Table of contents

An analysis is presented of the collisionless transport of particles and energy from a tokamak reactor plasma to a divertor target. Account is taken of the cooling effects of both unburnt fuel from the reactor and of secondary electrons emitted from the target. Even so, the temperature of the exhaust plasma is high and the potential of the target sheath exceeds the thresholds for unipolar arcing unless the burn-up fraction is impracticably low, i.e. f_B < 10⁻³. It would thus appear that the exhaust of a reactor by purely collisionless processes will pose formidable problems, and it is desirable to introduce additional mechanisms for cooling the electrons in the exhaust plasma.

A number of new methods are discussed for determining the electron heat conduction coefficient χ_e in a tokamak from the experimental observation of the space-time evolution of the temperature perturbations induced by internal disruptions. In the Oak Ridge Tokamak (ORMAK) the various average values of χ_e and the radial dependence of χ_e are found to be consistent with and more precise than the χ_e(r) determined by conventionally analysing the electron power balance equation. The net result of these measurements is to conclusively prove that the dominant radial electron heat transport mechanism in tokamaks is a microscopic, diffusive process.

An analytical theory of ideal-MHD ballooning modes that can be excited in finite-β equilibria is carried out on model configurations which include the effects of the increase of the poloidal field toward the outer edge of the plasma column and the dependence of the rate of magnetic shear on the poloidal angle. The relevant growth rates and eigensolutions are, in fact, significantly different from those derived on the basis of 'low-β' model configurations that omit one or both of the effects mentioned above, and provide different indications for the expected interaction between ideal-MHD and kinetic modes. For each value of the shear parameter , the normalized growth rate Γ becomes real at a critical value of the dimensionless pressure gradient parameter G. When the latter is increased at constant , Γ is found to increase only up to a saturation point, after which it decreases and tends to vanish at a second critical value of G.

Variations of the intensities of spectral lines are utilized to determine the extent to which the impurity concentrations of ORMAK-produced plasmas are altered by neutral-beam injection and, in some cases, by the simultaneous introduction of a puff of hydrogen. Concurrent variations of oxygen emissions resulting from alterations in the profiles of electron temperatures and concentrations are taken into account through solving the coupled continuity equations of the several ionic species of this element. Ad-hoc transport velocities are utilized and a complete re-cycling model is assumed.

Extensive numerical studies of ideal-MHD instabilities have been carried out to gain insight into the parametric dependence of critical β's in tokamaks. The large number of interrelated equilibrium quantities involved in establishing a critical β has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the parameter regimes appropriate to both current and reactor-sized plasmas. A moderate dependence on the pressure profile and a strong variation with the current profile is found. The principal result is that, for aspect ratio R/a ≈ 3, critical β's are of the order of 2% for circular cross-sections and 5% for plasmas with elongation K ≈2; somewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analysed to compare critical β as a function of toroidal mode number n. It is concluded that the infinite-n analytic ballooning theory provides a sufficient condition for ideal-MHD internal-mode stability. Low-n free-boundary modes appear to set a lower lim̀it.

Encouraging results with neutral-beam heating and adiabatic compression of tokamak plasmas have prompted new experiments which will study the approach to high-β states. As projected tokamak β-values become non-negligible (average β of 4% is the goal), the models previously used for transport calculations will become inadequate. The models will now be required to account for the evolution of the magnetic geometry, along with the change in plasma parameters. An axisymmetric-transport model is presented, which should be useful for studying the approach to higher β-values in tokamak experiments. Results from transport calculations with this model allow an analysis of the limits to β in two seemingly unrelated experiments: electron heating by neutral injection in the ORMAK device and adiabatic compression in the ATC experiment. By extrapolating empirical models for plasma transport, it is found that flux conserving (FCT) equilibria ought to be accessible by means of neutral beam heating. Finally, it is found that the nature of cross-field transport may be expected to change as significant β-values are reached. Enhanced transport from ballooning instabilities is likely to play a role as important as that now played by sawtooth (m = 1) and saturated (m = 2) instabilities. New techniques for describing this transport are required.

The non-linear behaviour of the drift-tearing instability is investigated within the two-fluid theory. It is shown analytically and verified in numerial computations that diamagnetic effects and ion gyroviscosity, which determine the frequency of the linear mode, are quenched at a magnetic-island size of the order of the resistive-layer width. For finite island width, growth and saturation of the mode depend only on resistivity and current profile, while its frequency is determined by the rotation of the plasma.

Experimental and theoretical studies of runaway electrons in toroidal devices are reviewed here, with particular reference to tokamaks. The complex phenomenology of runaway effects, which have been the subject of research for the past twenty years, is organized within the framework of a number of physical models. The mechanisms and rates for runaway production are discussed first, followed by sections on runaway-driven kinetic relaxation processes and runaway orbit confinement. Next, the equilibrium and stability of runaway-dominated discharges are reviewed. Models for runaway production at early times in the discharge and the scaling of runaway phenomena to larger devices are also discussed. Finally, detection techniques and possible applications of runaways are mentioned.

Plasma transport across the magnetic field is studied in the presence of resonant helical magnetic perturbations giving rise to isolated magnetic islands.

Profiles that are stable against MHD instabilities are given in a cylindrical current-carrying stellarator. The comparison theorem, i.e. the guiding principle for stabilization, is obtained in the same way as in a tokamak. As the external rotational transform due to an ℓ = 2 helical field increases, the MHD properties become better than those of a tokamak, and the minimum value of q(a) providing simultaneous stabilization of MHD modes can be reduced to a value lower than two, even without a conducting shell. In an ℓ = 3 stellarator, however, as is shown from the Euler equation, the configuration becomes more unstable than in a tokamak, and strong current profile tailoring is necessary to stabilize the modes.

The radiation instability occurring in a multi-component plasma due to the 'temperature screening' effect is studied. This instability results in the formation of heavy-ion clusters within a time shorter than the radiation cooling time of the plasma