ON THE PROBLEM OF MAGNETIC CORONAL HEATING BY TURBULENT RELAXATION

Three developments in the basic theory for heating the solar corona by Taylor-Heyvaerts relaxation are presented. First of all, a general expression is derived for coronal heating in response to small footpoint motions by intermediate relaxation to a state that lies between the ideal MHD state and the lowest energy linear force-free field. It depends on the ratio (omegatau(r)) of the relaxation time (tau(r)) to the timescale (omega-1) for foot-point motions: when this is much smaller than unity, there is complete relaxation to the linear force-free state, and when it is much larger the deviation from the ideal state is small but it is in practice still sufficient to provide the observed heating. Second, a well-known difficulty with linear force-free fields, namely, that in a semi-infinite region such fields have infinite energy, is resolved: it is shown that the only possible relaxed state is a potential field, so that any excess magnetic helicity is ejected to infinity. Third, it is suggested that in practice the solar corona may be in a state not of complete relaxation but of partial relaxation, in which open fields continually relax to a potential state and eject magnetic helicity into the solar wind, while closed fields relax to a linear force-free state by means of small-scale reconnections.