Quasi-radial basis functions applied to boundary element solutions for the Grad–Shafranov equation

Abstract

The Grad–Shafranov equation for axisymmetric fusion plasma has been transformed into a boundary integral equation by expanding the inhomogeneous current density term into a set of ‘quasi’-radial basis functions (RBFs). These quasi-RBFs are derived in such a way that a particular solution for the Grad–Shafranov equation will be a simple Gaussian function. Two or three stages of eigenvalue iterations are required together with a nonlinear optimization to update the scaling factor of each quasi-RBF. It has been found that excellent accuracy of the boundary element solution can be realized with a small number of quasi-RBFs when adopting RBF-dependent scaling factors.