Mathematical solutions of the one-dimensional neutron transport equation

Abstract

Considering the case of one speed, steady state, isotropic scattering in homogeneous media with plane symmetry, this thesis developes the solution of the one-dimensional neutron transport equation by three separate techniques The method of K. M. Case which makes use of the theory of generalized functions in forming a semi-classical eigenfunc- tion expansion with both a continuous spectrum and a finite discrete spectrum is developed. Converting the neutron transport equation to an integral equation and then to a singular integral equation, a solution is found in a method due to T. W. Mullikin which has very useful convergence properties. Applying the method due to N. Weiner and E. Hopf to the integral equation form of the neutron transport equation, a solution is developed which depends heavily on complex variable theory. The similarities, differences, advantages and disadvantages in the three methods are pointed out, and specific example solutions are presented.