Theory of Electron-Ion Temperature Relaxation in Strongly Magnetized Plasmas

Strongly magnetized plasmas characterized by gyrofrequency larger than the plasma frequency are known to exhibit novel transport properties. Here, we study the electron-ion equilibration in strongly magnetized plasmas. We observe that strong magnetization significantly restricts energy exchange between parallel and perpendicular directions during intraspecies collisions, resulting in extended temperature anisotropy relaxation times. Consequently, during ion-electron equilibration, neither species maintains an isotropic Maxwellian distribution, making anisotropy a critical factor in determining the temperature evolution. We derive a general evolution equation for the temperatures and anisotropies of both species. It is found that when electrons are strongly magnetized and ions are weakly magnetized, the magnetic field significantly suppresses the electron perpendicular energy exchange rate while slightly enhancing the parallel exchange rate compared to the weak magnetization regime. Conversely, both ion perpendicular and parallel energy exchange rates slightly increase relative to their weakly magnetized counterparts. The anisotropy relaxation rates obtained from the theory are in good agreement with the previously published results from the strongly coupled non-neutral plasma experiments and the molecular dynamics simulations.