Magnetic reconnection solutions based on a generalized Ohm's law

It is known that exact magnetic reconnection solutions can be constructed for collisionally dominated resistive plasmas. In this paper we refine the collisional resistive description by invoking an Ohm's law that includes Hall current and plasma inertial contributions. We first demonstrate the surprising fact that the analytic treatment of both two and three dimensional current sheet reconnection remains valid for the generalized Ohm's law description. A discussion of planar reconnection shows that while the influence of inertial effects is generally small, the Hall current is likely to be important in most physically realistic plasma regimes, even for turbulent current sheet models. In particular, by influencing the magnetic and electric fields within the current sheet, the Hall current can be expected to have a strong influence on the particle acceleration capabilities of magnetic merging solutions. We also address the extent to which the new solutions alleviate the need for enhanced, anomalous resistivities to moderate the large current densities that arise in collisional resistive merging.