Rapid motion of filaments in active regions. The integral form of equations of motion

The equations of motion of a filament are derived in the integral form. Three components of the force are expressed through surface integrals of the components of the Maxwellian tensor at the level of the chromospere. It is shown that in the filament vicinity the field, transverse with respect to the filament, has an inversion region. This is the necessary condition for the equilibrium of the current in an external field. On the surface of the chromosphere, a line appears which is called the channel of the filament - the axis of the structure, frequency observed in the chromosphere and having an appearance of a palm-tree branch. During the filament's ascent, this line is shifted to the weak-field region; this is connected with the phenomenon of separation of the flare ribbons