The study of relativistic thermal plasmas, where \(kT_e \gtrsim m_e c^2\), is of growing importance in the field of high energy astrophysics. Models of the observed \(\gamma\)-ray burst sources require the existence of such high temperatures, as do some of the models of active galactic nuclei.
The question of self-consistency arises; can the particles maintain a Maxwellian distribution, or is the cooling too great? The timescale for two body relaxation via Coulomb collisions is well-known in the nonrelativistic limit (Spitzer, 1956), but is invalid at the temperatures being considered here. No relativistic generalization existed, although some approximate expressions have been given (Gould, 1982a; Lightman & Band, 1981).
In the first half of this thesis I derive an exact expression for the fully relativistic energy exchange rate in terms of an integral over the scattering cross section, and evaluate it for the cases of electron-proton, electron-electron and proton-proton relaxation. I compare the resulting timescales with the major energy-loss timescales -- those of bremsstrahlung, pair-production, pion production and synchrotron cooling -- to find in what temperature ranges it is possible to consider the particle distribution to be Maxwellian.
In the presence of an equipartition magnetic field synchrotron cooling dominates, and the electron distribution is only Maxwellian for temperatures \(kT_e \lesssim m_e c^2\). When there is no magnetic field bremsstrahlung is the dominant cooling process and the electron distribution can be Maxwellian for \(kT_e \lesssim 10 m_e c^2\). Protons cool much more slowly, and their distribution can remain Maxwellian at all temperatures of interest.
So it is reasonable to investigate thermal relativistic plasmas, and to build more detailed models of such systems. Since the problem is highly non-linear, detailed modelling requires computer simulation. In the second half of this thesis I describe the development of a computer program to model a thermal plasma slab at mildly relativistic temperatures. I present the results for the equilibrium structure of constant temperature slabs and for time dependent, cooling models.
@phdthesis(SS-thesis, author = "Susan Stepney", title = "Relativistic thermal plasmas", school = "Institute of Astronomy, University of Cambridge", month = sep, year = 1983 )