On the boundary conditions for the neutron transport equation

TL;DR

This paper analyzes the boundary conditions for the neutron transport equation, emphasizing the importance of medium-independent conditions based on mathematical and physical reasoning.

Contribution

It provides a detailed analysis of boundary conditions for the neutron transport equation, advocating for medium-independent criteria grounded in mathematical and physical principles.

Findings

Boundary conditions should not depend on specific medium properties.

Mathematical and physical analysis guides the selection of boundary conditions.

The 'golden rule' is to establish conditions independent of medium specifics.

Abstract

The solution of the linear transport equation used for the study of neutral particle fields requires the imposition of appropriate boundary conditions. The choice of the conditions to impose for an infinite medium is not straightforward. The question has been given different formulations in the literature with various justifications based on some physical reasoning. Some aspects of the question are here analysed, from both the mathematical and the physical point of view. It is concluded that the inspiring golden rule should be the establishment of conditions that do not require any reference to the properties of the specific medium being considered for their justification.