# Hybrid-Kinetic Simulations of Ion Heating in Alfv\'{e}nic Turbulence

## TL;DR

This paper uses hybrid-kinetic simulations to study ion heating mechanisms in Alfvénic turbulence relevant to the near-Earth solar wind, revealing how energy cascades and particle distributions evolve at sub-ion scales.

## Contribution

It introduces novel diagnostics and detailed analysis of ion heating processes, especially near the ion-Larmor scale, highlighting the role of kinetic-Alfvén waves and non-thermal distribution features.

## Key findings

- 75-80% of turbulent energy heats ions
- Spectral steepening beyond -2.8 in sub-ion-Larmor range
- Non-Maxwellian velocity distribution wings observed

## Abstract

We present three-dimensional, hybrid-kinetic numerical simulations of driven Alfv\'{e}n-wave turbulence of relevance to the collisionless near-Earth solar wind. Special attention is paid to the spectral transition that occurs near the ion-Larmor scale and to the origins of preferential perpendicular ion heating and of non-thermal wings in the parallel distribution function. Several novel diagnostics are used to show that the ion heating rate increases as the kinetic-Alfv\'{e}n-wave fluctuations, which comprise the majority of the sub-ion-Larmor turbulent cascade, attain near-ion-cyclotron frequencies. We find that ${\approx}75$-$80\%$ of the cascade energy goes into heating the ions, broadly consistent with the near-Earth solar wind. This heating is accompanied by clear velocity-space signatures in the particle energization rates and the distribution functions, including a flattened core in the perpendicular-velocity distribution and non-Maxwellian wings in the parallel-velocity distribution. The latter are attributed to transit-time damping and the pitch-angle scattering of perpendicularly heated particles into the parallel direction. Accompanying these features is a steepening of the spectral index of sub-ion-Larmor magnetic-field fluctuations beyond the canonical $-2.8$, as field energy is transferred to thermal energy. These predictions may be tested by measurements in the near-Earth solar wind.