STEADY LINEAR X-POINT MAGNETIC RECONNECTION

In the main part of this paper a model for linear reconnection is deve loped with a current spike around the X-point and vortex current sheet s along the separatrices, which are resolved by the effects of viscosi ty and magnetic diffusivity. The model contains three regions. In the external ideal region, diffusion effects are negligible, and the flow is purely radial but becomes singular both along the separatrices and at the X-point. Near the separatrix there is a self-similar boundary l ayer with strong electric current and vorticity, where resistivity and viscosity resolve the singularity and allow the flow to cross the sep aratrix. A composite solution is set up that matches the external and separatrix solutions. Near the origin diffusion also resolves the sing ularity and is described approximately by a biharmonic solution. A cla ssification of steady two-dimensional reconnection regimes is proposed into viscous reconnection (M(e) > Re), extra slow linear) reconnectio n (M(e) < R(me)(-1)), slow reconnection (R(me)(-1) < M(e) less than or equal to R(me)(-1/2)), and fast reeonnection (R(me)(-1/2) < M(e)), wh ere M(e) is the dimensionless reconnection rate, R(me) the magnetic Re ynolds number, and Re the Reynolds number, all based on the Alfven spe ed far from the reconnection point. Also, an antireconnection theorem is proved, which has profound effects on the nature of linear reconnec tion. It states that steady two-dimensional MHD reconnection with plas ma flow across the separatrices is impossible in a plasma which is inv iscid, highly sub-Alfvenic, and has uniform magnetic diffusivity.