A Generalized Eigenvalue Formulation for Core-Design Applications

Abstract

The adoption of multiplication eigenvalue is a well-established approach for the design of nuclear reactors. However, despite its popularity and nice physico-mathematical properties, this eigenvalue formulation is not able to provide quantitative information about what parameters the designer has to modify. In this paper, a novel generalized eigenvalue formulation is introduced to disclose the full potential of the neutron transport equation for core design applications. To illustrate the advantages of this new design-oriented approach with respect to traditional methods, some relevant problems arising in the physics of reactors are solved, such as the determination of the absorber density in the control rods and of the fissile concentration in the molten salt fast reactor.

Keywords:

• Neutron transport equation
• eigenvalue problems
• density eigenvalue problem
• core design

Disclosure Statement

No potential conflict of interest was reported by the authors.

Acknowledgments

This work has been carried out under the auspices of the Italian National Group of Mathematical Physics (Gruppo Nazionale di Fisica Matematica, GNFM) of the National Institute of High Mathematics (Instituto Nazionale di Alta Matematica, INDAM)