Guide Field Effects on the Distribution of Plasmoids in Multiple Scale Reconnection

TL;DR

This study investigates how a finite guide magnetic field influences plasmoid distribution in high-Lundquist-number reconnection, revealing different power-law behaviors depending on force-free conditions and merger dynamics, with implications for particle acceleration.

Contribution

It introduces statistical models for plasmoid distributions considering guide field effects, including force-free and non-force-free scenarios, and analyzes their impact on flux and velocity distributions.

Findings

Plasmoid distribution follows a power law with index 7/4 or 1 based on merger velocity dependence.

Force-free and non-force-free models exhibit distinct distribution indices in terms of guide field flux.

Force-free models predict more rapidly moving large flux plasmoids, supported by observational evidence.

Abstract

The effects of a finite guide field on the distribution of plasmoids in high-Lundquist-number current sheets undergoing magnetic reconnection in large plasmas are investigated with statistical models. Merging of plasmoids is taken into account either assuming that guide field flux is conserved resulting in non-force-free profiles in general, or that magnetic helicity is conserved and Taylor relaxation occurs to convert part of the summed guide field flux into reconnecting field flux towards minimum energy states resulting in force-free profiles. It is found that the plasmoid distribution in terms of reconnecting field flux follows a power law with index 7/4 or 1 depending on whether merger frequencies are independent of or dependent on their relative velocity to the outflow speed, respectively. This result is approximately the same for the force-free and non-force-free models, with non-force-free models exhibiting indices of 2 and 1 for the same velocity dependencies. Distributions in terms of guide field flux yield indices of 3/2 for the non-force-free model regardless of velocity dependence. This is notably distinct from the indices of 11/8 and 1 for the force-free models independent of and dependent on velocity, respectively. At low guide field fluxes the force-free models exhibit a second power law index of 1/2 due to non-constant flux growth rates. The velocity dependent force-free model predicts the production of slightly more rapidly moving large guide field flux plasmoids which is supported by observational evidence of flux ropes with strong core fields. Implications are discussed on particle acceleration via Fermi processes.