The shear Alfvén continuous spectrum of axisymmetric toroidal equilibria in the large aspect ratio limit

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Abstract
Analytic forms for the MHD continuous spectra in axisymmetric tokamak equilibria are derived using an expansion scheme in powers of the small inverse aspect ratio. Resulting formulae for the shear Alfvén continuum have been evaluated for the shear Alfvén wave heating experiment on the Tokapole II device at the University of Wisconsin-Madison. Mode coupling, induced by toroidicity or non-circularity, is shown to occur, in first order, on and near rational surfaces for particular poloidal and toroidal mode numbers. The coupling is shown to produce gaps in the spectrum, analogous to the gaps which appear in the energy spectrum of a single electron in a periodic potential lattice.