A circuit model for filament eruptions and two-ribbon flares

A circuit model is derived for solar filament eruptions and two-ribbon flares. In the model the filament is approximated as a line current and the current sheet as infinitely thin. The model reproduces the slow energy buildup and eruption of the filament and the energy dissipation in a current sheet at the top of postflare loops during the two-ribbon flare. The two circuits considered are that of the filament and its return current and that of the current sheet and its return current. These circuits are inductively coupled, and free energy stored in the filament in the pre-flare phase is found to be transferred to the sheet during the impulsive phase and rapidly dissipated there. In the solutions for the evolution of the filament current sheet system four phases are distinguished: (1) a slow energy buildup, (2) a 'metastable' state, (3) the eruptive phase, and (4) a postflare phase. These phases are described in detail.