Optimized magnetic reconnection solutions in three dimensions

It has recently been shown that there is a well defined upper limit to the rate of magnetic merging for two-dimensional flux pile-up solutions. This r ate, derived by equalizing the dynamic and magnetic pressures in the reconn ection region and saturating the magnetic field in the current layer, leads to a significant enhancement of the classical Sweet-Parker merging limit. In this study we explore optimal merging rates in the case of three-dimensi onal fan and spine reconnection solutions. The ideas of optimization and sa turation are first illustrated using an exact fan solution. We go on to sho w that while spine solutions seem ineffective as flare release mechanisms, optimized fan solutions have energy release characteristics typical of mode st events.