Properties of two-dimensional, straight, magnetic arcade equilibria in the solar corona are studied in an MHD framework. Sequences of MHD equilibria are obtained by solving the Grad-Shafranov equation with the footpoint displacement or entropy prescribed. It is shown that no multiple solutions, or bifurcations, result, in contrast with the approach prescribing the axial magnetic field or pressure. The physical conditions for which the footpoint displacement or entropy must be specified are discussed, and the limiting configurations for infinite footpoint displacement and infinite entropy are addressed.
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Finn et al. (1990) studied this question.