Table of contents

The influence of impurities on the dissipative trapped-ion instability is investigated considering all possible cases of ion impurities in the banana, plateau or Pfirsch-Schlüter regimes. It is found that impurities lead to very significant stabilizing effects on these modes. In particular, the instability is quenched when the impurities are in the Pfirsch-Schlüter regime, and also for plateau impurities, provided the impurity density gradients are directed as the main plasma density gradient. In the case of impurities in the banana regime, a sufficient condition for complete stabilization of the instability has been found in the case of sufficiently sharp and positive impurity gradients. In the unstable cases, there is a noticeable upward shift and shrinking of the unstable range increasing with impurity concentration. These features have been discussed quantitatively, in terms of impurity parameters, both with reference to present-day experiments and for future experiments with reduced impurity levels.

A system for servo-control of the plasma position in a tokamak discharge is described. Measurements of the stability boundary of the servo-loop in the Cleo-Tokamak apparatus are presented and compared with a theoretical model. They show reasonable agreement. Using servo-control, the discharge time was extended from 110 ms to nearly 200 ms, and the plasma remained within ±10 mm of the centre of the vacuum vessel for up to 140 ms. The instability caused by a deliberately applied vertical field with positive gradient was stabilized.

The paper presents a numerical study of the effect of impurity gradients on collisionless drift waves. In the region where the usual simplifying hypotheses (wavelength transverse to the containment field greater than Larmor radii; longitudinal phase velocity differing greatly from thermal velocities) permitting analytical solution of the dispersion relation are not justified, this study provides a series of data on the extent of unstable zones and on the influence on the representative parameters of impurities. It confirms the appearance of an ion branch, possibly more unstable than the electron branch, which can develop on small wavelengths along the magnetic field and which cannot easily be stabilized by shearing the field lines. It is shown that the expected effect of this instability is to introduce into the contained plasma the impurities present at its boundary.

The overall efficiency of a thermonuclear reactor depends markedly on the efficiency of neutral-beam injection. The model of the injector system is based on direct conversion of the unneutralized portions of the ion beam. The injection efficiency is estimated from assumptions on the performances of the components of the injection system. Based on this model, deuterium or tritium atoms derived from negative ions and between 100 keV and 1000 keV in energy can be injected into the reactor with an efficiency of 80 to 90%. Without direct conversion this efficiency will drop to 65 to 85%. For energies around 100 keV, D⁺ ions can be used to obtain a system efficiency of about 75%, which is higher than can be obtained with ions. The same model predicts 80% efficiency below 200 keV for injection of ³He atoms derived from positive ions, and less than 70% efficiency between 200 keV and 700 keV using ³H⁻ ions.

Transport coefficients, relating ion and impurity fluxes, and their fluxes of energy, to the density and temperature gradients, are derived from neoclassical theory. The ions are assumed to have mean free paths much longer than the torus connection length. The banana-plateau transition is shown to depend upon additional parameters which are not present in the electron-ion problem. Only two different ion masses are considered, but the heavier ions may have an arbitrary number of different possible ionization states. The mass ratio is arbitrary; the small mass-ratio limit is considered in detail, however. In that limit, the critical value of the collisionality parameter υ₁*, for the transition from banana regime to plateau regime for the fluxes due to ion-impurity collisions, is shown to be ∼(n₁/n_i)(m₁/m_i)^1/2, where i denotes light ions and I denotes impurities. The plateau regime values of the corresponding transport coefficients are proportional to this parameter, which may be much smaller than unity, in typical cases. The modification of electron transport properties due to impurities is also discussed.

A numerical procedure for determining the hydromagnetic stability of axisymmetric systems is described. The growth rates and eigenfunctions are determined by means of a modified initial value method. A number of tokamak configurations have been studied and stability boundaries and growth rates are given. With a conducting wall on the plasma the fundamental toroidal mode is stable and the m = 1 mode is stable for q ⪆ 1/2.

