How is the magnetic reconnection derived from magnetohydrodynamics equations?

TL;DR

This paper explains how magnetic reconnection can be derived from magnetohydrodynamics equations, emphasizing diffusion dynamics and initial magnetic field conditions, in an accessible way for students.

Contribution

It provides a clear, diffusion-based derivation of magnetic reconnection from MHD equations suitable for educational purposes.

Findings

Magnetic reconnection results from diffusion of magnetic field components.

Initial magnetic field conditions are crucial for reconnection.

Reconnection aligns with qualitative diffusion explanations.

Abstract

We clarify how magnetic reconnection can be derived from magnetohydrodynamics (MHD) equations in a way that is easily understandable to university students. The essential mechanism governing the time evolution of the magnetic field is diffusion dynamics. The magnetic field is represented by two components. It is clarified that the diffusion of a component causes a generation of another component that is initially zero and, accordingly, that the magnetic force lines are reconnected. For this reconnection to occur correctly, the initial magnetic field must be directed oppositely in the two regions, e.g., $y>0$ and $y<0$; must be concave (convex) for $y>0$ ($y<0$); and must be saturated for $y$ far from the x axis, which would indicate the existence of the current sheet. It will be clear that our comprehension based on diffusion runs parallel to the common qualitative explanation about the magnetic reconnection.