Eigenvalue Spectrum of the Neutron Transport Operator for a Fast Multiplying System

Abstract

The eigenvalue spectrum of the neutron transport operator for fast multiplying systems is discussed under the continuous energy treatment and with the assumption of isotropic distribution of the neutrons emitted by scattering and fission. In particular, the sufficient conditions are presented for the existence and non-existence of what is known as the fundamental mode. Further, it will be shown that, if the energy transfer kernel is positive almost everywhere, then the eigenvalue for the fundamental mode is strictly larger than the real part of any other eigenvalue and there are no non-negative eigenfunctions excepting the fundamental mode.