Fractional Transport in Strongly Turbulent Plasmas

TL;DR

This paper investigates particle energization in strongly turbulent plasmas, demonstrating that classical Fokker-Planck models fail due to anomalous transport, and introduces a fractional transport equation that better captures the observed power-law energy distributions.

Contribution

It derives and validates a fractional transport equation from simulation data, providing a new approach to model anomalous particle energization in turbulent plasmas.

Findings

Classical Fokker-Planck fails to reproduce energy distributions.

Particles perform Levy flights, indicating anomalous transport.

Fractional transport equation accurately models high-energy tails.

Abstract

We analyze statistically the energization of particles in a large scale environment of strong turbulence that is fragmented into a large number of distributed current filaments. The turbulent environment is generated through strongly perturbed, 3D, resistive MHD simulations, and it emerges naturally from the nonlinear evolution, without a specific reconnection geometry being set up. Based on test-particle simulations, we estimate the transport coefficients in energy space for use in the classical Fokker-Planck (FP) equation, and we show that the latter fails to reproduce the simulation results. The reason is that transport in energy space is highly anomalous (strange), the particles perform Levy flights, and the energy distributions show extended power-law tails. Newly then, we motivate the use and derive the specific form of a fractional transport equation (FTE), we determine its parameters and the order of the fractional derivatives from the simulation data, and we show that the FTE is able to reproduce the high energy part of the simulation data very well. The procedure for determining the FTE parameters also makes clear that it is the analysis of the simulation data that allows to make the decision whether a classical FP or a FTE is appropriate.