Temperature equilibration in a fully ionized plasma: electron-ion mass ratio effects

TL;DR

This paper compares theoretical and molecular dynamics approaches to electron-ion temperature equilibration in plasmas, focusing on the classical limit and the effects of the electron-ion mass ratio.

Contribution

It derives the classical limit of BPS's temperature equilibration rate and examines the validity of the small electron-ion mass ratio approximation.

Findings

Classical limit of BPS rate derived

Validation of m_e/m_i --> 0 approximation analyzed

Comparison between theory and molecular dynamics discussed

Abstract

Brown, Preston, and Singleton (BPS) produced an analytic calculation for energy exchange processes for a weakly to moderately coupled plasma: the electron-ion temperature equilibration rate and the charged particle stopping power. These precise calculations are accurate to leading and next-to-leading order in the plasma coupling parameter, and to all orders for two-body quantum scattering within the plasma. Classical molecular dynamics can provide another approach that can be rigorously implemented. It is therefore useful to compare the predictions from these two methods, particularly since the former is theoretically based and the latter numerically. An agreement would provide both confidence in our theoretical machinery and in the reliability of the computer simulations. The comparisons can be made cleanly in the purely classical regime, thereby avoiding the arbitrariness associated with constructing effective potentials to mock up quantum effects. We present here the classical limit of the general result for the temperature equilibration rate presented in BPS. We examine the validity of the m_electron/m_ion --> 0 limit used in BPS to obtain a very simple analytic evaluation of the long-distance, collective effects in the background plasma.