Exact statistical analysis of nonlinear dynamic nuclear-power reactor models by the Fokker--Planck method. I. Reactor with direct power feedback

Journal Article · Tue Mar 01 04:00:00 EST 1977 · Nucl. Sci. Eng.; (United States)

OSTI ID:7095605

Dutre, W L; Debosscher, A F

The paper presents an exact and complete statistical analysis 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, autocovariance function, and power spectral density, are calculated and compared to the results of a linearized analysis.

• Research Organization: Univ., Louvain, Belgium
• OSTI ID: 7095605
• Journal Information: Nucl. Sci. Eng.; (United States), Journal Name: Nucl. Sci. Eng.; (United States) Vol. 62:3; ISSN NSENA
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
220100* -- Nuclear Reactor Technology-- Theory & Calculation
FEEDBACK
KINETICS
NEUTRON FLUX
NONLINEAR PROBLEMS
POWER REACTORS
RADIATION FLUX
REACTOR KINETICS
REACTOR NOISE
REACTORS
STOCHASTIC PROCESSES