Stationary stagnation point flows in the vicinity of a 2D magnetic null point: I. Systems with vanishing electric field and an X-type magnetic null point

TL;DR

This paper analytically investigates stationary resistive MHD flows near 2D magnetic null points, identifying conditions under which magnetic reconnection occurs and clarifying the topological structure of such plasma flows.

Contribution

It provides an analytical framework for understanding the boundary between reconnective and non-reconnective solutions near magnetic null points in resistive MHD.

Findings

Not all non-ideal flows are reconnective.

Pure resistive MHD allows only reconnection-like solutions.

Flow topology near X-points is crucial for energy dissipation.

Abstract

The appearance of eruptive space plasma processes, e.g., in eruptive flares as observed in the solar atmosphere, is usually assumed to be caused by magnetic reconnection. The process of magnetic reconnection is often connected with singular points of the magnetic field. We therefore analyse the system of stationary resistive/non-ideal magnetohydrodynamics (MHD) in the vicinity of singular points of flow and field to determine the boundary between reconnection solutions and non-reconnective solutions. We find conditions to enable the plasma to cross the magnetic separatrices also inside the current sheet, close to the current maximum. The results provide us with the topological and geometrical skeleton of the resistive MHD fields. We therefore have to perform a local analysis of almost all non-ideal MHD solutions with a generalized non-idealness. We use Taylor expansions of the magnetic field, the velocity field and all other physical quantities, including the non-idealness, and with the method of a comparison of the coefficients, the non-linear resistive MHD system is solved analytically. It turns out that not every non-ideal flow is a reconnective flow and that pure resistive/non-ideal MHD only allows for reconnection-like solutions, even if the non-idealness is localized to the region around the magnetic null point. It is necessary that the flow close to the magnetic X-point is also of X-point type to guarantee positive dissipation of energy and annihilation of magnetic flux. If the non-idealness has only a one-dimensional, sheet-like structure, only one separatrix line can be crossed by the plasma flow, similar to reconnective annihilation solutions.