TY - JOUR

T1 - The linear Boltzmann equation in slab geometry

T2 - Development and verification of a reliable and efficient solution

AU - Stamnes, K.

AU - Lie-Svendsen, null

AU - Rees, M. H.

PY - 1991/10

Y1 - 1991/10

N2 - We show that the linear Boltzmann equation can be cast in a fonn mathematically identical to the radiation transport equation. A multi-group procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative transfer problem, and we utilize existing software to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of our formalism to include external forces and spherical geometry are also feasible.

AB - We show that the linear Boltzmann equation can be cast in a fonn mathematically identical to the radiation transport equation. A multi-group procedure is used to reduce the energy (or velocity) dependence of the transport equation to a series of one-speed problems. Each of these one-speed problems is equivalent to the monochromatic radiative transfer problem, and we utilize existing software to solve this problem in slab geometry. The numerical code conserves particles in elastic collisions. Generic examples are provided to illustrate the applicability of this approach. Although this formalism can, in principle, be applied to a variety of test particle or linearized gas dynamics problems, it is particularly well suited to study the thermalization of suprathermal particles interacting with a background medium when the thermal motion of the background cannot be ignored. Extensions of our formalism to include external forces and spherical geometry are also feasible.

UR - http://www.scopus.com/inward/record.url?scp=0037578704&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037578704&partnerID=8YFLogxK

U2 - 10.1016/0032-0633(91)90022-3

DO - 10.1016/0032-0633(91)90022-3

M3 - Article

SN - 0032-0633

VL - 39

SP - 1435

EP - 1463

JO - Planetary and Space Science

JF - Planetary and Space Science

IS - 10

ER -