# Constraints on ion vs. electron heating by plasma turbulence at low beta

## TL;DR

This paper demonstrates that in low-beta, weakly collisional plasmas, Alfvénic fluctuations do not produce ion heating within the gyrokinetic approximation, and ion heating mainly results from compressive fluctuations or non-gyrokinetic mechanisms, with specific exceptions in the Hall limit.

## Contribution

The study provides a theoretical framework showing that ion heating in low-beta plasmas is primarily due to compressive fluctuations and identifies conditions where Alfvénic fluctuations can contribute to ion heating.

## Key findings

- Alfvénic fluctuations produce no ion heating in low-beta plasmas within the gyrokinetic approximation.
- Ion heating is mainly due to compressive fluctuations or non-gyrokinetic mechanisms.
- In the Hall limit, Alfvénic and compressive cascades couple, leading to species-specific heating.

## 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, Alfv\'enic 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"). Because these fluctuations energetically decouple from the Alfv\'enic 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 Alfv\'enic ones well above the Larmor scale (viz., at the ion inertial or ion sound scale), so the Alfv\'enic and compressive cascades join and then separate again into two cascades of fluctuations that linearly resemble kinetic Alfv\'en 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.