Energy relaxation and the quasiequation of state of a dense two-temperature nonequilibrium plasma

A first principles approach to the equation of state (EOS) and the transport properties of an interacting mixture of electrons, ions, and neutrals in thermodynamic equilibrium was presented recently in Phys. Rev. E 52, 5352 (1995). However, many dynamically produced plasmas have an electron temperature $T_e$ different from the ion temperature $T_i.$ The study of these nonequilibrium (non-eq.) systems involves (i) calculation of a quasiequation of state (quasi-EOS) and the needed non-eq. correlation functions, e.g., the dynamic structure factors $S_{{\mathrm{ss}}^{\prime }}(k,\omega )$, where $s$ is the species index; and (ii) a calculation of relaxation processes. The energy and momentum relaxations are usually described in terms of coupling constants determining the rates of equilibriation. Simple Spitzer-type calculations of such coupling constants often use formulas obtained by averaging the damping of a single energetic particle by the medium. However, a different result is obtained for the energy-loss rate $〈{\mathrm{dH}}_e/dt〉$ of the electron subsystem when calculated from the commutator mean value $〈[H_e,H{]}_{-}〉$, where $H_e$ and $H$ are the Hamiltonians of the electron subsystem and the total system. This result corresponds to energy relaxation via the interaction of the normal modes of the hot system with the normal modes of the cold system. Such a description is particularly appropriate for dense plasmas. The evaluation of the commutator mean values within the Fermi golden rule (FGR), or more sophisticated Keldysh or Zubarev methods, yields formulations involving the dynamic structure factors of the two subsystems. The single-particle and normal-mode methods are conceptually very different. Here we present calculations of the energy relaxation of dense uniform two-temperature aluminum plasmas, and compare the usual Spitzer-type estimates with our more detailed FGR-type results. Our results show that the relaxation rate is more than an order of magnitude smaller than that given by the commonly used theories.