Distributions of particles accelerated by strong Alfv\'enic turbulence

TL;DR

This paper develops a unified model for particle acceleration in turbulent collisionless plasmas, predicting power-law energy distributions in both non-relativistic and relativistic regimes, consistent with observations and simulations.

Contribution

It introduces a curvature acceleration mechanism driven by strong Alfvénic turbulence that explains the formation of power-law tails in particle energy distributions.

Findings

Non-relativistic momentum distribution scales as p^{-3}.

Ultrarelativistic energy distribution scales as γ^{-3}.

Model aligns with heliospheric observations and simulation results.

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 $. This model provides a unified framework for understanding particle acceleration in both energy regimes, complementing existing analytical approaches. Its predictions 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.