Close Encounters in Coulomb and Gravitational Scattering. I. Relaxation of Isotropic TestParticle Distributions by LikeParticle Collisions
Abstract
A procedure for solving the Boltzmann equation is developed and applied to the problem of describing the effects of close encounters in Coulomb and gravitational scattering. An initialvalue problem is considered in which spatially homogeneous, isotropically distributed test particles relax to equilibrium by means of likeparticle Coulomb collisions with a fixed Maxwellian background. The time evolution of the test particle's velocity distribution is calculated using the Boltzmann and FokkerPlanck collision terms, and the results are compared. Close encounters are shown to be unimportant, relative to the cumulative effects of distant encounters, for nearequilibrium initial conditions, but to very important for highly nonequilibrium initial conditions, leading to a view of the way in which energetic test particles thermalize that is qualitatively different from that derived from consideration of distant encounters alone. That identicalparticle effects assume a new importance due to close encounters is noted. Contrary to accepted views, the KolmogorovFeller and Boltzmann collision terms are shown not to be equivalent for isotropic distribution.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1992
 DOI:
 10.1086/171231
 Bibcode:
 1992ApJ...389..558S
 Keywords:

 Boltzmann Transport Equation;
 Celestial Mechanics;
 Coulomb Collisions;
 FokkerPlanck Equation;
 Isotropic Media;
 Particle Collisions;
 Boundary Value Problems;
 Energetic Particles;
 Gravitational Fields;
 Maxwell Equation;
 Astrophysics;
 CELESTIAL MECHANICS;
 STELLAR DYNAMICS;
 PLASMAS