Variational characterizations of the effective multiplication factor of a nuclear reactor core

TL;DR

This paper introduces new variational formulas for calculating the effective multiplication factor in nuclear reactor analysis, applicable to both transport and diffusion equations, enhancing theoretical understanding and computational approaches.

Contribution

It provides novel inf-sup and sup-inf variational characterizations for the effective multiplication factor in reactor physics, unifying transport and diffusion models.

Findings

Derived new inf-sup and sup-inf formulas

Unified treatment of transport and diffusion equations

Enhanced theoretical framework for reactor analysis

Abstract

We derive some new inf-sup and sup-inf formulae for the so-called effective multiplication factor arising in the study of reactor analysis. We treat in a same formalism the transport equation and the energy-dependent diffusion equation.