Table of contents

Quasilinear expressions for anomalous particle and energy fluxes arising from electrostatic plasma turbulence in a Tokamak are reviewed. Further clarifications are made, and the position taken in a previous report (Ross, 1989, Comments Plasma Phys. Contr. Fusion 12, 155) is modified. There, the total energy flux, Q_j, and the conductive heat flux, q_j, were correctly defined, and the anomalous Q_j was correctly calculated. It was shown that the anomalous energy transport can be described by Del .Q_j*, where Q_j*=³/₅Q_j, with all remaining source terms such as (p_j Del .V_j) cancelling. A revised discussion is given of the identification of the anomalous conductive flux, q_j, in which the distinction between Q_j and Q_j* is reconsidered. It is shown that there is more than one consistent way to define q_j. Transport calculations involving only theoretical electrostatic turbulent fluxes are unaffected by these distinctions since Q_j or Q_j*, rather than Q_j, is the quantity naturally calculated in theory. However, an ambiguity remains in experimental transport analysis if the measured particle flux Gamma _j=n_jV_j is to be used in the energy equation to identify the convective terms. This is because the author cannot be sure in general how properly to treat the source terms p_j Del .V_j or (p_j Del .V_j).

Electrostatic wave propagation transverse to a magnetic field B is analyzed in the range of the ion cyclotron frequency in a toroidal device. The electrostatic ion cyclotron waves are excited by means of an electromagnetic signal injected through an antenna system located in the centre of the plasma. For the first time the backward mode is detected in hydrogen and deuterium plasmas. A comparison between the theoretical dispersion relation and the experimental results permits an indirect accurate estimate of the ion temperature, typically in the range 0.05-0.3 eV.

The theory of the resistive evolution of an axisymmetric toroidal plasma hinges on calculating self-consistent conditions on the plasma velocity. These conditions ensure that the plasma proceeds along a sequence of equilibrium states, and at finite aspect ratio involve computing the averages of certain equilibrium quantities around flux surfaces at every time step. The authors utilize the established representation of a large aspect ratio Tokamak equilibrium to show that for this case the flux-surface averages can be evaluated analytically. The resulting transport equations, which can be developed to high order in inverse aspect ratio, are explicitly 1-D while containing effects of both toroidicity and shaping.

Most treatments of ion-cyclotron radio frequency (ICRF) surface waves in Tokamaks use either the equations of magnetohydrodynamics (MHD), or the cold-plasma equations, with the approximation that the electric field parallel to the ambient magnetic field is very small. Although this assumption seems to be well justified, it eliminates the slow wave and its associated hybrid resonances, which turn out to be quite important in studying coaxial and surface modes. In particular, it was believed that coaxial modes do not exist unless there is a vacuum gap between the plasma and vessel wall. It will be shown that this is not the case when the full cold-plasma model is used, and the reason for this result will be considered. Furthermore, it will be seen that for practical purposes, the role of the plasma-vacuum boundary in confining most of the mode to the edge region seems to be taken on by the lower-hybrid resonance layer when a continuous density profile is assumed. The effect of the lower-hybrid resonance layer on the other surface waves predicted in a Tokamak seems to be small.

An integral formulation of pinch equilibrium gives kinetic pressure profiles for plasmas with cylindrical symmetry. This simplified method offers an alternative to solving the Grad-Shafranov equation and leads to closed-form expressions obtained analytically. Results include the explicit dependence of equilibrium on the externally-generated field B₀, and field reversal appears as an intrinsic feature of screw-pinches. Basic insight into Z-pinches, screw-pinches, and (F, theta ) relations comes from the same formalism.

With the use of consistent orderings in epsilon approximately rho _s/a and delta approximately k_{perpendicular to} rho _s model equations are derived for the drift instabilities from the electrostatic two-fluid equations. The electrical resistivity eta included in the system allows the dynamics of both the collisional drift wave instability ( eta not=0) and the collisionless ion temperature gradient driven instability ( eta =0). The model equations also include effects of sheared velocity flows in the equilibrium plasma. The model equations used extensively in earlier nonlinear studies are obtained as appropriate limits of the model equations derived in the authors' work. The effects of electron temperature fluctuations are also discussed.

The authors describe measurements of nonlinear interactions between drift waves and low-frequency flute-like modes in the UMIST quadrupole. They present experimental measurements of the bispectrum, and also results from a technique of 'amplitude correlation' which they believe provides a more direct way of determining the direction of the energy flow. On the basis of the results they propose a model of energy flow in the drift-wave spectrum: the observed spectrum contains regions of growth at high frequency and damping at low frequency, with flow down the spectrum via a cascade mediated by the flute-like modes.

The authors have numerically simulated previously-reported experiments first demonstrating soft-X-ray gain in the 3 to 2 transition in hydrogenic sodium ions at 54.2 AA and find a good agreement with the measured time evolution of this gain. Additionally, they derive from their theoretical model the possibility of obtaining a small gain in the 4 to 2 transition at 40.2 AA. They discuss the results, especially the duration of the gain under the aspect of different lengths of the plasma-producing laser pulses.