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Relativistic transformation of phase-space distributions

Treumann, R. A., R. Nakamura, and W. Baumjohann (2011), Relativistic transformation of phase-space distributions, Annales Geophysicae, 29, 1259-1265, doi:10.5194/angeo-29-1259-2011, 7 Journal pages, also in arXiv:1105.2120v1 [physics.space-ph].

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
Further information
  author = {R. A. Treumann and R. Nakamura and W. Baumjohann},
  journal = {Annales Geophysicae},
  month = {jul},
  note = {7 Journal pages, also in arXiv:1105.2120v1 [physics.space-ph]},
  pages = {1259-1265},
  title = {{Relativistic transformation of phase-space distributions}},
  volume = {29},
  year = {2011},
  url = {http://arxiv.org/abs/1105.2120},
  doi = {10.5194/angeo-29-1259-2011},
%0 Journal Article
%A Treumann, R. A.
%A Nakamura, R.
%A Baumjohann, W.
%D 2011
%V 29
%J Annales Geophysicae
%P 1259-1265
%Z 7 Journal pages, also in arXiv:1105.2120v1 [physics.space-ph]
%T Relativistic transformation of phase-space distributions
%U http://arxiv.org/abs/1105.2120
%U www.ann-geophys.net/29/1259/2011/
%8 jul
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