Table of contents

Steady-state neoclassical diffusion calculations are described for conditions appropriate to tokamaks. Particle loss by diffusion is balanced by neutral recycling. It is found that with the boundary condition that the particles convect out their own energy, the electron temperature and current density are large at the boundary. The means by which the behaviour of the temperature at the boundary may be brought closer to that observed in experiments are discussed.

Numerical studies on the stability of kink and resistive tearing modes in a current-carrying linear stellarator are presented for various current profiles and helical fields. In the case of an ℓ = 2 helical field, the magnetic shear vanishes and the stability diagram is given by the straight lines with ι^σ + ι^δ = const., where ι^σ is the rotational transform due to the plasma current and ι^δ is that due to the helical field. For the ℓ = 2 stellarator with , the magnetohydrodynamic stability against kink and tearing modes is improved compared to that in tokamaks. When an ℓ = 3 helical component exists, magnetic shear plays an important role in the stability properties. The stability diagrams become fairly complex; they are, however, understandable from properties of the Euler equation. It should be noted that the internal kink modes are made more unstable than in a tokamak, because of the ℓ = 3 helical field.

Recently, the conditions for stability of an arbitrarily shaped, finite-pressure toroidal plasma against localized ideal and resistive modes were presented. The characteristic time scale for local instability with respect to ideal modes is small compared with that for resistive modes so that an investigation of ideal local stability is a prerequisite for an assessment of non-ideal local stability. Here we consider the stability of a particular class of non-circular cross-section tokamak equilibria with respect to such modes. The equilibria are described analytically so that no ordering or expansion procedure is necessary, and both ideal and resistive stability are investigated over the whole plasma region. The effects of plasma shape (vertical elongation and triangularity), as well as aspect ratio are investigated and particular reference is made to next-generation tokamak designs (e.g. JET).

Various discharge cleaning techniques have been studied in Microtor. It was found that high temperature discharges are not only ineffective in reducing the oxygen on the wall, and hence in the plasma, but may even induce trapping. Oxygen can be removed from the wall by a low-temperature, partially ionized hydrogen plasma by conversion to water vapour. The amount of loosely bound oxygen on the surface is thus reduced below 1% of a monolayer. The residual amount of the oxygen in the plasma is near 10¹⁰ atom · cm⁻³, and represents a significant improvement over previous tokamak results.

This paper examines the stability against ballooning modes of plasma equilibria in toroidally linked mirror configurations consisting of a number of quadrupole minimum-B mirrors linked toroidally. On the basis of the Kruskal-Oberman energy principle, a class of displacements is identified which are potentially unstable, and a necessary criterion for stability is derived. The criterion is obtained from the eigenvalues of an ordinary differential equation, which determines the variation of the displacement along a field line. The coefficients in the equation are determined by the configuration, and by inserting various model configurations, estimates are obtained of the maximum value of β consistent with stability. In cases of interest, quite high β-values are obtained.

Experimental results of the interaction of short (1.5 ns) CO₂ laser pulses with solid targets at a flux reaching 10¹³ W/cm² are presented. An attempt is made to carry out a global series of measurements and interpret them in the light of currently available theory. The absorption, reflection, ion and X-ray emission (line and continuum) and in considerable detail the infra-red emission spectra of the plasma in the vicinity of the incident 10.6 µm radiation as well as its harmonics were measured. From the emission spectra the existence of the parametric decay and the stimulated Brillouin backscatter instabilities was identified. Furthermore, the energy and angular dependence of the reflected-light calorimetry in addition to the X-ray and ion emission results are found to be consistent with the hypothesis that the interaction of high power CO₂ lasers with plasmasis dominated by non-linear effects such as the parametric decay instability.

