Study of Forward and Backward Scattering in Two-Region Milne Problem for Non-absorbing Medium Using a Synthetic Kernel

Abstract

In this work, the effect of an extremely anisotropic scattering function on the two-region Milne problem is studied. This scattering function divides the neutrons resulting from the collisions into three parts; part ($l)$ which moves backward, part (m) which moves forward, and part (n) which emerge isotropically from the collisions, where $l$ + m + n = 1. The integral version of the transport equation is solved using trial functions based on Case’s eigenmodes and exponential integral function. Hence, the solution to the Milne problem is formulated in terms of characteristic quantities such as the extrapolation length and the fractional scalar flux discontinuity. Numerical results for the analytically evaluated quantities are presented. Some of our numerical results are compared with the available published results.

Keywords:

• Radiative transfer
• Milne problem
• two-regions
• synthetic kernel

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

All data generated or analyzed during this study are included in this article.