R. J. Hastie

Ideal MHD ballooning stability in the vicinity of a separatrix

Using a model tokamak equilibrium, the influence of a magnetic separatrix on the stability of the plasma against ideal MHD ballooning modes is investigated. It is found that there is no significant stabilizing effect from the strong global shear near the separatrix, but rather that marginal stability is controlled mainly by the poloidal position of the X-point. A physical interpretation of these results is given.

On the difficulty of determining tearing mode stability

The effect of local pressure gradients and of a local flattening of the pressure profile (p to 0) around the resonant surface of a tearing mode is investigated in toroidal geometry. It is shown that the stability index Delta , calculated from the ideal outer region, is modified by local profile changes in a way reminiscent of the favourable curvature stabilization of linear and nonlinear tearing mode layer theory. If the width of the region of pressure flattening is of the order of the linear resistive layer width, the stabilization from the ideal outer region compensates for the loss of pressure gradient stabilization from the layer, and the overall stability of the mode is largely unaffected. For pressure flattening over a larger region, however, the mode can be strongly destabilized. Since the flattening region may then still be too small to resolve experimentally, this result implies the essential difficulty of determining the tearing mode stability of experimental profiles.

Stability of general plasma equilibria. III

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.

Resistive ballooning modes and the second region of stability

Resistive ballooning modes are unstable in the first region of ideal ballooning stability. The authors show that in contrast the second region is largely stable to resistive ballooning modes.

Stability of anisotropic-pressure tokamak equilibria to ideal ballooning modes

The effect of pressure anisotropy on the stability of ideal-MHD ballooning modes is studied for a large-aspect-ratio tokamak of circular cross-section. Significant increase of the perpendicular energy of electrons or ions can cause strong modifications of the stability boundary, especially at low shear.

Alpha particle induced magnetoacoustic instability in a thermonuclear plasma

The authors show that in a thermonuclear plasma the magnetosonic wave propagating normal to the magnetic field can be unstable. The growth rate is small, however, and the wave is easily stabilized by perpendicular thermal conduction.