Charged Particle Motion in a Plasma: Electron-Ion Energy Partition

Abstract

This paper considers plasmas in which the electrons and ions may have different temperatures. This is a case that must be examined because nuclear fusion processes, such as those that appear in ICF capsules, have ions whose temperature runs away from the electron temperature. A fast charged particle traversing a plasma loses its energy to both the electrons and the ions in the plasma. We compute the energy partition, the fractions E e /E 0 and E I /E 0 of the initial energy E 0 of this 'impurity particle' that are deposited into the electrons and ions when it has slowed down into a "schizophrenic" final ensemble of slowed particles that has neither the electron nor the ion temperature. This is not a simple Maxwell-Boltzmann distribution since the background particles are not in thermal equilibrium. We perform our calculations using a well-defined Fokker-Planck equation for the phase space distribution of the charged impurity particles in a weakly to moderately coupled plasma. The Fokker-Planck equation holds to first sub-leading order in the dimensionless plasma coupling constant, which translates to computing to order n ln n (leading) and n (sub-leading) in the plasma density n. An examination of the energy partition for the general case, in which the background plasma contains two different species of particles that are not in thermal equilibrium, has not been previously presented in the literature. We have new results for this case. 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. Since the charged particle does not come to rest, but rather comes into a statistical distribution, the energy loss obtained by a simple integration of a dE/dx has an ambiguity on the order of the plasma temperature. Our Fokker-Planck formulation provides an unambiguous, precise definition of the energy fractions. For equal electron and ion temperatures, we find that our precise results agree well with a fit obtained by Fraley, Linnebur, Mason, and Morse. 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.