Fokker-Planck equation for Coulomb relaxation and wave-particle diffusion: Spectral solution and the stability of the Kappa distribution to Coulomb collisions

Wucheng Zhang and Bernie D. Shizgal
Phys. Rev. E 102, 062103 – Published 2 December 2020

Abstract

The present paper considers the time evolution of a charged test particle of mass m in a constant temperature heat bath of a second charged particle of mass M. The time dependence of the distribution function of the test particles is given by a Fokker-Planck equation with a diffusion coefficient for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. For the mass ratio m/M0, the steady distribution is a Kappa distribution which has been employed in space physics to fit observed particle energy spectra. The time dependence of the distribution functions with some initial value is expressed in terms of the eigenvalues and eigenfunctions of the linear Fokker-Planck operator and also interpreted with the transformation to a Schrödinger equation. We also consider the explicit time dependence of the distribution function with a discretization of the Fokker-Planck equation. We study the stability of the Kappa distribution to Coulomb collisions.

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  • Received 15 September 2020
  • Accepted 2 November 2020

DOI:https://doi.org/10.1103/PhysRevE.102.062103

©2020 American Physical Society

Physics Subject Headings (PhySH)

Plasma PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Wucheng Zhang

  • Department of Physics and Astronomy, University of British Columbia Vancouver British Columbia, Canada V6T 1Z1

Bernie D. Shizgal*

  • Department of Chemistry University of British Columbia Vancouver, British Columbia, Canada V6T 1Z1

  • *shizgal@chem.ubc.ca

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Vol. 102, Iss. 6 — December 2020

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