Magnetic Field Confinement in the Corona: The Role of Magnetic Helicity Accumulation

A loss of magnetic field confinement is believed to be the cause of coronalmass ejections (CMEs), a major form of solar activity in the corona. Themechanisms for magnetic energy storage are crucial in understanding how a fieldmay possess enough free energy to overcome the Aly limit and open up.Previously, we have pointed out that the accumulation of magnetic helicity inthe corona plays a significant role in storing magnetic energy. In this paper,we investigate another hydromagnetic consequence of magnetic-helicityaccumulation. We propose a conjecture that there is an upper bound on the totalmagnetic helicity that a force-free field can contain. This is directly relatedto the hydromagnetic property that force-free fields in unbounded space have tobe self-confining. Although a mathematical proof of this conjecture for anyfield configuration is formidable, its plausibility can be demonstrated withthe properties of several families of power-law, axisymmetric force-freefields. We put forth mathematical evidence, as well as numerical, indicatingthat an upper bound on the magnetic helicity may exist for such fields. Thus,the accumulation of magnetic helicity in excess of this upper bound wouldinitiate a non-equilibrium situation, resulting in a CME expulsion as a naturalproduct of coronal evolution.Comment: 6 figures, ApJ in pres