Probability distribution for neutron density of two energy group point kinetics system

Abstract

The probability distribution of the number of neutrons and delayed neutron precursors in a multiplying assembly of various types of reactivities is developed for two energy groups. The space independent point reactor kinetics model for six precursors group of delayed neutrons is considered. The problem is formulated in terms of the probability distribution, generating function which satisfies a partial differential equation, derived in this paper. The probability distribution of two energy group delayed neutrons and the density of the precursors are obtained by solving this system of reactor kinetics model by adopting the mathematical methods. At the point, when the system is formulated in an operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the kinetics system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as time-dependent exponential perturbation theory. Every Magnus approximate corresponds in perturbation theory to a partial re-summation of infinite terms with the important additional property of preserving, in any order, certain symmetries of the exact solution. The first, second and third Magnus expansions are described and used to predict the first moment of fast, thermal and multi-group of delayed neutrons precursor for the two-energy point kinetics reactor system. The validity of the presented method is tested with the aid of the eigenvectors and eigenvalues of the kinetics system in the matrix form by comparing with the conventional methods.