Energetic Particle Acceleration in Compressible Magnetohydrodynamic Turbulence

Magnetohydrodynamic (MHD) turbulence is an important agent of energetic particle acceleration. Focusing on the compressible properties magnetic turbulence, we adopt test method to study acceleration from Alfv\'en, slow and fast modes in four regimes that may appear a realistic astrophysical environment. Our studies show (1) second-order Fermi mechanism drives particles cascade processes three by particle-turbulence interactions, regardless whether shock wave appears; (2) not only can power spectra maximum rates reveal inertial range but also recover scaling energy ratio relationship between modes; (3) mode dominates particles, especially case super-Alfv\'enic supersonic for sub-Alfv\'enic very high range, Alfv\'en significant at early stage acceleration; (4) results power-law distribution certain evolution time. From perspective particle-wave interaction, this paper promotes understanding both behavior acceleration, which will help insight into involved MHD turbulence.