Relativistic transformation of phase-space distributions
Abstract
We investigate the transformation of the distribution function in the relativistic case, a problem of interest in plasma when particles with high (relativistic) velocities come into play as for instance in radiation belt physics, in the electron-cyclotron maser radiation theory, in the vicinity of high-Mach number shocks where particles are accelerated to high speeds, and generally in solar and astrophysical plasmas. We show that the phase-space volume element is a Lorentz constant and construct the general particle distribution function from first principles. Application to thermal equilibrium lets us derive a modified version of the isotropic relativistic thermal distribution, the modified J\"uttner distribution corrected for the Lorentz-invariant phase-space volume element. Finally, we discuss the relativistic modification of a number of plasma parameters. Keywords: Relativistic invariance of the one-particle distribution function, J\"uttner distribution, relativistic plasma parameters
Keywords
Cite
@article{arxiv.1105.2120,
title = {Relativistic transformation of phase-space distributions},
author = {R. A. Treumann and R. Nakamura and W. Baumjohann},
journal= {arXiv preprint arXiv:1105.2120},
year = {2011}
}
Comments
7 pages, paper appeared in Ann Geophys., in the printed version the sums should be replaced by products as here in this arXiv-version