Unique determination of model coronal magnetic fields using photospheric observations

We show that the nonradial field-boundary condition (or the line-of-sight boundary condition) for the Laplacian-like equation developed by Bogdan and Low (1986) is sufficient to uniquely determine the model coronal magnetic field provided the electric currents are horizontal (or zero, the current-free case) at the solar surface as well as in the solar atmosphere between the photosphere and the source surface. The derived recursion formulae for the spherical harmonic coefficients can be used to determine the spherical harmonic coefficients in the solutions of the horizontal current models very efficiently.