EQUILIBRIUM AND STABILITY OF CORONAL FORCE-FREE MAGNETIC-FIELD CONFIGURATIONS - THE CASE OF ONE IGNORABLE VARIABLE

Using numerical relaxation techniques, we show that, in the case of on e ignorable variable, only part of the theoretically predicted coronal force-free magnetic field equilibria are stable. A basic parameter, d etermined by the conditions at the photosphere and related to the tota l energy in the system (as well as to the fall of the magnetic field i ntensity with the heliocentric distance) is identified: it is only wit hin certain (continuous) ranges of values of this parameter that stabl e equilibria can exist. When an unstable analytical equilibrium state is used to set up the initial conditions for the problem it (i) either decays to a lower total energy, relaxed state (not predicted by the t heory) or (ii) it runs away, without reaching any relaxed state.