ANGEO Annales Geophysicae ANGEO 1432-0576 Copernicus GmbH Göttingen, Germany 10.5194/angeo-29-1259-2011 Relativistic transformation of phase-space distributions Treumann R. A. 1 2 4 Nakamura R. 3 Baumjohann W. 3 Department of Geophysics and Environmental Sciences, Munich University, Munich, Germany Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA Space Research Institute, Austrian Academy of Sciences, Graz, Austria visiting: International Space Science Institute, Bern, Switzerland 19 07 2011 29 7 1259 1265 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.ann-geophys.net/29/1259/2011/angeo-29-1259-2011.html The full text article is available as a PDF file from http://www.ann-geophys.net/29/1259/2011/angeo-29-1259-2011.pdf

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 Jüttner distribution corrected for the Lorentz-invariant phase-space volume element. Finally, we discuss the relativistic modification of a number of plasma parameters.

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