Stability of general plasma equilibria. III

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Abstract
For pt.II see ibid., vol.23, p.265 (1971). A general method for investigating stability of low-frequency electrostatic oscillations of magnetically confined plasma, which was developed in Part I (1968) for equilibria with closed field lines (e.g. multipoles), is extended to axisymmetric toroidal equilibria with finite magnetic shear (e.g. Tokamaks). The analysis encompasses all perturbations whose parallel wavelengths are comparable to equilibrium scale lengths and whose perpendicular wavelengths are comparable to ion Larmor radii. Once the problem of reconciling these characteristics with toroidal periodicity has been overcome, the investigation of any axisymmetric toroidal equilibrium becomes very similar to that of closed line equilibria and the ion and electron charge densities resulting from an arbitrary potential perturbation are calculated by a small Larmor radius expansion as in Part I. Using these expressions the determination of stability is reduced to a single one dimensional integro-differential equation-which must be solved numerically for each given equilibrium. In the most general case this requires considerable computation, but in many circumstances one can use simpler approximate forms of this equation which are also derived.