J. W. Connor

Toroidal rotation and momentum transport

The authors re-examine the transport of momentum in a collisional plasma rotating at sonic speeds. The slowing down rate due to collisional transport is found to be classical ( tau m-1 approximately nu ii rho i2/a2) and the presence of impurities does not change the order of magnitude of this theoretical result. Thus collisional transport theory cannot explain the anomalously high loss rates observed experimentally. Some existing theories of collisional momentum loss are discussed in detail.

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.

Micro-tearing stability in Tokamaks

The resonant layer equations governing tearing and micro-tearing modes in toroidal geometry are formulated and solved for a plasma in the banana regime and for wavelengths in the intermediate collisionality range nu e< omega *e< nu e/ epsilon . It is shown that stability of such tearing modes is determined by a competition between destabilizing trapped electron dissipation and stabilizing effects arising from ion magnetization and collisional broadening of the passing-electron Landau resonance. Analytic stability criteria are derived, but for realistic parameters these modes are predicted to be stable.

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.

Heat-pulse propagation in tokamaks and the role of density perturbations

Studies of the propagation of heat pulses, launched by a sawtooth collapse or by modulated auxiliary heating, yield information on transport properties in the Tokamak. Corresponding values of the thermal conductivity are often found to be significantly larger than values obtained from power balance calculations. A full treatment of the heat pulse must, however, include possible coupling to an associated density pulse. Such effects are discussed in the context both of neoclassical transport theory and of a model of anomalous transport due to drift waves. It is found that the discrepancies between heat pulse and power balance measurements could arise from coupling between density and temperature perturbations due to the presence of off-diagonal terms in the transport matrix.