Table of contents

On the basis of a high-β, long-wavelength ordering, the Chew-Goldberger-Low (CGL) equations are used to discuss the dynamics and linear stability of a general anisotropic, plasma-vacuum tokamak. The multiple time-scale method is used to derive a reduced set of non-linear MHD equations. To lowest order, the perpendicular component of pressure, p_⊥ ( is not necessarily constant on the flux surfaces, ψ. A simple example of such an equilibrium is given; a heuristic treatment of the Fokker-Planck equation shows that equilibria of this type can only be established by near-perpendicular injection. For practical distribution functions representative of a beam-injected plasma, comparison with the Andreoletti energy principle shows that the CGL principle never overestimates stability. For = (1/2)' (p_|| + p_⊥ constant on flux surfaces, the MHD linear stability of an anisotropic tokamak to long-wavelength modes is identical (within the ordering) with that for the equivalent scalar-pressure tokamak. A similar result has recently been obtained in the limit of short-wavelengths for fixed-boundary modes (ballooning).

A tokamak reactor must have an ignition point which is compatible with the constraints imposed by MHD stability. One important consideration in this regard is the achievable value of β. For a wide class of transport scaling laws, ignition is energetically possible only if β exceeds a specified value, denoted by β_min; β_min must be less than the upper bound on β consistent with MHD stability. For energy confinement times of the form τ_E ∝nT^j, j<1, algebraic relationships for β_min in terms of j and the parameters of the device are obtained. These results are then applied to a typical design of a tokamak ignition experiment.

A non-linear, two-dimensional, resistive MHD computer code to study the non-linear behaviour of the m = 0, 1, and 2 tearing modes in a reversed field pinch is used. For the cases m ≠ 0, a co-ordinate transformation which assumes helical symmetry is employed to reduce the dimensionality of the problem from three to two. The force-free Bessel function model equilibrium is used. It is found that the most dangerous resistive instability in this case is the m = 1 tearing mode, because of its larger growth rate and extended period of exponential growth.

A summary is given of the present status of research on plasma-surface interactions in tokamaks. Three groups of important interactions are considered: recycling of the principal ion species, usually hydrogen or deuterium; the release and effect of low-Z contaminants; and the release and effect of high-Z contaminants. In each case the basic physical processes are reviewed and the relevant data from particlebeam measurements are summarized. Emphasis is given to discussing the effect of the various surface interactions in present-day tokamak discharges and in future fusion reactors. Surface studies in tokamaks are reviewed and methods of controlling the surface interactions and their effects are considered.

For tokamak plasmas which are sufficiently large and/or dense that the ionization source on axis may be neglected, particle balance is achieved by the inward diffusion due to the Ware pinch compensating the outward flow due to both neoclassical and anomalous diffusion. Insertion of measured data into the particle flux balance relation determines the anomalous particle diffusion coefficient D_A; comparison of the results from a variety of tokamaks implies that the dominant dependence on machine and/or plasma parameters is D_A ∝ 1/n. Particle flux balance also implies an upper bound on the central value of β_e, the limiting value being obtained when the plasma parameters are chosen such that D_A≪D_NEO. This limit has been computed for circular-cross-section tokamaks, and the results so obtained are of the same order as magnetohydrodynamic beta limits.

Magnetic-field measurements on a small tokamak, TOSCA, are described. Modified Rogowski and saddle coils are used to determine toroidal multipole moments of the plasma current density, from which the plasma position and shape are derived. Results are presented for a plasma distorted by a hexapole magnetic field.