Magnetic reconnection via current sheets

A general picture of magnetic reconnection in the frame work of 2D incompressible resistive magnetohydrodynamic theory is presented. Numerical studies of (quasi-) steady state driven reconnection reveal current sheet formation for Mach numbers M = u/vA exceeding the Sweet-Parker reconnection rate MSP = η/LvA)1/2. Since the thickness δ of the current sheet is found to be invariant to a change of the resistivity η, its length Δ increases rapidly with decreasing η or increasing M, which can be written in the form Δ ∼ (M/MSP)4, so that Δ reaches the global system size L within a short range of the parameter M/MSP. The reconnection process is therefore rather slow. This picture agrees in essence with Syrovatsky's theory of current sheets and disproves Petschek's mechanism of fast magnetic reconnection. A theory of the solution in the external and in the diffusion region is developed and analytical expressions in agreement with the simulation results are obtained by means of a variational principle. For sufficiently long current sheets the tearing mode becomes unstable in spite of the stabilizing effect of the inhomogeneous flow. The tearing mode contributes to the overall reconnection process, but a general assessment of this effect in the asymptotic regime of almost vanishing η is difficult