Magnetic nulls in interacting dipolar fields

TL;DR

This paper investigates the behavior of magnetic nulls in dipolar fields considering electron inertia, revealing limits on line distinguishability, constraints on current density, and the dynamics of current sheet formation.

Contribution

It introduces a new understanding of magnetic nulls by incorporating electron inertia effects, establishing limits on magnetic line distinguishability and current density constraints.

Findings

Magnetic field lines are distinguishable only when separated by more than a certain scale.

Electron inertia sets a minimum distance for line distinguishability near nulls.

Derived a time scale for the formation of thin current sheets at nulls.

Abstract

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field-lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance $\Delta_d$. Electron inertia ensures $\Delta_d\gtrsim c/\omega_{pe}$. The lines that lie within a magnetic flux tube of radius $\Delta_d$ at the place where the field strength $B$ is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where $B=0$,vanishes, then distinguishable lines come no closer to the null than $\approx (a^2c/\omega_{pe})^{1/3}$, where $a$ is a characteristic spatial scale of the magnetic field. The behavior of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.