Fundamental eigenvalues of the linear transport equation

Abstract

In neutronic applications of the linear transport theory, an important role is played by two parameters characterizing a given reactor system. The fundamental time constant α, which is an eigenvalue of the transport operator with the largest real part, and the constant γ which is the number with the largest absolute value such that if the fission neutron source in the transport equation is multiplied by 1/γ then the equation has a solution. It follows from the physical reasons that both α and γ should be real and the corresponding eigenfunctions non-negative. This fact has also been confirmed theoretically in many important cases. In this paper there will be considered an auxiliary eigenvalue problem for the neutron transport equation leading to a convenient method of calculating the constants α and γ and the corresponding eigenfunctions. The properties of the fundamental solution to the auxiliary eigenvalue problem will be shown to be such that the proposed calculational method is well convergent.