Approximate Treatments of Neutron Wave Propagation Problems in Three-Dimensional System

Abstract

Neutron wave propagation problems, espetially the Milne and the albedo problems, are investigated by making use of the Wiener-Hopf technique for treating the Boltzmann equation with an isotropic one-term degenerate kernel in a semi-infinite prism. A pole of the solution of the integral-transformed Boltzmann equation corresponds to an eigenvalue—or physically, to a complex wave number varying on the two-dimensional complex plane with transverse buckling and wave oscillation frequency. In the Milne problem, the solution ceases to exist when the imaginary part of the complex wave number exceeds σmin. In the albedo problem, however, the solution always exists irrespectively of the oscillation frequency ω, and the discrete eigenvalue presents a continuous spectrum as soon as ω exceeds a critical frequency ωc. Detailed forms of solutions are derived for the case of constant velocity, and complex eigenvalues are evaluated numerically.