The linear force-free field in a spherical shell using a new method to determine the coefficients of the eigenfunction expansion

The linear force-free field of a plasma in between spherical shells is found allowing for inhomogeneous boundary conditions. A three-dimensional solution is found by analysis and used as a benchmark to test a solution in terms of an expansion of eigenfunctions where the coefficients are determined by a new method. Alternative methods are also applied in the context of the spherical shell example and used to illustrate some mathematical constraints that can affect their validity. The solution is used to model the solar coronal field in the presence of a large low-latitude coronal hole; SOHO-MDI data provide the inner boundary conditions.