The Canberra Tokamak LT-3 exhibits a delay between the application of the toroidal electric field and the main rise in gas current indicating bulk ionization of the gas. During this "prebreakdown" phase the electric field is high and the current is dominated by runaway electrons. The rotational transform is very low, however, and the condition for compensation of transverse particle drifts is not satisfied. A theoretical model is considered which includes only the curvature drift of the runaways. This provides estimates of the maximum energy an electron achieves before it is lost to the walls and a critical condition on the current when the transition to particle containment and total gas breakdown should occur. Measurements of runaway electron energies and gas currents in LT-3 are in agreement, within experimental and theoretical accuracy, with the predictions of the model. The effect of a compensating perpendicular magnetic field also confirms the model. The mechanisms governing the duration of the delay to breakdown remain obscure. In view of the short particle lifetime a means of re-introducing electrons, such as secondary emission, seems indicated. The prebreakdown phase may be avoided by pre-ionization to densities above a critical value. The particle drifts are then compensated and no delay occurs before the onset of exponential ionization increase.

The stability of ion Bernstein waves (frequency ω, wave number ) in a plasma with two ion species pumped by a magneto-acoustic wave (ω_p, _p) which propagates perpendicularly to the static magnetic field is studied. The background plasma is assumed to be infinite, homogeneous and collision-free. If ω_p > |ω| is properly chosen, ion Bernstein waves become unstable (decay instability, non-linear Landau instability) at rather low values of the pump electric field amplitude |_D|. The instability is excited by the relative drift motion of different species induced by the pump wave. Assuming |⋅(_a−_b)|≪1 (_a = displacement for particles of species a, a = e, 1, 2) the general non-linear dispersion relation is approximately solved in a deuterium-tritium plasma for two different : In case A (=_⊥ ∥ _p) only the relative ion motion _d⋅_t comes into play; this gives rise to decay instabilities which are only present in plasmas with two ion species. The instabilities of case B(k_⊥ ⊥ k_p, k_z ≠ 0) caused mainly by the relative electron-ion drift motion are similar to those in plasmas with only one ion species. For given |_p| the growth rates in both cases are equal in order of magnitude (for low values of ω_p, case A is slightly more favourable); however, in case A the theory is valid up to considerably higher values of |_p|. Some effects depending substantially on the presence of two ion species are discussed in detail.

The gross MHD instabilities of straight cylindrical plasmas with elongated cross-section are investigated by solving the linearized MHD equations as an initial boundary-value problem on the computer. The linearized equations are Fourier-analysed along the ignorable co-ordinate of the equilibrium in order to reduce the computation to two dimensions. The method is applied to find the fixed-boundary instabilities of an equilibrium with rectangular walls. Starting with an arbitrary initial perturbation and following it for many Alfvén transit times, we find that the dominant instability overwhelms all stable oscillations after several e-folding times. We determine the growth rates of the fastest growing instabilities as a function of the equilibrium parameters. Then we examine the spatial structure of the physical variables (¹, ¹, p¹). We find that the cross-section of the velocity field displays a distinctive convection pattern. This structure becomes spatially concentrated around the point of maximum rotational transform as the equilibrium current is decreased to the marginal point, and concentrates near the wall as the current is increased. Given the equilibrium p'(ψ) = J_zc ψ/ψ_c, ψ (wall) = 0, we find that the marginal current density J_zc for each mode increases as the cross-section is elongated. But the growth rates of the higher azimuthal m-modes increase with elongation and their intervals of instability overlap with the lower m-modes.

The ∇B drift in the toroidal magnetic field leads to relatively large radial displacements as the parallel velocity of an ion passes through zero. If collisional scattering into this velocity band is unable to balance the enhanced radial diffusion, a minimum will develop in the velocity distribution. This happens when ρ_θ/r_n > (rν_i/vΘ)^½, where = r/R is the inverse aspect ratio of the torus, Θ = B_θ/B_φ is the ratio of poloidal and toroidal components of the magnetic field, v = (2T/M)^½ is the ion thermal speed, ρ_θ = Mv/eB_θ is the ion Larmor radius in the poloidal magnetic field, r_n is the density scale length, and ν_i is the ion-ion collision frequency. As ρ_θ/r_n increases, the minimum deepens, and beyond (rν/vΘ)^1/3 the distribution has a loss-band character. The analysis is restricted to the "plateau" collisional regime. The velocity distribution is derived by solving the collisional kinetic equation, including the radial loss and an isotropic source term. The radial loss term is dominant only over a limited velocity band, the resonant band. Solutions valid within the resonant and non-resonant velocity ranges are matched at the transition between these ranges.

