Numerical Solution to Critical Problem of Finite Cylindrical Reactors by Variational Method

Abstract

Making use of the variational method, an expression is derived for the upper and lower bounds of the largest eigenvalue of the one-velocity transport equation, in terms of the Rayleigh quotient. It is found that the error contained in the eigenvalue thus obtained increases or decreases in keeping with the error inherent in the trial function used for expressing the neutron flux distribution. The first approximation for the eigenvalue and the extrapolation distances of finite cylindrical reactors are determined by using the asymptotic flux shape as trial function. The second and third approximations for the eigenvalue are derived by supplementing the asymptotic function with additional orthogonal terms. It is proposed to combine the eigenvalue determined by the variational method with the second approximation of the flux obtained by applying the integral transport operator to the asymptotic flux. Evidence is presented to prove the convergence of an iterative procedure devised for successively applying the ...