Force-free magnetic flux ropes: inner structure and basic properties

Abstract

ABSTRACT There are two main properties of a shielded magnetic flux rope. The first is the net electric current through its cross-section should be zero, i.e. $I = 0$. The second is the existence of a non-zero pressure of external magnetic field ${{B_{ex}^2} {/ {\vphantom {{B_{ex}^2} {8\pi}}}} {8\pi }}$ in order to keep in balance the magnetic rope with the strong force-free inner structure in a rarefied solar atmosphere. The first condition requires the existence of a special cylindrical surface within the magnetic flux rope on which the current density j changes sign, so that the direction of the current at the rope’s periphery (return current) is opposite to the current at its axis (direct current). Numerical calculations have shown that, when the pressure ${{B_{ex}^2} {/ {\vphantom {{B_{ex}^2} {8\pi }}}} {8\pi }}$ drops to a certain limit, an indefinite increase in the electric current density j and the force-free parameter $\alpha $ takes place in the vicinity of this special surface resulting in a dissipative collapse of the system. Such a drop in ${{B_{ex}^2} {/ {\vphantom {{B_{ex}^2} {8\pi }}}} {8\pi }}$ may happen due to a multitude of reasons with the most obvious reason being the uprise of a magnetic flux rope into rarefied layers of the chromosphere or corona. Due to the dissipative collapse a violent energy release begins in a thin azimuthal shell at the periphery of the twisted magnetic flux tube. On the basis of these properties of the force-free magnetic flux rope, the problems of plasma instabilities excitation and coronal heating are discussed.