Particle acceleration in relativistic Alfv\'enic turbulence

Strong magnetically dominated Alfv\'enic turbulence is an efficient engine of non-thermal particle acceleration in a relativistic collisionless plasma. We argue that in the limit of strong magnetization, the type of energy distribution attained by accelerated particles depends on the relative strengths of turbulent fluctuations $\delta B_0$ and the guide field $B_0$. If $\delta B_0\ll B_0$, the particle magnetic moments are conserved and the acceleration is provided by magnetic curvature drifts. Curvature acceleration energizes particles in the direction parallel to the magnetic field lines, resulting in log-normal tails of particle energy distribution functions. Conversely, if $\delta B_0 \gtrsim B_0$, interactions of energetic particles with intense turbulent structures can scatter particles, creating a population with large pitch angles. In this case, magnetic mirror effects become important, and turbulent acceleration leads to power-law tails of the energy distribution functions.