# Particle Energy Diffusion in Linear Magnetohydrodynamic Waves

## TL;DR

This study investigates how relativistic particles gain energy through interactions with linear magnetohydrodynamic waves, highlighting the roles of gyroresonance and transit-time damping in different turbulence conditions.

## Contribution

It reveals the significance of resonance broadening by mirror forces and the dominance of TTD in certain regimes, advancing understanding of particle acceleration in astrophysical turbulence.

## Key findings

- Resonance broadening enables more particles to undergo TTD.
- Gyroresonance dominates when turbulence cutoff scale is smaller than Larmor radius.
- TTD alone can account for hard-sphere-like acceleration in high-energy phenomena.

## Abstract

In high-energy astronomical phenomena, the stochastic particle acceleration by turbulences is one of the promising processes to generate non-thermal particles. In this paper, we investigate the energy-diffusion efficiency of relativistic particles in a temporally evolving wave ensemble that consists of a single mode (Alfv\'en, fast or slow) of linear magnetohydrodynamic waves. In addition to the gyroresonance with waves, the transit-time damping (TTD) also contributes to the energy-diffusion for fast and slow-mode waves. While the resonance condition with the TTD has been considered to be fulfilled by a very small fraction of particles, our simulations show that a significant fraction of particles are in the TTD resonance owing to the resonance broadening by the mirror force, which non-resonantly diffuses the pitch angle of particles. When the cutoff scale in the turbulence spectrum is smaller than the Larmor radius of a particle, the gyroresonance is the main acceleration mechanism for all the three wave modes. For the fast-mode, the coexistence of the gyroresonance and TTD resonance leads to anomalous energy-diffusion. For a particle with its Larmor radius smaller than the cutoff scale, the gyroresonance is negligible, and the TTD becomes the dominant mechanism to diffuse its energy. The energy-diffusion by the TTD-only resonance with fast-mode waves agrees with the hard-sphere-like acceleration suggested in some high-energy astronomical phenomena.