Neutrons probability distribution of the coupled reactors kinetics system via Magnus expansion

Abstract

The precise modeling of nuclear reactor physics is an essential topic of research that advances improve strategies, methods, and models. Reflected reactors constitute a standout amongst the most significant points of nuclear reactors. So, a precise mathematical model should be advanced to foretell the behavior of neutron flux of reflected systems, which involve the core and the reflector regions. The focus of this article is to develop a specific mathematical technique based on Magnus expansion to pave the way for approximate exponential exemplification of the solution of the reactor kinetic systems. In this model, the first, second, and third approximations of Magnus expansion are used to predict the first moment of the core, reflector neutrons, and precursors of group I for the reflected systems. For the two-point kinetic systems, the problem is expressed in terms of the probability distribution and generating function which satisfy a system of partial differential equations involved in this paper. The derivation of the innovative method MEM (Magnus Expansion Method) is exhibited to solve the coupled differential equations for the two-point kinetics equations, which include multi-groups of delayed neutrons, and to compare the conventional methods for reflected reactors. The validity of the system is tested according to the different types of reactivity (step, ramp, and sinusoidal reactivity).