Tearing mode instability in a multiple current sheet system

The tearing mode and magnetic reconnection are studied for multiple current sheet systems by two-dimensional magnetohydrodynamic (MHD) simulations. Both the linear and nonlinear evolution of this process are anaylsed for laminar perturbations. The results illustrate the existence of a linear regime with a symmetric and antisymmetric mode and agree with previous analytic results (Otto and Birk, 1992). The nonlinear evolution shows a number of interesting new features and may explain some properties in corresponding studies of turbulent reconnection. For wavelengths larger than twice the current sheet separation the evolution of antisymmetric modes leads to an entire reconfiguration of the magnetic field and converts a major portion of the magnetic energy into kinetic energy. Antisymmetric modes with smaller wavelengths and symmetric modes are found to saturate. The influence of the value of the resistivity on the reconnection rate decreases in the nonlinear evolution, and the ratio of current sheet separation to wavelength seems to be of major importance. A comparion of the dynamics of periodic current sheets with the evolution of only two current sheets indicates that some of the results for the periodic system also apply to the evolution of only two interacting current sheets. The results are discussed with respect to observations of large-scale plasma and magnetic field reconfigurations in the magnetosheath and near the Earth's bow shock.