Coalescence of magnetic islands, sloshing, and the pressure problem

The coalescence of magnetic islands in the high Lundquist number regime is studied. Within the resistive magnetohydrodynamics model, the coalescence rate is known to stall (sloshing) in the limit of high Lundquist number. Previously, this stalling has been associated with the presence of a secondary tearing mode. Here it is shown that this stalling results from high magnetic pressure gradients, which result from thin current sheets at high Lundquist number. This phenomenon is frequently referred to as the “pressure problem” in flux pile-up reconnection studies. Sensitivity of the dynamic solution is presented, over a wide range of resistivities.