Stability of force-free magnetic configurations and the problem of solar coronal heating

The coronal magnetic field in active regions is considered as a force-free configuration with longitudinal electric currents induced by photospheric pulsations. Such a system represents the excess magnetic energy that may be released via plasma instabilities. It is shown that this configuration remains stable in the perfect MHD limit due to the line typing effect, when magnetic field footpoints are anchored to the photosphere plane Z=0. So resistive instabilities are analyzed and unstable perturbations, similar to the tearing mode, have been revealed. According to Taylor, tearing mode growth results in local reconnections of field lines and relaxation of the system to the minimum energy state with the constraint of global magnetic helicity conservation. The extension of this theory was used, describe plasma heating process phenomenologically as permanent relaxation of the magnetic configuration. Such approach allows to express the rate of coronal heating in terms of the photospheric driver