Time‐dependent localized reconnection of skewed magnetic fields

Abstract

We describe and analyze a model for time‐varying, localized reconnection in a current sheet with skewed magnetic field orientations on opposite sides. As in Petschek's description, disruption is initiated in a localized part of the current sheet known as the diffusion region, and the disturbances are subsequently propagated into the system at large through magnetohydrodynamic (MHD) waves. The MHD waves therefore play the dominant role in energy conversion, and collectively they form an outflow for plasma streaming toward the current sheet and a field reversal region joining magnetic field lines from opposite sides. We restrict the analysis to an incompressible plasma, in which case the Alfvén wave and the slow shock merge to form shocks bounding the field reversal or outflow region, and to the case of weak reconnection, which implies that the reconnection electric field is much smaller than the product of the characteristic values of the external field strength and Alfvén speed. It is then possible to perform a perturbation analysis of the MHD equations which govern the plasma and field behavior. The analysis can be formulated as a mixture of three well‐known problems. The problem of determining the appropriate combination of MHD waves corresponds to the Riemann problem, which also specifies the tangential field and flow components in the field reversal region. These results, it is important to note, are not sensitive to variations in the reconnection rate. Reconnection also acts as a source of surface waves, and their analysis determines the behavior of the perpendicular field and flow components and the shape of the shocks. Lastly, the field reversal region can be considered as a thin boundary layer in our treatment, and the external disturbances can therefore be solved in a way similar to the flow around a thin aerofoil. The model presented here can be applied to the Earth's magnetopause, where reconnection is considered to be the dominant process coupling the solar wind and the magnetosphere. In particular, the results can be used to interpret different manifestations of reconnection such as accelerated plasma flows along the magnetopause and flux transfer events.