Lie group analysis of the point-reactor neutron kinetics equations for various reactivity models. (15th September 2021)

• Record Type: Journal Article
• Authors: O'Rourke, Patrick F.; Ramsey, Scott D.; Temple, Brian A.
• Is Part Of: Annals of nuclear energy. Volume 160(2021)
• Publication Date: 2021-09-15
• Subjects: Lie Group Analysis -- Point-reactor neutron kinetics equation -- Nordheim-Fuchs model -- Polynomial insertion model -- Fuchs Ramp-Insertion model; Nuclear energy -- Periodicals; Nuclear engineering -- Periodicals; 621.4805
• DOI: 10.1016/j.anucene.2021.108366
• Languages: English
• ISSNs: 0306-4549

Abstract

Highlights: Obtain symmetry determining equations for the point-reactor kinetics equation. Symmetries used as a geometric interpretation of the ODE with its solutions. Symmetries allowed for the discovery of new analytical and approximate solutions. Abstract: This work applies Lie Group Theory to the nonlinear point-reactor neutron kinetics equations for several reactivity feedback and reactivity insertion models. The goal of this work is to connect known analytical solutions to their corresponding Lie groups as well as to obtain new analytical solutions and the circumstances from which they arise. The reactivity models we consider are the Nordheim-Fuchs Model, an arbitrary-order polynomial reactivity insertion model, and the Fuchs Ramp-Insertion Model. In all three models, we generalize the analysis when possible and obtain analytical solutions in every case. For the first two models, we succeed in finding the Lie groups corresponding to classical solutions and find additional solutions that were otherwise unknown. For the final model, we obtain a reduced-order nonlinear kinetics equation which is not analytically solvable, but by applying a second-order truncation, we find a novel closed-form solution and demonstrate its validity with a numerical example.