Particle Acceleration and Fractional Transport in Turbulent Reconnection

TL;DR

This paper investigates particle acceleration in turbulent reconnection environments with multiple current sheets, demonstrating that fractional transport equations better model energy distributions than classical Fokker-Planck equations due to Levy flight behavior.

Contribution

It introduces a fractional transport equation approach to accurately model particle acceleration in turbulent reconnection, accounting for Levy flights in energy space.

Findings

Power-law energy distributions with index 1-2 are achieved.

Classical Fokker-Planck equations fail to reproduce simulation results.

Fractional transport equations successfully model the energy distributions.

Abstract

We consider a large scale environment of turbulent reconnection that is fragmented into a number of randomly distributed Unstable Current Sheets (UCS), and we statistically analyze the acceleration of particles within this environment. We address two important cases of acceleration mechanisms when the particles interact with the UCS: (a) electric field acceleration, and (b) acceleration through reflection at contracting islands. Electrons and ions are accelerated very efficiently, attaining an energy distribution of power-law shape with an index $1-2$, depending on the acceleration mechanism. The transport coefficients in energy space are estimated from the test-particle simulation data, and we show that the classical Fokker-Planck (FP) equation fails to reproduce the simulation results when the transport coefficients are inserted into it and it is solved numerically. The cause for this failure is that the particles perform Levy flights in energy space, the distributions of energy increments exhibit power-law tails. We then use the fractional transport equation (FTE) derived by Isliker et al., 2017, whose parameters and the order of the fractional derivatives are inferred from the simulation data, and, solving the FTE numerically, we show that the FTE successfully reproduces the kinetic energy distribution of the test-particles. We discuss in detail the analysis of the simulation data and the criteria that allow judging the appropriateness of either an FTE or a classical FP equation as a transport model.