Distributions of particles accelerated by strong Alfv\'enic turbulence

Abstract

This work presents a model for generating nonthermal power-law tails of particles' energy probability density functions in turbulent collisionless plasmas, applicable to both non-relativistic and relativistic scenarios. We propose that strong Alfv\'enic turbulence energizes plasma particles through curvature acceleration, particularly for particles with Larmor radii comparable to the scales of turbulence. When the energy density of the energized particles increases, the efficiency of the energy exchange process diminishes. As a result, the acceleration process saturates, leading to power-law distributions of particle momentum and energy. In the non-relativistic case, the momentum probability density function scales as $f(p) dp \propto p^{-3} dp $, while in the ultrarelativistic case, the energy probability density function scales as $ f(\gamma) d\gamma \propto \gamma^{-3} d\gamma $, where $\gamma$ is the Lorentz factor. This model provides a unified framework for understanding particle acceleration in both energy regimes, complementing existing analytical approaches. The predicted scalings are consistent with available observations of energetic ion distributions in the heliosphere and with the findings from numerical simulations of ultrarelativistic particle acceleration in magnetically dominated plasma turbulence.