Numerical Simulation of Reconnection in an Emerging Magnetic Flux Region
Abstract
The resistive MHD equations are numerically solved in two dimensions for an initialboundaryvalue problem which simulates reconnection between an emerging magnetic flux region and an overlying coronal magnetic field. The emerging region is modelled by a cylindrical flux tube with a poloidal magnetic field lying in the same plane as the external, coronal field. The plasma betas of the emerging and coronal regions are 1.0 and 0.1, respectively, and the magnetic Reynolds number for the system is 2 × 10^{3}. At the beginning of the simulation the tube starts to emerge through the base of the rectangular computational domain, and, when the tube is halfway into the computational domain, its position is held fixed so that no more flux of plasma enters through the base. Because the timescale of the emergence is slower than the Alfvén timescale, but faster than the reconnection timescale, a region of closed loops forms at the base. These loops are gradually opened and reconnected with the overlying, external magnetic field as time proceeds. The evolution of the plasma can be divided into four phases as follows: First, an initial, quasisteady phase during which most of the emergence is completed. During this phase, reconnection initially occurs at the slow rate predicted by the Sweet model of diffusive reconnection, but increases steadily until the fast rate predicted by the Petschek model of slowshock reconnection is approached. Second, an impulsive phase with largescale, supermagnetosonic flows. This phase appears to be triggered when the internal mechanical equilibrium inside the emerging flux tube is upset by reconnection acting on the outer layers of the flux tube. During the impulsive phase most of the flux tube pinches off from the base to form a cylindrical magnetic island, and temporarily the reconnection rate exceeds the steadystate Petschek rate. (At the time of the peak reconnection rate, the diffusion region at the Xline is not fully resolved, and so this may be a numerical artifact.) Third, a second quasisteady phase during which the magnetic island created in the impulsive phase is slowly dissipated by continuing, but lowlevel, reconnection. And fourth, a static, nonevolving phase containing a potential, currentfree field and virtually no flow. During the short time in the impulsive phase when the reconnection rate exceeds the steadystate Petschek rate, a pileup of magnetic flux at the neutral line occurs. At the same time the existing Petschekslowmode shocks are shed and replaced by new ones; and, for a while, both new and old sets of slow shocks coexist.
 Publication:

Solar Physics
 Pub Date:
 September 1984
 DOI:
 10.1007/BF00151321
 Bibcode:
 1984SoPh...94..315F
 Keywords:

 Computational Astrophysics;
 Magnetic Field Configurations;
 Magnetic Flux;
 Solar Magnetic Field;
 Boundary Value Problems;
 Current Density;
 Hydrodynamic Equations;
 Magnetohydrodynamics;
 Shock Wave Propagation;
 Solar Physics