Stochastic Fluctuation in a Uranium-Enriching Cascade Using the Centrifuge Process

The parameters of a uranium-enriching cascade, i.e., the cut and the separation factor, are considered to be fluctuating stochastically. The covariance matrices of the total uranium flow and ²³⁵UF₆ flow were derived by the classical stochastic theory for evaluating the effect of stochastic fluctuations of these parameters to steady-state plant performance. Also the stationary random process theory is applied to the kinetic equations of the cascade, and the autocorrelation function of the ²³⁵UF₆ flow and enrichment is derived for evaluating the time behavior of the plant performance caused by random fluctuation of these system parameters. Numerical values illustrate the response of product flow and enrichment to the fluctuations, which are both time independent and dependent, of the cut and the separation gain of stages and centrifuges. These data lead to a conclusion concerning the tolerances of centrifuge parameters and stage controllers.