Table of contents

The generation of longitudinal currents in a magnetically confined plasma with travelling monochromatic electromagnetic waves of finite amplitude propagating at some angle to the external magnetic field is considered. By averaging over the particle cyclotron gyration period, the kinetic equation for the distribution function of electrons interacting with an electromagnetic wave is derived. This equation is solved for the case of low-frequency waves, on the assumption that the bounce period of electrons trapped by the wave field is small compared to the typical times of Coulomb collisions (in which case, the driving current is largest). From the solution obtained, analytic expressions for the driving current and the absorbed power, which are valid for a wide range of wave phase velocities, are found. The current drive method considered and the method using the wave packet are compared.

Previously, the production of stable high-beta plasmas in the University of Wisconsin Levitated Toroidal Octupole has been reported. The plasma beta measured in the bad-curvature region ranges from β ~ 8% to 44% (n_e ≈ (2–5) × 10¹³ cm⁻³, B_pol ≈ 200–860 G) in macroscopically stable plasmas with decay times in excess of 1000 Alfvén times. In this paper, theoretical work performed on non-MHD effects to explain the significant enhancement of plasma stability above the ideal-MHD ballooning instability limit of 4% is described. The effects are included in finite-n MHD theory and a detailed kinetic treatment including finite Larmor radius (FLR) and heat flow along field lines. The FLR effects are sufficient to explain the stability of the β = 8% plasma through coupling of the ballooning mode to a stable oscillatory ion drift wave. This cannot explain the stability of the more collisional, larger-gyroradius β = 44% plasma. Equilibrium diamagnetism is strongly affected by ion gyroviscosity in this plasma, and the role of this effect on the equilibrium and stability is discussed.

Convective transport of fast ions in the toroidal field ripples of a tokamak was investigated experimentally and theoretically. Comprehensive numerical computations of this effect were performed on the basis of the previously developed theory. Simultaneously, detailed experimental studies were made of the energetic ions in the T-4 and T-10 tokamaks. The experiments demonstrate that the ion distribution function is substantially different from the Maxwellian one, being strongly enriched with fast particles at the plasma column periphery. The local trapped-ion distribution is, in addition, asymmetric throughout the plasma cross-section. A detailed comparison with the numerical results shows that the observed effects can be explained in terms of the kinetic convective transport theory. Kinetic convection is shown to contribute significantly to energy transport. With increasing ion temperature, convective ripple transport may become dominant. Therefore, the variation of rippling may become an effective means of controlling the temperature and ignition regimes of a thermonuclear reactor. The results obtained demonstrate that transport processes in modern tokamaks have to be described in terms of kinetic theory.

Experimentally measured growth rates of the positional instability of vertically elongated plasmas in Doublet III are compared with those obtained from a numerical code based on linear perturbation theory. The relevant elements of the circumstances of the experiment have been included in the code. The perturbations of plasma currents and currents in the wall of the vacuum vessel as well as in the coils surrounding the plasma are included in the model. The modelling of the complicated external circuitry of the coils is based on a simple assumption which was supported by observation. Comparison of the measured growth rates with those calculated suggests that the essential phenomena are adequately described by the model.

The paper considers the transport of banana particles in a rippled magnetic field over the entire energy range. It is shown that all familiar regimes of ripple transport – ripple-plateau, banana-drift and stochastic – can be described in a unified manner. The general expression obtained for the rippled fluxes of banana particles describes, apart from the already familiar regimes, also the as yet unstudied energy region between the drift and stochastic regimes. A generalized ripple-banana thermal conductivity coefficient, , is calculated.

Analytical and numerical results of physical processes taking place around the second-harmonic resonance surface in ICRF heating are presented. It is shown that (1) symmetry of transmission coefficients follow from Onsager's reciprocity relation of the dielectric tensor, and (2) direct dissipation around the cyclotron harmonic layer is mostly due to the Bernstein branch and depends on k_||, becoming low for low k_||. The latter has the consequence that mode conversion and reflection are sensitively reduced by damping, but transmission is not.

Edge-plasma turbulence was investigated over a wide range of plasma and field parameters in the Caltech research tokamak. Fluctuation levels and spectra were measured using Langmuir probes in the region r/a = 0.75–1.0. Under almost all conditions the edge plasma was turbulently unstable, with a broadband fluctuation spectrum in the drift-wave range of frequencies f = 10–1000 kHz. A stable state was observed only in the very cold, low-current discharges formed at unusually high neutral filling pressure. Otherwise, the relative fluctuation level as monitored by the ion saturation current J⁺ was very high, in the range ⁺/⁺ ≅ 0.2–0.8, while the fluctuation power spectra were roughly invariant in shape. The relative fluctuation level was always highest near the wall and decreased monotonically toward the plasma centre. The same edge turbulence was observed with or without an outer limiter present. The relative fluctuation level was observed to be independent of the local collisionality over a range of nearly 100. The radial variation of ⁺/⁺ can be related to the radial density scale length L_n by ⁺/⁺ ≅ (3–5)ρ_s/L_n.

