A Unified Phenomenology of Ion Heating in Low-$\beta$ Plasmas: Test-Particle Simulations

TL;DR

This paper presents a unified framework for ion heating in low-beta plasmas, bridging stochastic and resonant processes through a simple empirical formula validated by simulations, applicable across astrophysical environments.

Contribution

It introduces a generalized empirical formula that unifies stochastic and resonant ion heating regimes, confirmed by simulations across various plasma conditions.

Findings

The empirical formula accurately captures ion heating across different turbulence regimes.

Simulations confirm the scalings in the solar wind and other astrophysical plasmas.

Provides a versatile subgrid model for large-scale plasma simulations.

Abstract

We argue that stochastic and resonant ion heating, often viewed as distinct processes in low-$\beta$ collisionless plasmas, are the far limits of a continuum controlled by nonlinear broadening of turbulent fluctuations, and thus by the normalized cross helicity. We propose a simple empirical formula that captures both regimes, generalizing that commonly used to describe stochastic heating. Simulations of test ions interacting with turbulence confirm our scalings across a wide range of different ion and turbulence properties, including with a steep ion-kinetic transition range as seen in the solar wind. Our results provide a unified framework for understanding ion heating processes across diverse astrophysical environments from black-hole accretion disks to the solar corona, also providing a compact and versatile subgrid model for larger-scale simulations.