Ballooning Modes or Fourier Modes in a Toroidal Plasma?

The relationship between two different descriptions of eigenmodes in a torus is investigated. In one the eigenmodes are similar to Fourier modes in a cylinder and are highly localised near a particular rational surface. In the other they are the ballooning modes which extend over many rational surfaces. A model which represents both drift waves and resistive interchanges is used to investigate the transition from one of these structures to the other. In this simplified model the transition depends on a single parameter which embodies the competition between toroidal coupling of Fourier modes which enhances ballooning and another which diminishes ballooning. As the coupling is increased each Fourier mode acquires a sideband on an adjacent rational surface and these sidebands then expand across the radius to form the extended mode described by the conventional ballooning mode approximation. This analysis shows the ballooning approximation is appropriate for drift waves in a tokamak but not for resistive interchanges in a pinch. In the latter the conventional ballooning effect is negligible but they may nevertheless show a ballooning feature. This is localised near the same rational surface as the primary Fourier mode and so does not lead to a radially extended structure.