Singular eigenfunctions for linear transport in an exponential atmosphere

Journal Article · Mon Sep 01 00:00:00 EDT 1980 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.524681· OSTI ID:5018977

Larsen, E W; Pomraning, G C; Badham, V C

We prove that under an explicit condition on the parameters in the isotropic-scattering linear transport equation for an exponential atmosphere, the continuum eigensolutions developed by Millikin and Siewert are complete on the half range 0<..mu..< or =1. We also treat numerically the equation for the outgoing flux, which can be derived using these eigenfunctions, and we show that excellent numerical results are obtained if the above condition is satisfied, while poor results are obtained if the condition is sufficiently violated. Finally, we describe a method for constructing elementary solutions of the anisotropic-scattering transport equation for an exponential atmosphere.

• Research Organization: Theoretical Division, University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 5018977
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 21:9; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

654001* -- Radiation &amp; Shielding Physics-- Radiation Physics
Shielding Calculations &amp; Experiments
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANISOTROPY
EIGENFUNCTIONS
EQUATIONS
FUNCTIONS
INTEGRAL EQUATIONS
SCATTERING
TRANSPORT THEORY