The power-law spectra of energetic particles during multi-island magnetic reconnection

TL;DR

This paper introduces a new model for particle acceleration during magnetic reconnection, showing that power-law energy spectra with an index of -1.5 are a near-universal outcome under certain conditions, matching observations in space plasmas.

Contribution

The paper develops a self-consistent model including pressure anisotropy and pitch-angle scattering, deriving a closed-form solution for particle energy distribution during magnetic reconnection.

Findings

Power-law spectra with index -1.5 are a universal feature.

The model predicts energetic particle energy fluxes match observed spectra.

Total energetic particle energy can reach parity with magnetic free energy.

Abstract

Power-law distributions are a near universal feature of energetic particle spectra in the heliosphere. Anomalous Cosmic Rays (ACRs), super-Alfv\'enic ions in the solar wind and the hardest energetic electron spectra in flares all have energy fluxes with power-laws that depend on energy $E$ approximately as $E^{-1.5}$. We present a new model of particle acceleration in systems with a bath of merging magnetic islands that self-consistently describes the development of velocity-space anisotropy parallel and perpendicular to the local magnetic field and includes the self-consistent feedback of pressure anisotropy on the merging dynamics. By including pitch-angle scattering we obtain an equation for the omni-directional particle distribution $f(v,t)$ that is solved in closed form to reveal $v^{-5}$ (corresponding to an energy flux varying as $E^{-1.5}$) as a near-universal solution as long as the characteristic acceleration time is short compared with the characteristic loss time. In such a state the total energy in the energetic particles reaches parity with the remaining magnetic free energy. More generally, the resulting transport equation can serve as the basis for calculating the distribution of energetic particles resulting from reconnection in large-scale inhomogeneous systems.