Magnetic field-line reconnection in a highly-conducting incompressible fluid: properties of the diffusion region

The properties of the field and flow near a two-dimensional X-type magnetic neutral line are considered for an incompressible, inviscid, conducting fluid in the steady state. In this region the magnetic field is not ‘frozen’ into the plasma, and finite conductivity effects must be considered. In the region surrounding the X line, it has hitherto been assumed that the field lines to lowest order form systems of hyperbolae (the field components increasing linearly with distance from the null), while the fluid flow lines form systems of rectangular hyperbolae with fluid flow perpendicular to the field on the axes of symmetry of the field lines. The assumption of such a configuration was based upon a somewhat cursary consideration of the governing equations, a detailed examination never having been carried out. We present the results of such an examination, which reveal that the above configuration is not a valid solution of the MHD equations, and that, for the case studied, the field to lowest order must form a neutral sheet. The properties of the field and flow parallel to the plane of symmetry are also considered. It is found that non-uniform fields and flows may exist within the diffusion region, in support of recent convection-region studies. This work shows clearly the need for more detailed and careful consideration of such systems.