Coupled Mode Effects on Energy Transfer Rates in Two Temperature Plasmas

We investigate the effects of collective modes on the temperature relaxation rates in fully coupled electron-ion systems. Firstly, the well-understood limit of weakly coupled plasmas is considered and the coupled mode formula within the random phase approximation is derived starting from the Lenard-Balescu kinetic equation. We show how the frequency integration can be performed by standard methods without applying additional approximations. Due to the well-defined approximation scheme, the results can serve as a benchmark for more approximate theories and numerical simulations in this limit. The coupled mode electron-ion transfer rates show a considerable reduction compared to the Fermi-Golden Rule approach for certain parameters and very small changes for other systems. We demonstrate how these coupled mode effects are connected to the occurrence of ion acoustic modes and under which conditions they occur. Interestingly, coupled mode effects can also occur for plasmas with very high electron temperatures; a regime, where the Landau-Spitzer approach is believed to give accurate results. Finally, we extend the approach to systems with strongly coupled ions by applying static local field corrections. This extension can substantially increase the coupled mode effects.