Magnetic Energy Release in Flux Pile-up Merging

The problem of pressure limitations on the rate of flux pile-up magnetic reconnection is studied. We first examine the recent suggestion of Jardine and Allen (1998) for moderating the build-up of magnetic pressure in the current sheet by considering inflows with nonzero vorticity. An analytic argument shows, however, that unbounded magnetic pressures in the limit of small resistivities can be avoided only at the cost of unphysical dynamic pressures in the plasma. Hence, the pressure limitation on the reconnection rate in a low-beta plasma cannot be avoided completely. Nevertheless, we demonstrate that reconnection can be more rapid in a new solution that balances the build-up in dynamic pressure against both the plasma and magnetic pressures. This exact MHD solution has the characteristics of merging driven by the coalescence instability. The maximum energy release rate of the model is capable of explaining a modest solar flare.