Constraints on ion versus electron heating by plasma turbulence at low beta

Abstract

It is shown that in low-beta, weakly collisional plasmas, such as the solar corona, some instances of the solar wind, the aurora, inner regions of accretion discs, their coronae, and some laboratory plasmas, Alfvénic fluctuations produce no ion heating within the gyrokinetic approximation, i.e., as long as their amplitudes (at the Larmor scale) are small and their frequencies stay below the ion Larmor frequency (even as their spatial scales can be above or below the ion Larmor scale). Thus, all low-frequency ion heating in such plasmas is due to compressive fluctuations ("slow modes"): density perturbations and non-Maxwellian perturbations of the ion distribution function. Because these fluctuations energetically decouple from the Alfvénic ones already in the inertial range, the above conclusion means that the energy partition between ions and electrons in low-beta plasmas is decided at the outer scale, where turbulence is launched, and can be determined from magnetohydrodynamic (MHD) models of the relevant astrophysical systems. Any additional ion heating must come from non-gyrokinetic mechanisms such as cyclotron heating or the stochastic heating owing to distortions of ions' Larmor orbits. An exception to these conclusions occurs in the Hall limit, i.e., when the ratio of the ion to electron temperatures is as low as the ion beta (equivalently, the electron beta is order unity). In this regime, slow modes couple to Alfvénic ones well above the Larmor scale (viz., at the ion inertial or ion sound scale), so the Alfvénic and compressive cascades join and then separate again into two cascades of fluctuations that linearly resemble kinetic Alfvén and ion cyclotron waves, with the former heating electrons and the latter ions. The two cascades are shown to decouple, scalings for them are derived, and it is argued physically that the two species will be heated by them at approximately equal rates. †

On the violation of the zeroth law of turbulence in space plasmas

“…vary slowly in time compared with the ion-cyclotron frequency, that there is a strong background magnetic field, and that the correlation length l of a perturbation in the field-parallel direction is much larger than its field-perpendicular correlation length l ⊥ (Schekochihin et al 2009). The resulting system (gyrokinetics) is still quite complex, and significant further simplification is possible using an expansion in β e ∼ β i 1 (Zocco & Schekochihin 2011;Schekochihin et al 2019). In this case, the ion-thermal speed is small compared with the Alfvén speed, implying there is minimal coupling between perpendicular (Alfvénic) motions and ion-compressive (kinetic) degrees of freedom, even for ion-Larmor-scale fluctuations (Schekochihin et al 2019).…”

The Enhancement of Proton Stochastic Heating in the Near-Sun Solar Wind

“…The difficulty in observing Landau damping and the concurrent radial heating profile is that it preferentially produces higher parallel temperatures, in conflict with the ion temperature anisotropy T ⊥ /T > 1 observed in the corona and the inner heliosphere for r < 0.5 au. We point the reader to various review articles containing descriptions of solar wind turbulence properties (Chen 2016), heating mechanisms proposed by the community (Cranmer et al 2015), as well as the historical development of the field through theory and observations (Schekochihin 2019).…”

Nonlinear Reconnection in Magnetized Turbulence

“…Numata & Loureiro 2015;Shay et al 2018). Therefore, if reconnecting eddies are a common occurrence -the conditions for which are worked out in this paper -then one might expect turbulence to be efficient at generating nonthermal populations and different electron-to-ion temperature ratios, which are indeed observed or expected in different space and astrophysical plasmas (see, e.g., Schekochihin et al 2019, and references therein). Moreover, the very observability of reconnecting turbulence depends, obviously, on whether truly reconnecting eddies are the norm or an exception.…”