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