Dispersion relations of toroidal plasma surface waves in quasi-electrostatic state

Dispersion relations of toroidal plasma-surface waves are studied by using the boundary element method for cold plasmas in a quasi-electrostatic state. When sinusoidal waves are assumed for the toroidal direction, a governing equation becomes the axisymmetric modified Helmholtz equation. Application of boundary conditions reduces the study to an analysis of an eigenvalue problem. Fundamental solutions that are used in the analysis depend on the toroidal mode number of the surface waves. Dispersion relations of circular cross-sectional plasmas are in good agreement with exact solutions for parameters of toroidal modes, poloidal modes, and the aspect ratio. Effects of the elongation ratio on the dispersion relations are also studied in the analysis of toroidal plasma with an oval cross section