Stochastic Theory of Neutron Transport in Nuclear Reactor

Abstract

The work is an extended version of the report presented at the conference ICTT-26. In the Part I we derive the forward and backward time-dependent linear stochastic equations for probability density of the integer number of neutrons and delayed neutron precursors in distributed model of a nuclear reactor. In the Part II we derive the distributed criticality stochastic equations and obtain the analytical solutions for asymptotic neutron number probability density function for a reactor in a close-to-critical state.

Keywords:

• Time-dependent Markov process
• stochastic equations
• nuclear reactor
• fluctuations
• criticality equations
• reactivity