Thermalization of the mildly relativistic plasma

In a recent paper [A. G. Aksenov, R. Ruffini, and G. V. Vereshchagin, Phys. Rev. Lett. 99, 125003 (2007).] we considered the approach of nonequilibrium pair plasma towards a 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 reaches kinetic equilibrium first, on a time scale t(k)less than or similar to 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 time scale t(th)less than or similar to 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 there, 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 scattering. Thus in all cases the plasma, even with a proton admixture, reaches a thermal equilibrium configuration on a time scale t(th)less than or similar to 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 time scales for reaching kinetic and thermal equilibria are determined.