Temperature Relaxation Rates in Strongly Magnetized Plasmas

Strongly magnetized plasmas, characterized by having a gyrofrequency larger than the plasma frequency ($\beta = \omega_c/\omega_p \gg 1$), are known to exhibit novel transport properties. Previous works studying pure electron plasmas have shown that strong magnetization significantly inhibits energy exchange between parallel and perpendicular directions, leading to a prolonged time for relaxation of a temperature anisotropy. Recent work studying repulsive electron-ion interactions showed that strong magnetization increases both the parallel and perpendicular temperature relaxation rates of ions, but in differing magnitudes, resulting in the formation of temperature anisotropy during equilibration. This previous study treated electrons as a heat bath and assumed weak magnetization of ions. Here, we broaden this analysis and compute the full temperature and temperature anisotropy evolution over a broad range of magnetic field strengths. It is found that when electrons are strongly magnetized ($\beta_e \gg 1$) and ions are weakly magnetized ($\beta_i \ll 1$), the magnetic field strongly suppresses the perpendicular energy exchange rate of electrons, whereas the parallel exchange rate slightly increases in magnitude compared to the value at weak magnetization. In contrast, the ion perpendicular and parallel energy exchange rates both increase in magnitude compared to the values at weak magnetization. Consequently, equilibration causes the electron parallel temperature to rapidly align with the ion temperature, while the electron perpendicular temperature changes much more slowly. It is also shown that when both ions and electrons are strongly magnetized ($\beta_i, \beta_e \gg 1$) the ion-electron perpendicular relaxation rate dramatically decreases with magnetization strength as well.