Natural resonances on rational surfaces in toroidal plasmas

The continuous frequency spectrum of the torsional Alfven wave in a toroidal plasma is known to contain gaps in the spectrum which are associated with mode coupling on and near rational surfaces. It is shown in this paper that the frequency spectrum is incomplete and that the gaps will be occupied by natural torsional wave resonances due to poloidally and radially localised standing waves on and near the rational surfaces. The natural resonances, previously assumed not to exist, may in fact play an important role not only in RF heating schemes but also in determining the stability of toroidal plasmas. Natural resonances of the ion acoustic wave are also discussed and shown to have many features in common with Mirnov oscillations