Contour dynamics modelling of collisionless magnetic reconnection

Fast magnetic reconnection is responsible for some of the more violent plasma phenomena, such as magnetic substorms in the earth’s magnetosphere and the internal disruptions, the so-called sawteeth in fusion experiments. Effects of finite electron inertia and parallel compressibility can enhance the reconnection over the rate given by resistivity. This becomes relevant in very hot as well as very dilute plasmas. The in this way calculated reconnection rates are comparable with those estimated from fusion experiments[1]. Two-fluid modelling of the tearing instability of a straight current layer has shown that current and vorticity gradients increase faster than exponentially and length scales shrink well below the intrinsic scales of the system (skin depth, ion gyroradius)[2,3]. An analytical treatment of a tearing mode in a straight current slab has been made possible by considering an equilibrium that consists of piecewise uniform regions of current density. This analysis can be extended to cylindrical geometry so that the linear stability of an annular region of generalized current density can be studied. In this paper we apply the method of contour dynamics [4,5] to follow the dynamics of a reconnecting tearing mode into the nonlinear regime