Internal structure of reconnecting current sheets and the emerging flux model for solar flares

We present a steady-state model for reconnecting current sheets, which relates the central values of temperature, density and pressure within the sheet to the prescribed external values of these parameters as well as the magnetic field strength and inflow velocity (or reconnection rate). The simplifying feature of our model is the assumption of quasi-one-dimensionality so that only variations across the sheet at the centre of symmetry are considered in detail. The dimensions of the sheet, the spatial profiles and their variation with the prescribed dimensionless parameters are obtained from the model. We also obtain the conditions on the dimensionless parameters for the existence of a steady state. A beta-limitation is discovered, such that steady reconnection is impossible when the plasma beta is too small. Also, the sheet dimensions may be an order of magnitude larger than previously thought. Finally, these general results are applied to the emerging flux model for solar flares. A state of thermal nonequilibrium ensues when the current sheet between the emerging and ambient flux reaches a critical height. The effect of the beta-limitation is to make this critical height decrease with increasing magnetic field strength.Now at A.W.R.E., Aldermaston, Berks., England.