Prompt neutron behaviour and the point reactor model in small critical and sub-critical fast assemblies

Abstract

According to a point reactor model of nuclear kinetics the prompt neutron density in a sub-critical fissile assembly decays exponentially with a time constant, usually termed α, which is linearly related to the reactivity by a constant prompt neutron generation time. This linear relationship between α and reactivity extrapolates to prompt critical at α = 0. Departures from this model have been reported by several observers. In assemblies driven by a pulsed neutron source, even when initial transients have been allowed to die away the prompt decay is not always found to be exponential and extrapolation of the relationship between assigned decay constants and reactivity does not always yield prompt critical at α = 0. Precise measurements of prompt decay for some VERA assemblies demonstrate the limited range of validity of the point reactor model. The measurements are compared with SWANTIME calculations. This time-dependent code is a multi-group multi-region diffusion theory version of the prompt kinetic equations. Though this treatment is not designed to analyse the decay in simple terms such as a sum of exponential decays, it does show that a softening of the spectrum occurs as the population decays. For this softer spectrum the decay exponent is smaller than for the corresponding steady state calculation and is no longer proportional to reactivity and so cannot be used directly as a measure of the reactivity of a subcritical reactor. Reactivities based on the ratio of prompt to delayed contributions to the measured decay agree with those based on conventional period measurements used to calibrate control rods; if a linear relationship is assumed between alpha and reactivity, errors in estimating subcritical reactivities can be as large as 20 per cent. To some extent this also provides a check that the delayed neutron data, in terms of relative abundances and decay constants are adequate for both 235U and 239Pu.