A better linear force-free field

Linear force-free fields are often used as approximate models for magnetic fields in the solar corona, calculated on the basis of boundary values measured in the low atmosphere. The problem that is set up and solved does not have a unique solution, however, and various particular solutions-motivated in large part by mathematical convenience-appear in the literature. A method is presented for calculating the linear force-free held that is consistent with the observed component of the magnetic field normal to the solar surface and has a minimum difference between the components tangent to the surface and the observed tangential field. The method is tested by application to a known tangent to the surface and the nonlinear solution.