Nonthermal particle acceleration from maximum entropy in collisionless plasmas

TL;DR

This paper proposes a maximum-entropy framework using generalized entropies to model nonthermal particle distributions with power-law tails in collisionless plasmas, linking plasma parameters to observed energy spectra.

Contribution

It introduces a novel maximum-entropy approach with generalized entropies to explain power-law tails in plasma particle distributions, connecting theory with simulation results.

Findings

Derived a formula for the power-law index based on plasma parameters.

Reproduced results from kinetic simulations of turbulence and reconnection.

Linked irreversible dissipation scales to particle energy distributions.

Abstract

Dissipative processes cause collisionless plasmas in many systems to develop nonthermal particle distributions with broad power-law tails. The prevalence of power-law energy distributions in space/astrophysical observations and kinetic simulations of systems with a variety of acceleration and trapping (or escape) mechanisms poses a deep mystery. We consider the possibility that such distributions can be modeled from maximum-entropy principles, when accounting for generalizations beyond the Boltzmann-Gibbs entropy. Using a dimensional representation of entropy (related to the Renyi and Tsallis entropies), we derive generalized maximum-entropy distributions with a power-law tail determined by the characteristic energy scale at which irreversible dissipation occurs. By assuming that particles are typically energized by an amount comparable to the free energy (per particle) before equilibrating, we derive a formula for the power-law index as a function of plasma parameters for magnetic dissipation in systems with sufficiently complex topologies. The model reproduces several results from kinetic simulations of relativistic turbulence and magnetic reconnection.