Exact statistical analysis of nonlinear dynamic power reactor models by the Fokker--Planck method. Part II. Reactor with on-off control

Journal Article · Thu Mar 01 04:00:00 EST 1979 · Nucl. Sci. Eng.; (United States)

OSTI ID:6400896

Debosscher, A F; Dutre, W L

The paper deals with the exact stochastic analysis of the low-frequency neutron density fluctuations in an on-off controlled nuclear power reactor without delayed neutrons and perturbed by Gaussian white reactivity noise. The stochastic process, being Markovian, is completely characterized by its first-order probability density function (pdf) and the transition pdf. The first-order pdf is the normalized solution to the time-independent Fokker--Planck equation (FPE). Using this pdf, a general expression for the moments is obtained. The conditions for stochastic stability in probability, in the mean, and in the mean-square are derived. The time-dependent FPE is solved using the Laplace transform technique, which results in four distinct expressions for the transition pdf, according to the relative magnitude of initial and final reactor power with respect to the regulator level. After Laplace inversion, a physical interpretation of the controller's effect on the stochastic process becomes possible. Finally, making use of the obtained pdf's, the spectral density of the reactor power fluctuations is calculated.

• Research Organization: Katholieke Univ., Leuven, Belgium
• OSTI ID: 6400896
• Journal Information: Nucl. Sci. Eng.; (United States), Journal Name: Nucl. Sci. Eng.; (United States) Vol. 69:3; ISSN NSENA
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
220100* -- Nuclear Reactor Technology-- Theory & Calculation
CALCULATION METHODS
EQUATIONS
KINETICS
MATHEMATICAL MODELS
MATHEMATICS
NONLINEAR PROBLEMS
POWER DISTRIBUTION
POWER REACTORS
REACTOR KINETICS
REACTOR KINETICS EQUATIONS
REACTOR NOISE
REACTORS
STATISTICS
STOCHASTIC PROCESSES