron population for a source-free system being governed by transcendental and polynomial algebraic equations in the transient and infinite time limit cases, respectively. For ²³⁹Pu, we solve the transcendental equation over a wider range of prompt multiplication factors and times than has been previously accomplished. We also reproduce and generalize associated solutions of the polynomial algebraic equation. In both cases, solutions are computed for successive generalizations of the quadratic approximation to higher-order maximum fission multiplicity.