Thermal disequilibration of ions and electrons by collisionless plasma turbulence

Abstract

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetised, turbulent plasma---and, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion discs around black holes. In the context of discs, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, ${\beta }_{\mathrm{i}}$: it ranges from $\sim 0.05$ at ${\beta }_{\mathrm{i}}=0.1$ to at least $30$ for ${\beta }_{\mathrm{i}}\gtrsim 10$. This energy partition is approximately insensitive to the ion-to-electron temperature ratio $T_{\mathrm{i}}/T_{\mathrm{e}}$. Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend towards a nonequilibrium state in which one of the species is significantly hotter than the other, viz., hotter ions at high ${\beta }_{\mathrm{i}}$, hotter electrons at low ${\beta }_{\mathrm{i}}$. Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high ${\beta }_i$ and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when ${\beta }_{\mathrm{i}}\lesssim 1$ and by linear phase mixing (Landau damping) when ${\beta }_{\mathrm{i}}\gg 1$