© Author(s) 2011. This work is distributed
under the Creative Commons Attribution 3.0 License.
Relativistic transformation of phase-space distributions
1Department of Geophysics and Environmental Sciences, Munich University, Munich, Germany
2Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA
3Space Research Institute, Austrian Academy of Sciences, Graz, Austria
*visiting: International Space Science Institute, Bern, Switzerland
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 Jüttner distribution corrected for the Lorentz-invariant phase-space volume element. Finally, we discuss the relativistic modification of a number of plasma parameters.