Hall Electric Fields and Magnetic Reconnection in Thin Current Sheets

John C. Dorelli

The role of Hall electric fields in the saturation of flux pile-up magnetic
reconnection is addressed.  Analytical solutions of the resistive Hall MHD
equations are obtained, describing stagnation point flows in a thin current
sheet.  The stagnation point flow solutions explain a number of interesting
effects observed in two-dimensional resistive Hall-MHD simulations of forced 
magnetic reconnection.  In particular, when Hall electric fields are important
within the current sheet, less pile-up of magnetic energy is required upstream
of hte current sheet to support a given reconnection electric field.  Fast
electron flows transport magnetic flux into the diffusion layer without
requiring a compensating drop in plasma pressure upstream of the current
sheet.  The maximum flux pile-up  reconnection rate allowed by the external
plasma pressure beomes independent of the Lundquist number, scaling like the
square root of the ion inertial length.  Thus, Hall electric fields provide
a possible solutions to the problem of flux pile-up saturation in 
two-dimensional, resistive MHD models of forced magnetic reconnection.