ON TOROIDAL MODE EIGENFREQUENCIES

The eigenfrequencies of the toroidal magnetohydrodynamic mode (guided mode) have been shown to be spatially dependent and the mathematical description inconsistent under some circumstances by Radoski and McClay. Hruska has indicated that use of non-perfectly conducting boundary conditions will remove the inconsistency and lead to eigenfrequencies of the vibrating string type. We show that retaining perfectly conducting boundaries can also lead to eigenfrequencies of the vibrating string type, if the parallel electric field is explicitly included. The eigenfrequencies are determined not only by boundary conditions at the ends of the magnetic field lines, but also by boundary conditions at the inner and outer radii bounding the cavity. © 1969.