Description
Magnetic reconnection is one of the fundamental dynamical processes in the solar corona. The method of studying reconnection in active region-scale magnetic fields generally depends on non-local methods (i.e. requiring information across the magnetic field under study) of magnetic topology, such as separatrix skeletons and quasi-separatrix layers. The theory of General Magnetic Reconnection is also non-local, in that its measure of the reconnection rate depends on determining the maxima of integrals along field lines. Here, we complement the above approaches by introducing a local theory of magnetic reconnection, that is one in which information about reconnection at a particular location depends only on quantities at that location. The theory connects the concept of the field line slippage rate, relative to ideal motion, to the underlying local geometry of the magnetic field characterized in terms of the Lorentz force and field-aligned current density. The theory is adaptable to the inclusion of different forms of non-ideal physics and relevant quantities, e.g. reconnection rates, are simple and fast to compute. Related to the last point, the theory can be easily computed in both simulations and magnetic field extrapolations and provide extra information that is not available from non-local theories. We present some illustrative examples.
