Particle Energy Diffusion in Linear Magnetohydrodynamic Waves.

In high-energy astronomical phenomena, the stochastic particle acceleration by turbulences is one of promising processes to generate non-thermal particles. In this paper, providing a temporally evolving wave ensemble, which consists of a single mode (Alfv\'en, fast or slow) of linear magnetohydrodynamic waves, we investigate the energy diffusion efficiency of relativistic particles. 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 very small fraction of particles, our simulations show that a significant fraction of particles are in the TTD resonance due 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 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 of high-energy astronomical phenomena.