Generalized Strategic Dual Image Method for Open Boundary Axisymmetrical Magnetic Field Problems

During the early 1990s, the strategic dual image (SDI) method for axisymmetric open boundary magnetic field problems was proposed. Although the method is powerful, the specific axis ratio of the ellipsoidal boundary has not been clarified, and therefore no further research has been done so far. Our aims are to clarify the relationship between the specific axis ratio of the ellipsoidal boundary and the harmonic solutions of Laplace equation, and to extend the strategic dual image method in general form. We have investigated the harmonic solutions of the Laplace equation in the oblate spheroidal coordinate to derive the explicit formula regarding the axis ratio and the averaging factor of Dirichlet and Neumann boundary value problems. Numerical analyses have also been carried out to verify the formula. We have determined the explicit formula regarding the axis ratio and averaging factor of Dirichlet and Neumann solutions, thus extending the SDI method in general form. Utilizing the derived formula, one can obtain the open boundary solutions of axisymmetrical magnetic field problems without alternating the existing software which are widely distributed through the Internet.