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On the uniqueness of the determination of the coronal potential magnetic field from line-of-sight boundary conditions

Authors:	J J Aly

Institution:	(1) Service d'Astrophysique, CEN Saclay, 91191 Gif-sur-Yvette Cédex, France

Abstract:	We consider a simple model in which the coronal magnetic field B is assumed to be potential in the region between the solar surface _o and an exterior source-surface ₁ of arbitrary shape. We prove that the boundary value problem that determines B from the value B _lof its component on ₀ along either $\hat l = \hat \omega$ (orthoradial direction) or $\hat l = \hat x$ (fixed direction) has at most one solution. On the other hand, we show that a solution can exist only if B _lsatisfies some solubility conditions.

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