Coronal magnetic field relaxation by null-point reconnection

We derive the minimum energy state resulting from complete magnetic reconnection in a translationally or axisymmetric MHD system, in the limit of a low plasma beta and high magnetic Reynolds number conditions appropriate to the solar corona. The results are necessary for determining the amount of energy that can be liberated by reconnection and, hence, are important for understanding coronal heating and other forms of solar activity. The key difference between our approach and previous work is that because of line tying at the high-beta photosphere, reconnection is limited to occur only at magnetic null points initially present in the system. We find that under these circumstances the minimum energy state is not the usual linear force-free field but a state in which the nonpotential component of the field is distributed uniformly on equal flux surfaces. We discuss the implications of our results for the Sun's corona and for laboratory plasmas.