Magnetic field evolution and reconnection in low resistivity plasmas

TL;DR

This paper explores the mathematical and physical aspects of magnetic field evolution in low resistivity plasmas, highlighting the roles of chaos, energy dissipation, and helicity in three-dimensional systems.

Contribution

It provides a clear analysis of how magnetic topology, energy, and helicity evolve in low resistivity plasmas, emphasizing the dominance of chaos in topology and the limited effect of resistivity on helicity.

Findings

Magnetic field line chaos dominates topology evolution in high magnetic Reynolds number regimes.

Energy dissipation requires large current densities and is not directly caused by chaos.

Magnetic helicity accumulates and is preserved despite chaos, until eruption.

Abstract

The mathematics and physics of each of the three aspects of magnetic field evolution -- topology, energy, and helicity -- is remarkably simple and clear. When the resistivity $\eta$ is small compared to an imposed evolution, $a/v$, timescale, which means $R_m\equiv\mu_0va/\eta>>1$, magnetic field line chaos dominates the evolution of field-line topology in three-dimensional systems. Chaos has no direct role in the dissipation of energy. A large current density, $j_\eta\equiv vB/\eta$, is required for energy dissipation to be on a comparable time scale to the topological evolution. Nevertheless, chaos plus Alfv\'en wave damping explain why both timescales tend to be approximately an order of magnitude longer than the evolution timescale $a/v$. Magnetic helicity is injected onto tubes of field lines when boundary flows have vorticity. Chaos can spread but not destroy magnetic helicity. Resistivity has a negligible effect on helicity accumulation when $R_m>>1$. Helicity accumulates within a tube of field lines until the tube erupts and moves far from its original location.