Particle Energy Diffusion in Linear Magnetohydrodynamic Waves

Abstract

Abstract In high-energy astronomical phenomena, the stochastic particle acceleration by turbulences is one of the promising processes to generate nonthermal 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 (Alfvén, 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 nonresonantly 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.