Test particle sampling and particle acceleration in a 2D coronal plasmoid-mediated reconnecting current sheet

TL;DR

This work investigates how electrons are accelerated to non-thermal energies in a 2D coronal current sheet shaped by plasmoid-mediated reconnection, using test particles governed by guiding center dynamics within a static MHD snapshot. By employing multi-stage importance sampling, the authors uncover a non-thermal power-law tail in the electron energy distribution, with the tail's presence and slope strongly depending on the validity of the guiding center approximation and the sampling strategy. The dominant acceleration mechanism identified is betatron acceleration near magnetic null points, while parallel electric-field effects are negligible in this configuration, highlighting the need for hybrid or full-orbit approaches to obtain converged power-law estimates. The study emphasizes that dynamic fields, 3D geometry, and near-null physics must be incorporated in future work to reliably model particle acceleration in solar flares and to constrain observational signatures such as hard X-ray emission.

Abstract

Context: Solar flares accelerate electrons, creating non-thermal energy distributions. However, the acceleration sites and dominant acceleration mechanisms remain largely unknown. Aims: We study the characteristics of electron acceleration and subsequent non-thermal energy distribution in a 2D coronal plasmoid-mediated reconnecting current sheet. Methods: We used test particles and the guiding centre approximation to transport electrons in a static coronal 2D fan-spine topology magnetohydrodynamic (MHD) snapshot. The snapshot was from a Bifrost simulation that featured plasmoid-mediated reconnection at a current sheet. To sample initial particle conditions that lead to non-thermal energies, we used importance sampling. In this way, the characteristics of the non-thermal electrons were statistically representative of the MHD plasma. Results: The energy distribution of the electrons forms a non-thermal power law that varies with our tolerance of the guiding centre approximation's validity, from no obvious power law to a power law with an exponent of -4 (the power law also depends on the statistical weighing of the electrons). The non-thermal electrons gain energy through a gradual betatron acceleration close to magnetic null points associated with plasmoids. Conclusions: In this static, asymmetric, coronal, 2D fan-spine topology MHD configuration, non-thermal electron acceleration occurs only in the vicinity of null points associated with magnetic gradients and electric fields induced by plasmoid formation and ejection. However, the guiding centre approximation alone is not sufficient to properly estimate the shape of the non-thermal power law since, according to our results, electron acceleration is correlated with the adiabaticity of the particles' motion. The results also show that the particle power law formation is biased by the test particle sampling procedure.

Figures (12)

• Figure 1: Plasma density of the MHD snapshot where we embedded test particles. The black streamlines show the magnetic field direction, and the two left panels shows the reconnection region in greater detail. The grid size is $8192^2$, and the resolution is 3.9 km.
• Figure 2: Normalised energy distribution of 10 million electrons before and after the first test particle simulation. The initial positions were sampled from the electron density of the MHD snapshot in Fig. \ref{['fig:mhdsnapshot']}. The initial velocities were sampled from a Maxwell-Boltzmann distribution at their initial temperature. The non-thermal electrons are too rare to be in the sample of this initial ensemble.
• Figure 3: Median relative energy gain as a function of initial position of the third electron ensemble. The function is normalised so that it can be used as a probability density distribution. The function is practically zero outside the reconnection region. Values above 15 all have the same colour.
• Figure 4: Normalised energy distribution after the third re-sampling of 13 million electrons. In this ensemble, the initial positions were sampled using Fig. \ref{['fig:proposaldist']} as a proposal distribution. The figure shows the final energy distribution with and without statistical weighting to account for the bias introduced by sampling from the proposal distribution, instead of the electron density. It also shows the distributions after applying a filter that excludes electrons outside the acceleration region, defined as the region displayed by the upper panel in Fig. \ref{['fig:nonthermalpaths']}. The distribution for energies lower than 10 eV is not shown.
• Figure 5: Magnetic field strength and field line segments of the current sheet overplotted with the trajectories of the 608 electrons with a final energy greater than 1 keV (excluding any particles with an initial energy above 1 keV). Their initial positions are shown as white dots, and the final positions as black dots.