Articles | Volume 29, issue 7
Ann. Geophys., 29, 1259–1265, 2011
Ann. Geophys., 29, 1259–1265, 2011

ANGEO Communicates 19 Jul 2011

ANGEO Communicates | 19 Jul 2011

Relativistic transformation of phase-space distributions

R. A. Treumann1,2,*, R. Nakamura3, and W. Baumjohann3 R. A. Treumann et al.
  • 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.