Quasi-static evolution of force-free magnetic fields and a model for two-ribbon solar flares

It is shown that a two-dimensional force-free field in the solar corona can evolve in a quasi-static manner toward an open configuration, assuming the coronal field is invariant with respect to translations parallel to the x-axis. The theoretical result is applied to the quantitative theory of the evolution of two-ribbon solar flares of Kopp and Pneuman (1976), and the results are discussed. It is concluded that the two-dimensional force is the principal mechanism for the opening of the coronal magnetic field prior to reconnection during a solar flare.