Table of contents

The plasma flow velocity into the divertor chamber of the FM-1 Spherator is determined by measuring the propagation velocity of ion acoustic waves. The observed parametric dependence of plasma flow into the divertor is consistent with the plasma sheath model, which is now frequently used for designing poloidal divertor devices.

The behaviour of low-frequency drift waves in a two-species plasma under the influence of a large-amplitude spatially uniform electric field oscillating at the ion-ion hybrid frequency and applied across an ambient static magnetic field has been studied. The threshold powers for the parametric excitation of these drift waves are calculated and the characteristics of the dispersion relation near threshold and well above threshold are examined. At large applied powers (much above threshold), interesting modifications of the natural drift modes are found.

The influence of a stochastically varying laser frequency or finite laser bandwidth upon non-linear reflection processes occurring for laser radiation incident on a plasma is considered. It is shown that the penetration efficiency can be greatly enhanced by introducing a certain amount of noisiness into laser radiation.

The feasibility of a hot plasma injector using a divertor based on a magnetic neutral point discharge is studied experimentally. An intense plasma current magnetic neutral point discharge is induced along a circular magnetic neutral line of the divertor, and the plasma is heated and injected inward to the central region. The plasma diffusing along the magnetic field lines is measured by a time-of-flight method using a pair of electrostatic double probes, and it is shown that the average energy of the diffusing plasma ions is 200 eV and the total amount of injected particles is 6 × 10¹⁶ particles per shot. The possible use of the divertor injector in a fusion reactor is discussed.

The stability of a finite-amplitude monochromatic Langmuir wave is considered in one dimension. A dispersion relation is obtained which includes the decay, purely growing and modulational instabilities. It is shown that for an infinite-wavelength Langmuir pump wave the modulational and oscillating two-stream instabilities are the same. It is also pointed out that the threshold for the modulational instability is equal to the threshold for the inverse oscillating two-stream instability, in which the Langmuir wave energy is converted into electromagnetic radiation.

An analytic model is presented for calculating the endloss from a linear θ-pinch. The model includes all the important physics features of previously derived theories (i.e. a throat condition and an area wave) as well as extends the results to include diffuse profiles. The results are compared with experiment. Despite the relative level of sophistication in the model, the conclusion is that the theory gives qualitative, but not quantitative agreement with experiment. The present theory does give better agreement than the previous theories, but nonetheless there are still significant differences with regard to experiment.

The equilibrium equations are solved for tokamaks with non-circular cross-sections, by the method of the expansion in powers of the inverse aspect ratio. The analysis is extended to a more general class of equilibria, especially to study the effect of non-uniformity of plasma current distribution.

For tokamaks with non-circular cross-sections, a simplified condition of stability against localized flute disturbances is obtained, which is a direct extension of Shafranov and Yurchenko's result. The kinds of variation of the cross-sections of the magnetic surfaces which improve the stability criterion are considered.

The effect of a finite-bandwith pump on the parametric instability is considered. First, the temporal problem with unequal damping rates is considered, with bandwidth modelled by a Kubo-Anderson process. Exact results are obtained for both the amplitudes and power in each decay mode, with an interesting asymmetry found. Next, the spatial problem with unequal group velocities is investigated for the cases of 1) finite homogeneous interaction region, and 2) linear density profile. Thresholds and growthrates are found including both the inhomogeneity and bandwidth effects. When values typical of laser fusion parameters are inserted, it is found that bandwidth may be an important method of stabilizing Raman and Brillouin scattering.

Present high-current ion sources for neutral injection experiments accelerate a mixture of atomic and molecular hydrogen species that are converted into neutral particles with different energies and neutralization efficiencies. Beam composition can have important effects on injection system efficiency, vacuum design, and first-wall loading. Beam composition measurements of the 20-keV LBL high-current sources are used to calculate the relative power in the various hydrogen and deuterium beam components expected at higher energies.

