Continuous Transition from Fast Magnetic Reconnection to Slow Reconnection and Change of the Reconnection System Structure

Abstract

This paper analytically investigates a series of two-dimensional MHD reconnection solutions over a wide variation of magnetic Reynolds number ($R_{em}^*$). A new series of solutions explains a continuous transition from Petschek-like fast regime to a Sweet-Parker-like slow regime. The inflow region is obtained from a Grad-Shafranov analysis used by Nitta et al. 2002 and the outflow region from a shock-tube approximation used by Nitta 2004, 2006. A single X-point (Petschek-like) solution forms for a sufficiently small $R_{em}^*$. As $R_{em}^*$ gradually increases, the solutions shifts to an X-O-X solution with a magnetic island between two X-points. When $R_{em}^*$ increases further, the island collapses to a new elongated current sheet with Y-points at both ends (Sweet-Parker-like). These reconnection structures expand self-similarly as time proceeds. As $R_{em}^*$ increases, the reconnection rate and the reducible fraction of the initial magnetic energy of the system decrease as power-law functions of $R_{em}^*$.