EXACT STATISTICAL-ANALYSIS OF NONLINEAR DYNAMIC NUCLEAR-POWER REACTOR MODELS BY FOKKER-PLANCK METHOD .1. REACTOR WITH DIRECT POWER FEEDBACK

An exact and complete statistical analysis is presented of the neutron density fluctuations resulting from Gaussian white reactivity noise in a point reactor model with proportional power feedback, but without delayed neutrons. The analysis includes the multiplicative effect of neutron density and reactivity variations. An exact solution of the time-independent Fokker-Planck equation is found, resulting in a gamma density function for the stationary first-order probability density of the power fluctuations. The time-dependent Fokker-Planck equation is solved for the Laplace transformed function, which can be written in terms of confluent hypergeometric functions. The subsequent inversion yields the transition probability density function. The most common first- and second-order statistical characteristics, such as moments, auto-covariance function, and power spectral density, are calculated and compared to the results of a linearized analysis.