Boundary conditions and plane magnetic reconnection

It is well known that several classical models of plane magnetic reconnection turn out to be more or less efficient according to the choosing of the boundary conditions. We prove analytically that one important datum, the variation of the area of the reconnection region, may be found, except by resistive effects, directly in terms of the flux and stream functions at the boundary. If we include the Hall effect in our model, the vertical component of the field at the boundary is also necessary. Since this area is a measure of the capacity of the system to keep the magnetic nozzle open, this provides a rigorous quantitative measure of the essential role of boundary conditions on the efficiency of the process.