Bifurcation analysis of magnetic reconnection in Hall-MHD systems

Abstract

The influence of the Hall-term on the width of the magnetic islands of the tearing-mode is examined. We applied the center manifold (CMF) theory to a Magneto-hydrodynamic (MHD)-system. The MHD-system was chosen to be incompressible and includes in addition to viscosity the Hall-term in Ohm’s law. For certain val-ues of physical parameters the corresponding center manifold is two-dimensional and therefore the original partial differential equations could be reduced to a two-dimensional system of ordinary ones. This amplitude equations exhibit a pitchfork-bifurcation which corresponds to the occurrence of the tearing-mode. Eigenvalue-problems and linear equations due to the center manifold reduction were solved numerically with the Arpack++-library. An important result of this analysis is the growth of the tearing mode island width by increasing the Hall-parameter, a feature which has been observed in recent numerical simulations of collisionless reconnec-tion. Key words: Hall-MHD, tearing instability, reconnection, bifurcation theory, center manifold theory PACS: 52.30.Cv, 52.35.Py, 52.35.Vd, 02.30.Oz