Acceleration of cosmic rays in presence of magnetohydrodynamic fluctuations at small scales

This work investigates the evolution of the distribution of charged particles (cosmic rays) due to the mechanism of stochastic turbulent acceleration (STA) in presence of small-scale turbulence with a mean magnetic field. STA is usually modelled as a biased random walk process in the momentum space of the non-thermal particles. This results in an advection-diffusion type transport equation for the non-thermal particle distribution function. Under quasilinear approximation, and by assuming a turbulent spectrum with single scale injection at sub-gyroscale, we find that the Fokker-Planck diffusion coefficients $D_{\gamma\gamma}$ and $D_{\mu\mu}$ scale with the Lorentz factor $\gamma$ as: $D_{\gamma\gamma}\propto\gamma^{-2/3}$ and $D_{\mu\mu}\propto\gamma^{-8/3}$. Furthermore, with the calculated transport coefficients, we numerically solve the advection-diffusion type transport equation for the non-thermal particles. We demonstrate the interplay of various mircophysical processes such as STA, synchrotron loss and particle escape on the particle distribution by systematically varying the parameters of the problem.Comment: 15 pages, 8 figures, Submitted, Comments are welcom