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Magnetic reconnection is an important physical process in various explosivephenomena 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 theorder of a microscopic length such as the ion larmor radius or the ion inertiallength. In this study, we investigated the pinching process of a current sheetby the Lorentz force in a low-{\beta} plasma using one-dimensionalmagnetohydrodynam- ics (MHD) simulations. It is known that there is an exactself-similar solution for this problem that neglects gas pressure. We comparedthe non-linear MHD dynamics with the analytic self-similar solution. From theMHD simulations, we found that with the gas pressure included the implosionprocess deviates from the analytic self-similar solution as t {\rightarrow} t0, where t 0 is the explosion time when the thickness of a current sheet of theanalytic solution becomes 0. We also found a pair of MHD fast-mode shocks aregenerated and propagate after the formation of the pinched current sheet as t{\rightarrow} t 0 . On the basis of the Rankine-Hugoniot relations, we derivedthe scaling law of the physical quantities with respect to the initial plasmabeta in the pinched current sheet. Our study could help us to estimate thephysical quantities in the pinched current sheet formed in a low-\b{eta}plasma.

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