A Stochastic Analysis of Power Doubling Time for a Subcritical System

Abstract

The power doubling time for a subcritical system is identified as a stochastic first-passage time problem. Using stochastic point kinetics equations, relations for the mean doubling time and the standard deviation in doubling time are derived. It is shown that the power doubling time for a subcritical system is independent of whether the system is fast or thermal, weakly depends on source strength, and is approximately proportional to the inverse of the reactivity for small negative values of the reactivity.

Keywords:

• Doubling time
• Nuclear reactor theory
• Point kinetics equations
• Stochastic differential equation
• Subcritical system

Mathematics Subject Classification:

• 82D75
• 60H10
• 60H35