Flare Filament with the Force-Free Structure of the Magnetic Field

This paper presents another model of a flare filament with a force-free magnetic field structure. The distribution of the magnetic field and currents within the volume of the rope is defined by the so-called flux function. To obtain a force-free solution, the Laplacian of this function must strictly depend only on the function itself. However, there are a large number of such functions, which raises the question: how does the choice of a particular flux function affect the physical properties of the magnetic flux rope constructed based on it? In previous studies, the author generally used an exponential dependence of the flux function on the coordinates, but in this article, a power function was used, and it turned out that the physical parameters of the flare ropes almost coincide. All force-free magnetic flux ropes have one common physical property: as the rope loop apex extends into the corona, the external pressure that prevents its lateral expansion steadily decreases, and upon reaching a certain critical reduction, the longitudinal magnetic field of the rope turns to zero at the current inversion surface (CIS). At this point, the force-free parameter and the azimuthal electric current experience a discontinuity at this surface, causing their values in the vicinity of the CIS to grow indefinitely (in magnitude). The electron drift velocity here inevitably exceeds the ion acoustic velocity, leading to the excitation of plasma ion-acoustic instability, a sharp drop in plasma conductivity within the rope, and the generation of a super-Dreicer electric field. Parker’s effect (alignment, with some delay, of the torque along the rope axis due to the transfer of azimuthal field to the energy release region) leads to quasi-periodic pulsations of hard flare radiation and ultimately ensures the flare release of a significant portion of the free magnetic energy stored in the long loop of the magnetic flux rope.