Table of contents

Using analytical methods, the authors investigate the axial region of the magnetic configurations of ℓ = 3 traps (stellarator and torsatron) when a uniform transverse field is present. They determine the conditions necessary for the existence of a rosette-type structure of the magnetic surfaces in the axial region as a function of various magnetic trap parameters such as toroidality, the angle of inclination of the helical conductors and the strength of the transverse field. Expressions are found for the critical transverse magnetic field value at which the rosette-type structure disappears.

The stabilization of the Alfvén wave instability in a two-component tokamak is investigated theoretically. It is assumed that the instability is caused by fast ions which form in the tokamak when fast neutral atoms are injected into it. Dissipation through collisions with trapped electrons is considered to be a stabilizing factor. The method developed by Timofeev for considering initial perturbations is employed. It is shown that the influence of dissipation through collisions with trapped electrons on the "local" growth rate of the instability of an ion beam is insignificant in cases of practical interest. Such collisional dissipation is also insignificant as regards the evolution of initial perturbations if the thermal spread of the beam is not too great. It can, however, play an appreciable role in the case of very diffuse beams. This opens up the possibility of suppressing Alfvén instability by injecting into a tokamak neutral atoms with a broad energy spectrum.

The transfer function of a magnetic mirror plasma containing a feedback loop is measured experimentally. The measurements are obtained in a configuration where 1) the interchange mode is weakly damped, and 2) the interchange mode is unstable, but stabilized by the feedback loop. The results are in good agreement with the theoretically derived transfer function involving parameters (e.g. damping rates) determined by fitting the theoretical curve to the data. This method of analysis has diagnostic utility for mode identification and the measurement of damping rates.

A hot plasma can be analysed by means of soft-X-ray fluxes using various absorbers. In the first part of the paper, the method of calculation of the flux as a function of T_e, Z_eff, n_e and their profiles is given. The problem of relativistic corrections in the evaluation of the Gaunt factor is also considered. As an example, in a 200-kA discharge in TFR, the measured fluxes are compared to those calculated for a Maxwellian electron distribution function. From this comparison, the electron temperature is determined and information on the impurity content in the plasma is obtained, in agreement with other independent measurements.

This paper reports calculations of the growth of Rayleigh-Taylor instabilities (1) in the ablator-pusher region such as may be caused by irregularities in an electron beam, and (2) in the pusher-fuel interface, a problem common to all inertial confinement fusion targets. For the first case, it is found that long density gradient scale lengths and scattering of the beam by the target both stabilize the shorter-wavelength instabilities, which would otherwise grow most rapidly of all. In the second case, it is found that moderately-short-wavelength instabilities may not degrade the target performance as much as has previously been supposed.

A set of linear inhomogeneous time-dependent ordinary differential equations is derived to describe the dynamical interaction of the long-wavelength m = 1 instability with the stable oscillations to which it couples. The equations provide an algorithm for determining the plasma response to external feedback control fields. The method is based upon the new Scyllac ordering developed by Weitzner. The results agree with the steady-state equation of Ribe and Rosenbluth. The obtained m = 1 growth rates also agree with previous new-ordering results for a pure ℓ = 0 or ℓ = 2 system, but for a combined ℓ = 0 and ℓ = 2 system the equations have two distinct unstable eigenvalues corresponding to horizontal and vertical growth rates.

The absorption coefficient of the magnetosonic wave at the ion cyclotron resonance is evaluated, in the limit of rare collisions, for a toroidal plasma with due allowance for the effect of the rotational transform. It is found that, when the parallel wave number k_z imposed by the external coupling structure is small, the power absorption is much larger than that previously evaluated; it is independent of k_z and does not vanish, as in a uniform magnetic field, for k_z = 0. The plasma loading of an external coupling structure and the radial dependence of the absorbed power are evaluated. A critical radius above which the toroidal modes overlap, allowing for a small Q-value of the launching structure over a wide density range, is deduced.

For a sharp-boundary, constant-pressure plasma model of axisymmetric equilibria the MHD-stability problem of axisymmetric perturbations is solved by analytic reduction to a one-dimensional problem on the boundary and subsequent numerical treatment, using the energy principle. The stability boundaries are determined for arbitrary aspect ratio, arbitrary β_p and elliptical, triangular and rectangular plasma crosssections, wall stabilization not being taken into account. It is found that axisymmetric stability strongly depends on the plasma shape and is almost independent of the safety factor q.

The effect of impurities on low-frequency drift modes of a toroidally confined plasma is investigated by the gyro-kinetic equation. It is assumed that the electrons are in the banana and the ions in the plateau regime. Impurity collision damping is found to be significant in the usual trapped-electron mode. A new instability due to the impurities can occur for normal profiles and impurities peaked at the centre. Quasilinear considerations show that impurities will be driven outward if such an instability occurs.