Some general scaling laws for the (idealized) linear theta pinch are derived with the magnetic field strength as the independent variable. These scaling laws are used to calculate machine parameters, such as length, confinement time, magnetic energy storage requirements, etc. for five potential linear theta-pinch applications of interest to CTR: (a) a confinement experiment to achieve the Lawson criterion; (2) a power-producing theta-pinch reactor; (3) a power-producing laser-heated reactor; (4) a radiation and materials test facility (FERF); and (5) a fusion/fission hybrid reactor. In each case the advantages of operating at large values of magnetic field strength are shown quantitatively. Some potential problem areas for the high-field (and therefore high-density) linear theta pinch are identified and discussed.

A procedure is described which allows the evaluation of the vacuum magnetic field produced in a torus by a given system of azimuthal currents under appropriate boundary conditions. The solution is given in the form of a power series of , the inverse aspect ratio, which converges for any smaller than a well-defined upper bound ^*. The first-order term of this series is explicitly computed by contour integration.

The stability of axially symmetric equilibria with respect to rigid displacements is studied by means of the energy principle. For horizontal displacements and flipping, the vacuum term is neglected, thus affording sufficient stability criteria. For vertical displacements the vacuum term is kept, thus yielding a necessary and sufficient condition. The resulting stability criteria are applied to simple algebraic equilibria and numerical results are presented.

Most investigations of feedback control of magnetically confined plasma have used the approach in which the control variable is the perturbed plasma density. In this paper, the use of another basic type of feedback control, namely the (φ-φ) type, in which the control variable is the local potential perturbation is examined. The basic equations for the study of electrostatic oscillations in inhomogeneous magnetized plasma are deduced and the results are applied to some known mirror instabilities. It is found that for present-day amplification systems the threshold densities set by microinstabilities can be increased by factors of the order of 100 or more and that, in some cases, geometric stabilization can also be achieved by feedback control.

Fluctuations and anomalous particle loss of a xenon afterglow plasma, which appear immediately after the decay of convective cells in an ℓ = 3 stellarator, are investigated experimentally. This instability is caused by a static electric field directed into plasma. The fluctuation propagates in the direction of the ₀×₀ rotation, which is parallel to the electron diamagnetic current, and is expressed as exp[i(mθ + nϕ − ωt)], m = 2 and n = − l , where θ is measured in the poloidal and ø in the toroidal direction.

A dispersion relation is derived from a model in which there is a difference of rotation velocity between ions and electrons, and the electron-ion collision in the electron motion parallel to the magnetic field is included. The difference in rotation velocities comes from the effect of finite ion Larmor radius and the centrifugal force. The dispersion relation derived here also includes the resistive drift instability. The growth rate takes maximum values on the rational magnetic surfaces. Predictions on the basis of the dispersion relations are in good agreement with observed wave propagation, frequency, growth rate, and plasma loss.

A study is made of the spectral distribution of the soft X-ray emission produced by the thermal part of the electron velocity distribution in the ST Tokamak. The slopes of the spectra are in good agreement with the prediction from laser measurement of electron temperature if radial profile effects are taken into account. The absolute intensity is a factor 5 to 100 larger than is expected for hydrogen bremsstrahlung. This enhancement can be quantitatively accounted for by recombination radiation from oxygen and heavy-metal impurities. The enhancement factor ζ was measured at different radii, in order to study the impurity distribution in the tokamak. These, as well as other experiments, in which high-Z gases (Xe, Kr, A) were pulsed into the discharge, indicated that, within the measuring accuracy, Z_eff does not vary substantially with radius.

Helium discharges have been produced in the ST Tokamak with electron densities exceeding 10¹⁴ cm⁻³, with less than 1% oxygen (and other light impurities) and less than 0.05% metallic impurities. In such discharges, the effect of the impurities on the plasma resistivity is relatively unimportant, and, consequently, the usual ambiguities about the radial current distribution are unusually small. We find, consistently with previous experiments and in spite of various quantitative differences, that the plasma resistance is determined by Spitzer resistivity, that the rise of electron temperature is limited by the development of the q = 1 surface and that the electron kinetic energy confinement time is equal to the average particle confinement time. Energy loss by electrons constitutes about three quarters of the total and is roughly divided between line radiation and kinetic energy transport.

In summarizing the results of this Conference, the first fact we note is that transition to toroidal machines is nearly complete now in both high- and low-β physics, with one exception, – the mirror machines.