Force-free magnetic flux ropes: String confinement of super-strong magnetic fields and flare energy release

Abstract

ABSTRACT A new class of force-free solutions for a horizontal magnetic filament with a circular cross-section is found, in which the magnetic field strength on the axis significantly (up to 2–3 orders of magnitude and more) exceeds the strength of the longitudinal external field that keeps the rope from lateral expansion. A weak transverse field leads to a small deviation from the force-free field structure and results in a density deficit and an increase in temperature on the rope axis. The possibility of a flare release of magnetic energy is shown when critical values ​​of the longitudinal electric current density in the filament are reached at which ‘anomalous resistance’ occurs, caused by the development of the current ion-sound plasma instability. It turns out to be much larger than the usual Coulomb resistance. The following values are determined: the scale of the current dissipation region, the electric field strength in it, which significantly exceeds the Dreicer value, and the possible energy of accelerated charged particles (up to hundreds of MeV). The critical density of the longitudinal current at which the plasma turbulence is excited does not depend on the presence of a super-strong field on the flux-rope axis, so that the current density depends only on the electron concentration, temperature, and anomalous conductivity. However, super-strong magnetic fields can manifest themselves in the fact that, in their presence, the excitation of plasma instabilities can occur at sufficiently high electron concentrations. This effect may explain the large number of accelerated particles sometimes observed in solar flares.