A one-dimensional analytical model is applied to super-compression of a structured slab. The time dependence of the laser light input power is derived to obtain optimum compression of structured slabs. The effect of thermal conduction on the compression is also considered.

Numerical computation of closed, vacuum magnetic field configurations is discussed. Comparisons are made of several representations of the fields of various stellarator systems. The calculations are extended to evaluate hybrid configurations which incorporate both stellarator-like fields and axisymmetric fields. Results are given to show that large shear, large rotational transform, and large magnetic-well depth can be obtained.

The paper studies the Hall effect in a gas-discharge plasma and its influence on the discharge dynamics. A qualitative analysis is made of the importance of the Hall effect in a non-cylindrical Z-pinch. It is shown that long before the instant of collapse of the plasma on the discharge axis, its electron component is strongly magnetized, and the Hall electric fields predominate over the Ohmic fields. The authors present the main results of a two-dimensional calculation in which the boundary conditions are used as a means of taking the Hall effect into account. The discharge dynamics obtained in the calculation are similar to the actual dynamics found for one of the non-cylindrical Z-pinch regimes.

Supplementary wave heating is examined for two-ion-species plasmas from the fundamental tritium cyclotron resonance (ω = ω_CT) to the first deuteron harmonic (ω = 2ω_CD). At the first harmonic, it is found that a sufficiently large parallel wavelength greatly reduces the region of confluence between the fast wave and ion Bernstein wave. Power absorption considerations neglecting mode conversion processes show that first-harmonic heating efficiency is relatively insensitive to the species concentrations and that a dominant ion heating can be expected. For minority heating at the fundamental deuteron resonance, it is shown that inclusion of the two-ion hybrid resonance absorption considerably lowers the Q from the case where only minority species cyclotron damping is considered.

Hydrodynamic calculations of shell implosions show a marked dependence on laser wavelength for wavelengths less than 1 μm. The coupling to the dense imploded shell rises from 6% at 1 μm to 33% at 0.1 μm, increasing possible energy multiplication in a pellet from approximately 60 to 400.

The ion velocity distributions of tokamak plasmas sustained by injected fast atomic beams fall into three categories, according to the partial pressure of the energetic-ion population, which in turn is determined by the plasma nτ_E, the injection energy, and the fraction of plasma fuelling performed by the beams. There are correspondingly three regimes of beam-driven reactor operation in D-T or D-D: thermonuclear; beam-target or TCT; and plasmas with ion pressure/electron pressure ≫ 1. This review treats the physical basis and plasma engineering parameters of beam-driven tokamak reactors. The theories of energetic-ion velocity distributions, stability, injection, and orbits are summarized. The many-faceted role of the energetic ions in plasma heating, fuelling, and current maintenance, as well as in the direct enhancement of fusion power multiplication and power density, is discussed in detail for the three reactor types. The relevant implications of recent experimental results from several beam-injected tokamaks are examined. The behaviour of energetic ions is found to be in accordance with classical theory, large total ion energy densities are readily achieved, and plasma equilibrium and gross stability are preserved. The status of neutral-beam injectors and of conceptual design studies of beam-driven reactors is reviewed briefly. The principal plasma-engineering problems are those associated directly with achieving quasi-stationary operation, particularly the problem of high-throughput particle exhaust. An especially attractive feature of beam-driven tokamak plasmas is their capability for useful application in devices of relatively small size.

During the last six years, it has become apparent that the tokamak device affords the most straightforward route to providing a significant fusion plasma in the laboratory, with considerable potential for eventual application in fusion power reactors. Consequently, four large tokamak projects are currently being pursued in several countries: (1) The TFTR (Tokamak Fusion Test Reactor) in the USA; (2) the JET (Joint European Torus) in the European Economic Community; (3) the JT-60 (Japanese Tokamak) in Japan; and (4) the T-20 in the USSR.

The International Fusion Research Council (IFRC)was created by the IAEA in 1971 [1 ] to advise the Agency on its activities in the field of nuclear fusion. Among the eleven members of the Council are representatives of the following countries: Australia (M.H. Brennan), France (M. Trocheris), FRG (G. von Gierke), Italy (B. Brunelli), Japan (K. Husimi), the Netherlands (CM. Braams), Sweden (B. Lehnert), UK (R.S. Pease), USA (E.E. Kintner) and USSR (E. Velikhov); D. Palumbo represents EURATOM. The present Chairman of the Council is Dr. R.S. Pease who succeeded Dr. C.N. Braams in 1976.