For typical Tokamak parameters, the predicted anisotropy in the ion velocity distribution is very weak, being of order 1%. However, it should be quite strong in existing stellarators. Observations in the Proto-Cleo stellarator are not inconsistent with theoretical predictions.

Neoclassical particle diffusion and heat transport are discussed for tokamak-like devices in the "banana" regime (ν_eff < ω_b) with helically perturbed magnetic fields such as might be produced by kink-like instabilities. The diffusion coefficient scales as D ∼(ν₁/ν) ξ² D_pl where ξ is related to the amplitude of the perturbation and ν is the collision frequency. For typical experimental parameters and sufficiently low collision frequency, transport is moderately enhanced over the axisymmetric result.

In the two-component torus concepts at present under consideration,high-energy neutral beams are injected tangentially into relatively small tokamak devices. The resulting fast ions are localized near the centre of the plasma discharge. Here we consider the effect of radial variations of density and temperature (of both the fast ion and target plasma components) on the overall power balance and break-even condition. For the radial profiles analysed, the minimum values of N_eτ_E and T_e required for break-even in a pure wet-wood burner decrease significantly for peaked fast-ion distributions. The implications of the reduced N_eτ_E requirements on machine size are examined for the transport scaling predicted in the trapped-ion regime.

The microwave heating rate for a plasma in a d.c. magnetic field is found by multiplying the emission rate for a relativistic electron in a d.c. magnetic field by a correction factor corresponding to the number of incident photons and integrating this expression over a particle velocity distribution. The correction factor which relates the absorption rate to the emission rate is found to be proportional to 1/ω³. The maximum heating rate always occurs below the electron cyclotron frequency. For electron temperatures greater than 50 keV, the heating rate decays as ln ω for frequencies well above the fundamental resonance. The maximum heating rate occurs at a lower frequency for higher-temperature plasmas. The highfrequency tail of the heating rate falls off more rapidly for a loss-cone velocity distribution than for a Maxwellian.

Transport processes across a strong magnetic field in axisymmetric magnetic traps are studied in two-fluid magnetohydrodynamics with anisotropic temperature. Account is taken of inertia and collisional viscosity, and of the nonuniformity of the equilibrium temperatures. In the case of low toroidality r/R ≪ 1, expressions are obtained and analysed for the heat and particle fluxes, and equations are obtained for the ambipolar electric field, the mean velocity of the plasma, and the electric current along the magnetic field lines.

A complex plasma injection device was investigated. It consists of a coaxial plasma accelerator with gas preionization and a spatially periodic sign-changing magnetic field used to guide the high-velocity plasma stream and to separate the slow one. A high-energy plasma stream with a total energy of ≥ 160 J (4 - 4.5 × 10¹⁷ particles) and an amount of impurities not exceeding 1% was obtained at the output of the magnetic system. It is seen that the guiding magnetic field does not penetrate into the leading fast plasma puff, which implies that the connection of the injector system to the magnetic traps should be simplified when a complex plasma injector of such type is used.

This paper reviews recent work on the focusing of high-power relativistic electron beams in diodes and discusses concepts for pulsed fusion based on this technology. The physics of high-current relativistic electron beam focusing using plasmas in high-current diodes is studied experimentally and with computer simulation. The physics of the beam interaction with dense targets and the requirements for break-even are briefly discussed.

The Conference was again held at Texas Tech University. It had five half-day sessions with five invited and thirty-five contributed papers. There were approximately sixty participants from Canada, France, India, Italy, Switzerland and the United States of America. The papers were primarily fusion oriented and there was more emphasis on the heating of hot, dense, toroidal plasmas than at the first topical conference, two years ago. The acknowledged competition to r.f. heating, in the fusion research area, is neutral injection. Most of the participants apparently felt that r.f. heating comes out quite favourably in comparisons between the two schemes.

A translation of the abstracts of all the articles for this issue into English, French, Russian and Spanish.