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

Abstract

We argue that two prominent theories of ion heating in low-$\beta$ collisionless plasmas -- stochastic and quasi-linear heating -- represent similar physical processes in turbulence with different normalized cross helicities. To capture both, we propose a simple phenomenology based on the power in scales at which critically balanced fluctuations reach their smallest parallel scale. 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 relevant to the solar wind.