The impurity radiation for typical tokamak parameters has been numerically calculated using an "average-ion model". Coronal equilibrium values for the emission of oxygen, iron, molybdenum, tungsten and gold were determined from the steady-state solutions of a set of related rate equations which included the effects of electron collisional ionization and excitation, dielectronic and radiative recombination, Δn = 0 and Δn ≠ 0 line transitions, and bremsstrahlung. The results for oxygen, iron, and molybdenum compare very well with other calculations. Since impurities diffusing in a tokamak are not expected to be in coronal equilibrium, time-dependent radiation calculations were also performed. A comparison of these non-equilibrium loss rates with those calculated under the assumption of coronal equilibrium indicates that coronal radiation calculations do not significantly underestimate the moderate- and high-Z impurity radiation losses for neoclassical diffusion velocities in large tokamaks, such as Princeton Large Torus and Tokamak Fusion Test Reactor. Finally, the detailed steady-state emission rates were used to investigate the effects of various concentrations of impurities on the n_eτ requirements for breakeven, ignition, and Q = 5 beam-driven reactor experiments.

The ion-ion hybrid resonance can occur at high plasma densities in tokamaks and thereby absorb energy from the fast magnetosonic mode which would otherwise propagate freely. Ion-cyclotron resonance regions, although they occur in the low-density peripheral plasma, can nonetheless cause sufficient absorption to compete with fundamental cyclotron resonance damping by ions. For the ion-ion hybrid resonance it is shown that: (1) the energy absorption occurs via a sequence of mode conversions. (2) A poloidal field component normal to the ion-ion hybrid mode conversion surface strongly influences the mode conversion process, so that roughly equal electron and ion heating occurs in the present proton-deuterium experiments, while solely electron heating is predicted to prevail in deuterium-tritium reactors. (3) The ion-ion hybrid resonance suppresses toroidal eigenmodes. (4) Wave absorption in minority fundamental ion-cyclotron heating experiments will be dominated by ion-ion hybrid mode conversion absorption for minority concentrations exceeding roughly 1%.

A moment method is derived for the transport of energetic ions in an infinite homogeneous hot plasma, in the absence of electromagnetic fields. Within the framework of the continuous-slowing-down approximation, the Fokker-Planck equation is solved rigorously for plane and point sources. Angular flux and scattering anisotropy are correctly taken into account. Calculated results are presented for protons and deuterons slowing down in boron hydride plasmas for several source energies and temperatures. Comparisons with available Monte-Carlo results have been made in the case of 3.5-MeV alpha-particle transport in high density D-T plasmas. Very good agreement has been achieved.

A simple neoclassical point model is presented for the ELMO Bumpy Torus experiment. Solutions for steady state are derived. Comparison with experimental observations is made and reasonable agreement is obtained.

A mode with azimuthal wave number m = 1 can be excited in a resistive plasma column as a result of reconnection of the magnetic field lines under conditions for which the ordinarily known internal kink mode given by the ideal MHD theory would be stable. In the absence of resistivity, magnetic reconnection would not be allowed and the relevant mode would be singular at a specified radius within the plasma column as in the case of the resistive tearing modes that are found for m ≥ 2. The analysis presented here is based on a set of moment equations that are appropriate for relatively high-temperature and low collisionality regimes. In these regimes, the mode growth rate tends to weaken considerably as the temperature increases and the mode acquires a frequency of oscillation with phase velocity close to the electron diamagnetic velocity, as a result of the effects of finite ion gyroradius and finite drift wave frequency, even in the absence of an equilibrium radial electric field.

The continuum X-ray emission from laser-heated targets gives a measure of the energy deposited in superthermal electrons and an estimate of the spectrum and the average electron energy. The validity of the analysis is, however, limited by possible non-collisional energy-loss processes in the pellet corona. If this effect is ignored, fits to experimental X-ray spectra from glass microspheres at 1.06-µm laser wavelength can be readily obtained showing 15%–48% of the absorbed energy in fast electrons.

The production of fast ions in laser-heated plasmas is shown to result from the large electric fields in the under-dense plasma which control the orbiting motion of super-thermal electrons produced in the processes of laser-energy absorption. The magnitude of the effect also requires that the fast electrons be reflected many times in the corona fields. The prolonged orbiting of the electrons results from the relatively high transparency of the dense plasma to the very energetic super-thermal electrons.

