Chapter 5 - Methods of solving neutron transport equation

Abstract

The most fundamental task in the nuclear reactor analysis is to compute the neutron flux as a function of space, direction, energy, and time. The governing equation for this behavior is the complex neutron transport equation. In most of the efficient nuclear reactor analysis, the solution from transport formalism is imperative, which necessitates accurate numerical solution. The neutron transport treatment and its solution are very complex. Because of this, most of the reactor designs are performed with the much simpler diffusion theory, where the angular dependence is integrated out. But solutions with the neutron transport theory are necessary when there is a large flux gradient, for example near absorbers or boundaries or when the neutron scattering is anisotropic. This chapter presents formalism of the neutron transport equation in the context of nuclear reactor, followed by several variants pertaining to integral and integro-differential forms of the neutron transport equation. This chapter briefly discusses the computation method to solve these forms on the neutral particle transport equation. In the end, the stochastic solution to the neutron transport equation based on the Monte Carlo's method is outlined. Due to the complexity involved, the solution to the neutron transport requires best of numerical schemes and vast computational resource and, thus, is an area of state-of-the-art research.