A Theoretical Model of Pinching Current Sheet in Low-beta Plasmas

TL;DR

This paper presents a theoretical and simulation-based study of the pinching process of a current sheet in low-beta plasmas, comparing MHD simulations with self-similar solutions and deriving scaling laws for physical quantities.

Contribution

It introduces a detailed MHD simulation analysis of current sheet pinching in low-beta plasmas and derives scaling laws based on Rankine-Hugoniot relations, extending previous idealized models.

Findings

Deviations from self-similar solutions when gas pressure is included.

Generation and propagation of MHD fast-mode shocks during pinching.

Derived scaling laws for physical quantities based on initial plasma beta.

Abstract

Magnetic reconnection is an important physical process in various explosive phenomena in the universe. In the previous studies, it was found that fast re- connection takes place when the thickness of a current sheet becomes on the order of a microscopic length such as the ion larmor radius or the ion inertial length. In this study, we investigated the pinching process of a current sheet by the Lorentz force in a low-{\beta} plasma using one-dimensional magnetohydrodynam- ics (MHD) simulations. It is known that there is an exact self-similar solution for this problem that neglects gas pressure. We compared the non-linear MHD dynamics with the analytic self-similar solution. From the MHD simulations, we found that with the gas pressure included the implosion process deviates from the analytic self-similar solution as t {\rightarrow} t 0, where t 0 is the explosion time when the thickness of a current sheet of the analytic solution becomes 0. We also found a pair of MHD fast-mode shocks are generated and propagate after the formation of the pinched current sheet as t {\rightarrow} t 0 . On the basis of the Rankine-Hugoniot relations, we derived the scaling law of the physical quantities with respect to the initial plasma beta in the pinched current sheet. Our study could help us to estimate the physical quantities in the pinched current sheet formed in a low-\b{eta} plasma.