This paper presents some novel interpretations of fusion plasmas which may be of interest to both fission and fusion scientists and engineers. A new fusion ignition parameter (Tn_eτ_E)_I is proposed which is proportional to β²B⁴ and inversely proportional to the fusion power density (P_Fusion) of a reacting plasma. Curves are given for many potential nuclear fusion fuels. The energy utilization factor in existing devices is defined as f = P_Fusion/P_Loss = (Tn_eτ_L)/(Tn_eτ_E)_I; in experimental plasmas, f has increased by about two orders of magnitude in the past decade and now exceeds 10⁻⁴ (a "nearest" f* exceeds 10⁻³). The f factor is also analogous to its fission counterpart in the four-factor neutron multiplication factor k = f η p, where f is the neutron thermal utilization factor. Past, present, and future fusion experiments are discussed briefly in this context.

The behaviour of the m = 0, n = 0; m = 1, n = 1 and m = 2, n = 1 low-frequency oscillations has been studied within the framework of the current disruption in TFR. The experimental observations show the fundamental role of the m = 2 mode in triggering and growth of the instability, the existence of two m = 1 modes near the q = 1 surface, one of which is directly connected with the m = 2 mode.

The results of experiments in which oxygen gas is injected at the current plateau of a quasistationary TFR deuterium plasma are presented. As a consequence of the injection, the molybdenum density in the plasma decreases, apparently because of a decreased molybdenum flux entering the plasma. This density decrease has a time constant which is a measure of the impurity particle confinement time τ_p. In this way, τ_p ≅ 50 ms is found at the plasma centre, and τ_p ≅ 20 ms at the periphery. The discharges studied have been simulated by using different forms of anomalous impurity diffusion. It is concluded that, for the conditions imposed by the experiments, it is necessary to use anomalous diffusion proportional to the impurity density gradients.

The linear, non-linear, and anomalous transport properties associated with various microinstabilities driven by cross-field currents in high-temperature plasmas are reviewed. Particular emphasis is placed on instabilities pertinent to the implosion and post-implosion phases of theta-pinch plasmas, e.g. Buneman (electron-ion two-stream), ion acoustic, lower-hybrid-drift, electromagnetic ion cyclotron, and ion-ion cross-field instabilities. Analytic studies of the non-linear and quasi-linear evolution of these instabilities are presented, together with a detailed comparison with computer simulation experiments to test the validity of the various theoretical models and non-linear saturation mechanisms. A general theoretical formalism is presented which describes, in a self-consistent manner, the macroscopic transport produced by the (shortwave-length) turbulence associated with the microinstabilities enumerated above. The experimental evidence that such a self-consistent anomalous transport model is required for describing the implosion behaviour (characterized by diffuse current sheaths) in rapidly pulsed theta pinches is reviewed, together with the early attempts at modelling these implosions numerically with a one-fluid (MHD) model including artificial viscosity. It is shown that fluid-numerical simulations that include (at each space and time step) the effects of anomalous transport in a fully self-consistent manner, explain several features of the experimental observations. The relevance of reflected ions to sheath structure and implosion dynamics is also discussed, and state-of-the-art hybrid-numerical studies (Vlasov ions and fluid electrons) of pinch implosions are presented, which include reflected ion dynamics as well as the anomalous transport associated with cross-field instabilities. Finally, instability mechanisms for producing long-time interpenetration of plasma and magnetic field in post-implosion theta pinches are discussed, together with estimates of the anomalous resistivity.

The Third International (Kiev) Conference on Plasma Theory took place at Trieste (Italy) from 5 to 9 April 1977. As is well known, the two previous Conferences on Plasma Theory, organized by the Ukrainian SSR and the USSR Academies of Sciences and supported by the International Union of Pure and Applied Physics, were held in 1971 and 1974 at the Institute for Theoretical Physics of the Academy of Sciences of the Ukrainian SSR in Kiev. The main purpose of the International Kiev Conferences on Plasma Theory is the discussion of problems of plasma physics, which are basic for such scientific and technical problems as controlled thermonuclear fusion, magnetohydrodynamic conversion of thermal into electric energy, creation of new radiowave sources, conquest of space, etc.