Thermalization of the mildly relativistic plasma

In the recent Letter [1] we considered the approach of nonequilibrium pair plasma towards thermal equilibrium state adopting a kinetic treatment and solving numerically the relativistic Boltzmann equations. It was shown that plasma in the energy range 0.1-10 MeV first reaches kinetic equilibrium, on a timescale t_{k}<10^{-14} sec, with detailed balance between binary interactions such as Compton, Bhabha and Moller scattering, and pair production and annihilation. Later the electron-positron-photon plasma approaches thermal equilibrium on a timescale t_{th}<10^{-12} sec, with detailed balance for all direct and inverse reactions. In the present paper we systematically present details of the computational scheme used in [1], as well as generalize our treatment, considering proton loading of the pair plasma. When proton loading is large, protons thermalize first by proton-proton scattering, and then with the electron-positron-photon plasma by proton-electron scattering. In the opposite case of small proton loading proton-electron scattering dominates over proton-proton one. Thus in all cases the plasma, even with proton admixture, reaches thermal equilibrium configuration on a timescale t_{th}<10^{-11} sec. We show that it is crucial to account for not only binary but also triple direct and inverse interactions between electrons, positrons, photons and protons. Several explicit examples are given and the corresponding timescales for reaching kinetic and thermal equilibria are determined.