Abstract
Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, 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 disks around black holes. In the context of disks, 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, [Formula: see text]: It ranges from [Formula: see text] at [Formula: see text] to at least 30 for [Formula: see text] This energy partition is approximately insensitive to the ion-to-electron temperature ratio [Formula: see text] Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high [Formula: see text] and hotter electrons at low [Formula: see text] Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high [Formula: see text] and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when [Formula: see text] and by linear phase mixing (Landau damping) when [Formula: see text].
Highlights
Plasma turbulence | particle heating | accretion flows in a differentially rotating accretion disk), transferred to ever smaller scales in the position–velocity phase space via a “turbulent cascade,” and converted into thermal energy of plasma particles via microscale dissipation processes
We find that turbulence promotes disequilibration of the species: When magnetic energy density is greater than the thermal energy density, electrons are preferentially heated, whereas when it is smaller, ions are
A certain fraction of the cascading energy is converted into ion heat and the rest continues on as a cascade of “kinetic Alfven waves” (KAWs), which heats electrons [6]
Summary
An Alfvenic turbulent cascade starts in the magnetohydrodynamic (MHD) inertial range, where ions and electrons move in concert. This approximation breaks down and the two species decouple at the ion Larmor scale, k⊥ρi ∼ 1, where k⊥ is the wave number perpendicular to the mean field At this scale, a certain fraction of the cascading energy is converted into ion heat (via linear and/or nonlinear phase mixing; see below) and the rest continues on as a cascade of “kinetic Alfven waves” (KAWs), which heats electrons [6]. The isothermal electron fluid equations are derived from the electron GK equation via an asymptotic expansion in the electron-to-ion mass ratio (me/mi)1/2 This is valid at scales above the electron Larmor radius and so covers a broad range including both the MHD and ion-kinetic (k⊥ρi ∼ 1) scales. We carefully tune the hypercollisionality and hyperdissipation coefficients to make the artificial dissipation effective only at the smallest scales
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