Toroidal and poloidal rotation has been measured in the Poloidal Divertor Experiment (PDX) tokamak in Ohmic and neutral-beam heated plasmas in a variety of discharge conditions and in both circular and diverted configurations. Rotation velocities were deduced from Doppler shifts of magnetic dipole (M1) lines and lines of optically allowed transitions in the visible and UV regions, from K_α emission, and also from an array of magnetic pickup loops. Poloidal and toroidal rotation velocities in Ohmically heated discharges were usually less than 3 × 10⁵ cm·s⁻¹. Near the plasma edge, the toroidal rotation velocity varies with poloidal angle both before and during neutral-beam injection. No systematic poloidal rotation was observed during neutral-beam injection centred about or displaced 10 cm from the horizontal midplane, which implies that the poloidal damping time τ_θ < 0.5 τ_ii consistent with theoretical estimates. The central toroidal rotation velocity during neutral-beam injection scales linearly with the quantity and is independent of plasma current and toroidal magnetic field. The toroidal rotation velocity is higher in deuterium than in hydrogen plasmas, and also in diverted discharges as compared with circular ones. Toroidal rotation decay times after injection range from 80–100 ms at the centre to 160–180 ms at half the minor radius. Modelling of the radial profile of toroidal rotation indicates a central momentum diffusivity of the order of 8 × 10³ cm²·s⁻¹. This is approximately a factor of three higher than the momentum diffusivity obtained from the decay time. All present theories are inadequate in accounting for the observed damping rate of v_ϕ.

Vertical poloidal asymmetries of hydrogen isotopes and low-Z impurity radiation in the PDX tokamak may be caused by poloidally asymmetric sources of these elements at gas inlet valves, limiters or vacuum vessel walls, asymmetric magnetic-field geometry in the region beyond the plasma boundary, or by ion curvature drifts. Low ionization states of carbon (C II to C IV) are more easily affected by edge conditions than is C V. Vertical poloidal asymmetries of C V are correlated with the direction of the toroidal field. The magnitude of the asymmetry agrees with the predictions of a quasi-fluid neoclassical model. Experimental data and numerical simulations are presented to investigate different models of impurity poloidal asymmetries.

Internal disruptions found by soft-X-ray and electron cyclotron emission measurements can be explained in terms of a non-linear evolution of the unstable m = 1/n = 1 internal kink mode and subsequent reconnection of the magnetic field lines due to finite resistivity. The linear growth rate is found to be proportional to for a fixed external rotational transform, where r_s denotes the position of the inner q = 1 surface.

Impurity sources and confinement times in the central cell of TMX were examined by studying the extreme ultraviolet (EUV) emissions from intrinsic and injected impurities. Impurity ions from gases puffed radially toward the central-cell plasma showed very little radial penetration into the plasma. The confinement times of highly ionized intrinsic and injected impurities in the central cell were of the order of or less than the deuterium ion confinement times; the ambient density ratios of O V to O VI indicate overall O VI confinement times near the axis of 0.3 to 3 ms. Impurities introduced into the central-cell plasma were not detected in either end-cell plasma, indicating that axial losses of impurities from the central cell were small. This result agrees with theoretical calculations of the axial confinement times and suggests that most of the losses were radial. The radial flux of impurity ions determined from the measured radial profiles of the ambient impurity ion densities is primarily outward; the magnitude of these fluxes also implies a short confinement time for impurity ions.

The nine-channel 337 μm interferometer/polarimeter on the TEXTOR tokamak has been used to detect and control the horizontal plasma position in two different ways. (1) The phase shift between two vertical probing beams located at a distance of x/a = ±0.6 from the vessel centre yields the difference of electron line densities along these trajectories and indicates displacements or asymmetries of the density profile. (2) Faraday rotation measurements on a probing beam passing vertically through the vessel centre allow horizontal shifts of the magnetic flux surfaces to be detected. Both the phase shift and Faraday rotation signals have been applied as control quantities to the TEXTOR feedback system, resulting in good positional stability for discharge durations of more than 2.5 seconds.

The radiation loss rate for iron ions has been determined at T_e = 45 eV in a theta-pinch plasma. The intensities of almost all strong vacuum-ultraviolet lines of Fe VII-XI ions were measured, and the total radiative power was obtained from the observed line intensities. The iron impurity concentration was derived from the absolute intensity of the Fe X forbidden line. The experimental radiation loss rate is compared with calculations.

Measurements are presented of Balmer alpha line profiles from plasma ions which have been neutralized by charge exchange with injected neutral hydrogen beams in the DITE tokamak. Doppler broadening of the Hα line is interpreted in terms of the ion temperature and line profiles are compared with neutral particle energy spectra in the regime where the plasma is transparent to the transport of neutrals from the core to the boundary. An asymmetry in the charge-exchange line profile is interpreted in terms of plasma rotation during neutral beam injection. The advantage of this method over conventional neutral analysis is seen in the context of the diagnosis of large, hot and dense tokamak plasmas.

A study of runaway electrons has been made during the current rise stage of discharges in tokamak LT-4. The bremsstrahlung from a small target just inside the plasma boundary was measured as a function of q (target). The correlation between X-ray bursts and integer q was established over a large range of q-values. It is suggested that lower-energy runaway electrons are carried with the expanding integer-q regions and that an upper limit could be placed on the energy of electrons surviving within the plasma.

A simple tandem-mirror coil system is found which has the property that the geodesic curvature of the paraxial magnetic field is locally small everywhere. This design approaches the ideal of a 'locally omnigenous' configuration in which the particle drift surfaces coincide with the magnetic flux surfaces. Thus, radial losses due to resonant ion and stochastic radial diffusion are minimized. Plasma distortion due to central-cell parallel currents and instability due to trapped particles are also greatly reduced. The advantages and disadvantages of the design for reactor applications are discussed.

The bounce-averaged particle drifts in an axisymmetric toroidal plasma are calculated for the case of a large-aspect-ratio tokamak equilibrium with circular surfaces but a local pressure gradient comparable with the ideal MHD ballooning limit: dp/dr ~B²/Rq².

A numerical study was carried out to find an extension of Trubnikov's formula for cyclotron radiation loss which is valid at relativistic temperatures. It is found that for temperatures up to 1000 keV the loss can be fit by minor modification of the original result.