Stochastic Particle Acceleration in Turbulence Generated by the   Magnetorotational Instability
  We investigate stochastic particle acceleration in accretion flows. It is believed that the magnetorotational instability (MRI) generates turbulence inside accretion flows and that cosmic rays (CRs) are accelerated by the turbulence. We calculate equations of motion for CRs in the turbulent fields generated by MRI with the shearing box approximation without back reaction to the field. The results show that the CRs randomly gain or lose their energies through the interaction with the turbulent fields. The CRs diffuse in the configuration space anisotropically: The diffusion coefficient in direction of the unperturbed flow is about twenty times higher than the Bohm coefficient, while those in the other directions are only a few times higher than the Bohm. The momentum distribution is isotropic, and its evolution can be described by the diffusion equation in momentum space where the diffusion coefficient is a power-law function of the CR momentum. We show that the shear acceleration efficiently works for energetic particles. We also cautiously note that in the shearing box approximation, particles that cross the simulation box many times along the radial direction suffer unphysical runaway acceleration by the Lorentz transformation, which needs to be taken with special care. 
Shigeo S. Kimura, Kenji Toma, Takeru K. Suzuki, and Shu-ichiro   Inutsuka
astro-ph.HE