A model for magnetic energy storage and Taylor's relaxation in the solar corona. I: Helicity-constrained minimum energy state in a half-cylinder
The paper is concerned with the problem of the existence of a minimum energy state in a set of all the magnetic fields B occupying a circular half-cylinder D, with a normal component vanishing on the vertical part of the boundary of D and taking prescribed axisymmetric values on its lower horizontal part, and having a given relative helicity. It is shown that the only possible solution is a constant-alpha force-free field B-alpha. The main properties of this type of field (in particular, its existence and uniqueness under the imposed conditions) are determined. The implications of the results obtained for the problem of the solar corona are discussed.