Relativistic transformation of phase-space distributions

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

@article{id1669,
  author = {Treumann, R. A. and Nakamura, R. and Baumjohann, W.},
  doi = {10.5194/angeo-29-1259-2011},
  journal = {Annales Geophysicae},
  language = {en},
  note = {7 Journal pages, also in arXiv:1105.2120v1 [physics.space-ph]},
  pages = {1259-1265},
  title = {Relativistic transformation of phase-space distributions},
  url = {http://arxiv.org/abs/1105.2120
www.ann-geophys.net/29/1259/2011/},
  volume = {29},
  year = {2011},
}

%O Journal Article
%A Treumann, R. A.
%A Nakamura, R.
%A Baumjohann, W.
%R 10.5194/angeo-29-1259-2011
%J Annales Geophysicae
%G en
%O 7 Journal pages, also in arXiv:1105.2120v1 [physics.space-ph]
%P 1259-1265
%T Relativistic transformation of phase-space distributions
%U http://arxiv.org/abs/1105.2120
www.ann-geophys.net/29/1259/2011/
%V 29
%D 2011