One-Speed Neutron Wave Propagation with a Source off the Interface

Abstract

One-speed diffusion and transport theory is used to solve the problem of neutron wave propagation in a two-region system. The source is at a finite distance “a” to the left of the interface of the adjacent half-spaces. The solution in both models corresponds to the interpretation of the classical wave problem. The waves propagate till they reach the interface. At the interface, there is a component which is reflected, whereas another component is transmitted. Two coupled singular integral equations were solved simultaneously to evaluate the coefficients. One of the equations is of the Riemann-Hilbert type with discontinuous coefficients. There exists a discrete separation constant for the diffusion model for all oscillation frequencies. For the transport model, it is seen that there is a limiting frequency above which the discrete waves apparently disappear. Thus, a mixture of discrete and continuum waves, incident to an interface from the left medium may give rise to purely continuum or to a mixture of discrete and continuum waves on the right. Also, it is seen that a purely continuum incident wave may give rise to both discrete and/or continuum transmitted components.