Properties of the Flare Energy Release in Force-Free Magnetic Flux Ropes

A straight cylindrical, electrically shielded magnetic flux rope is considered as the upper part of a weakly curved magnetic loop whose footpoints are fixed in the photosphere. All parameters of the flux rope depend on one variable—the distance \(r\) from the axis of its symmetry. As the flux rope rises into the rarefied solar atmosphere, the external pressure keeping the flux rope from lateral expansion drops continuously. At some critical value of it the longitudinal magnetic field of the flux rope vanishes on the magnetic surface where the longitudinal electric current changes its sign in accordance with the requirement for the total current to be shielded. At the same time, the azimuthal current and the force-free parameter near this surface grow indefinitely. Because of this growth, the electron drift velocity near this surface exceeds the ion-sound speed, leading to the excitation of a plasma ion-sound instability as a trigger of flare energy release. The plasma conductivity in the region of plasma turbulence drops by seven orders of magnitude. Rapid magnetic energy dissipation at the anomalous resistivity generates an inductive electric field in the plasma that exceeds considerably the Dreicer limit. This explains the efficient acceleration of particles in the region where the magnetic field weakens rapidly.