Close encounters in Coulomb and gravitational scattering. I - Relaxation of isotropic test-particle distributions by like-particle collisions

Details Close encounters in Coulomb and gravitational scattering. I - Relaxation of isotropic test-particle distributions by like-particle collisions Close encounters in Coulomb and gravitational scattering. I - Relaxation of isotropic test-particle distributions by like-particle collisions

Apr 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992apj...389..558s&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 389, April 20, 1992, p. 558-589.

Astronomy and Astrophysics

Astrophysics

8

Boltzmann Transport Equation, Celestial Mechanics, Coulomb Collisions, Fokker-Planck Equation, Isotropic Media, Particle Collisions, Boundary Value Problems, Energetic Particles, Gravitational Fields, Maxwell Equation

Scientific paper

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 initial-value problem is considered in which spatially homogeneous, isotropically distributed test particles relax to equilibrium by means of like-particle Coulomb collisions with a fixed Maxwellian background. The time evolution of the test particle's velocity distribution is calculated using the Boltzmann and Fokker-Planck collision terms, and the results are compared. Close encounters are shown to be unimportant, relative to the cumulative effects of distant encounters, for near-equilibrium 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 identical-particle effects assume a new importance due to close encounters is noted. Contrary to accepted views, the Kolmogorov-Feller and Boltzmann collision terms are shown not to be equivalent for isotropic distribution.

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