Example of exponentially enhanced magnetic reconnection driven by a spatially-bounded and laminar ideal flow

TL;DR

This paper investigates how ideal plasma flows can exponentially enhance magnetic reconnection rates in plasmas with vastly different spatial scales, providing insights into natural and laboratory plasma behavior.

Contribution

It introduces a model showing exponential growth of magnetic field line separation ratios driven by ideal flows, offering a new perspective on reconnection dynamics.

Findings

Reconnection rate can be exponentially enhanced by ideal flows.

Current density increases logarithmically with scale disparity.

Magnetic field evolution transitions to Alfvénic timescales after reconnection.

Abstract

In laboratory and natural plasmas of practical interest, the spatial scale $\Delta_d$ at which magnetic field lines lose distinguishability differs enormously from the scale $a$ of magnetic reconnection across the field lines. In the solar corona, plasma resistivity gives $a/\Delta_d\sim10^{12}$, which is the magnetic Reynold number $R_m$. The traditional resolution of the paradox of disparate scales is for the current density $j$ associated with the reconnecting field $B_{rec}$ to be concentrated by a factor of $R_m$ by the ideal evolution, so $ j\sim B_{rec}/\mu_0\Delta_d$. A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrarily chosen magnetic field lines, $\Delta_{max}/\Delta_{min}$, when calculated at various points in time. Reconnection becomes inevitable where $\Delta_{max}/\Delta_{min}\sim R_m$. A simple model of the solar corona will be used for a numerical illustration that the natural rate of increase in time is linear for the current density but exponential for $\Delta_{max}/\Delta_{min}$. Reconnection occurs on a time scale and with a current density enhanced by only $\ln(a/\Delta_d)$ from the ideal evolution time and from the current density $B_{rec}/\mu_0a$. In both resolutions, once a sufficiently wide region, $\Delta_r$, has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfv\'enic time scale. The Alfv\'enic evolution is intrinsically ideal but expands the region in which $\Delta_{max}/\Delta_{min}$ is large.