An analytic approach to toroidal eigen mode

Abstract

It has been shown that the failure of the classical WKB approach in reproducing the correct frequency spectrum and spatial structures of field line resonances should be attributed to the inability of the method to provide a natural solution close to the turning points. A direct analytic solution has been formulated to derive the toroidal field line resonance structure. Finally, the solutions thus obtained have been compared with the numerically found exact solutions in order to test the authenticity of the formalism.