Magnetic reconnection and thermal equilibration

TL;DR

This paper explores the slow dynamics of magnetic reconnection and thermal equilibration using Lagrangian coordinates, highlighting the importance of this approach often overlooked in traditional theories.

Contribution

It introduces a parallel analysis of magnetic reconnection and thermal equilibration using Lagrangian coordinates, challenging traditional perspectives and emphasizing their significance.

Findings

Magnetic topology changes occur much slower than the driving forces.

Thermal equilibration in air is significantly slower than air crossing time.

Lagrangian coordinates provide fundamental insights into these slow processes.

Abstract

When a magnetic field is forced to evolve on a time scale $\tau_{ev}$, as by footpoint motions driving the solar corona or non-axisymmetric instabilities in tokamaks, the magnetic field lines undergo large-scale changes in topology on a time scale approximately an order of magnitude longer than $\tau_{ev}$. But, the physics that allows such changes operates on a time scale eight or more orders of magnitude slower. An analogous phenomenon occurs in air. Temperature equilibration occurs on a time scale approximately an order of magnitude longer than it takes air to cross a room, $\tau_{ev}$, although the physical mechanism that allows temperature equilibration is approximately four orders of magnitude slower than $\tau_{ev}$. The use of Lagrangian coordinates allows the fundamental equations to be solved and both phenomena explained. The paradigms and presumptions of traditional theories of magnetic reconnection are so ingrained that the understanding gained from analyses using Lagrangian coordinates has been largely ignored. The theories of thermal equilibration and magnetic reconnection are developed in parallel to help readers obtain an understanding of the importance and implications of analyses using Lagrangian coordinates.