Electron-ion energy partition when a charged particle slows in a plasma: theory

The preceding paper [Brown, Preston, and Singleton Jr., Phys. Rev. E 86, 016406 (2012)] presented precise results for the partition of the initial energy E(0) of a fast particle into the ions and electrons--E(I)/E(0) and E(e)/E(0)--when the fast particle slows in a plasma whose ion and electron temperatures may differ. As emphasized in that paper, this is an important problem because nuclear fusion reactions, such as those that occur in an inertial confinement fusion capsule, involve ion temperatures that run away from the electron temperatures. As also noted in the preceding paper, a precise evaluation entails the use of a well-defined Fokker-Planck equation for the phase-space evolution of initially fast projectile particles. When the plasma has differing ion and electron temperatures, the projectiles must slow into a "schizophrenic" final ensemble of particles that has neither the electron nor the ion temperature. This is not a simple Maxwell-Boltzmann distribution since the electrons are not in thermal equilibrium with the ions. Thus, detailed calculations are required for the solution of the problem. These we provide here for a weakly to moderately coupled plasma. The Fokker-Planck equation holds to first subleading order in the dimensionless plasma coupling constant, which translates to computing to order n ln n (leading) and n (subleading) in the plasma density n. The energy partitions for a background plasma in thermal equilibrium have been previously computed, but the order n terms have not been calculated, only estimated. The "schizophrenic" final ensemble of slowed particles gives a new mechanism to bring the electron and ion temperatures together. The rate at which this new mechanism brings the electrons and ions in the plasma into thermal equilibrium will be computed.