Table of contents

Finite-β (plasma pressure/magnetic pressure) and resonant electron effects on the dissipative trapped-electron instabilities are analysed. These modifications are shown to have a strong stabilizing influence on the finite-ion-gyroradiusand electron-temperature-gradient-driven modes, respectively. For relevant tokamak parameters, complete stabilization may be possible. Stability criteria for radially local and non-local cases are presented.

The non-linear theory of one-dimensional mode-coupling stabilization for the dissipative trapped-electron instability is presented. This non-linear process couples unstable modes at low wave number to damped waves at high wave number. The regions of parameter space in which this process is applicable are carefully specified and the saturated wave spectra and anomalous transport coefficients are calculated numerically for a range of parameters of interest for large tokamak operation. The transport coefficients calculated are appreciably smaller than the usual γ/k² estimates in moderate- and high-temperature regimes.

The effect of uncertainties in plasma confinement and impurity concentration upon the performance of a D-T burning tokamak experiment power reactor is analysed. Steady-state performance parameters are established for ignition and beam-driven modes as a function of nτ and impurity concentration. The deleterious effect of wall-sputtered impurities on the burn cycle dynamics is examined for several potential first-wall materials. The effect of different confinement scaling laws — trapped-ion mode and pseudoclassical — on the burn cycle dynamics is studie.

The soft X-ray signal from the Adiabatic Toroidal Compressor (ATC) sometimes exhibits a 10% modulation with a frequency between 1 and 2 kilohertz. The radial profile of the soft X-ray signal and the electron temperature determined by laser scattering indicate that these fluctuations are associated with a limitation of the central electron temperature and a broadening of the temperature profile. By observing changes in the radial dependence of the relaxation oscillation during neutral counter injection, an increase of thirty to fifty percent in the radius where q = 1 has been measured.

The rapid isentropic compression of an initially uniform sphere of an ideal gas is compared with the homogeneous compression of a thin shell. A simple ablation model, in which the temperature of the ablated material remains constant, is incorporated which enables the properties of ablation-driven compression for these two cases to be compared. Expressions for power input, energy per unit mass, ablation efficiency and mass fraction compressed are all derived. Finally, the more complex self-regulating ablation model is used to illustrate the effect of a varying ablation temperature.

In a tokamak the attainable β-values are restricted by the limitations of MHD-stability. The necessary improvement of the β-value should, however, be possible by going over to a non-circular plasma cross-section. In this paper, the theoretical conditions for such an improvement are discussed (e.g. volume currents peaked on axis, flattened ends of the elongated cross-section and diamagnetic plasma). Experimental investigations of this problem have been carried out in the Belt Pinch, where plasma production and heating is achieved by fast magnetic compression. This heating method is unusual for a tokamak, but is, at present, the only method of approaching the interesting β-regime (<β> ≈ 10 – 50%) and, especially, β_pol > 1 operation.

The main result of the Belt Pinch experiments is that MHD-stability requires about the same q_crit-value (≈ 3) also needed in circular-cross-section tokamaks, at least for the present plasma parameters and time scale (b/a ≈ 10, R/a ≈ 7, <β> ≈ 50%, <β_pol> ≈5, T_e ≈T_i ≈ 25 – 40 eV, <n_e> ≈ 5 – 7 × 10¹⁴ cm⁻³, values approximately constant for the high-β-phase of 50 μs). Violation of q-condition, however, results in fast-growing modes which destroy the plasma equilibrium within several μs. Compared with such an unstable case, stability for t ≈ 50 μs means stable behaviour for about 20 MHD-growth-times. Numerical calculations indicate a further improvement in present and future experiments with suonger shock-heating and increased temperatures (T > 100 eV).

The implosion phase of a collisionless theta pinch without initial magnetic bias field has been studied experimentally. Characteristic properties of the turbulence in the sheath have been determined. The significance of the turbulence for the piston-induced radial plasma flow is discussed. The properties of the turbulent plasma are in good agreement with theoretical predictions for ion acoustic turbulence.

The transient build-up of the neutral-gas blanket in a theta-pinch reactor has been investigated. A hydrodynamic fluid code was developed to account for charge-exchange, ionization and energy transport in the plasma-neutral-gas interaction region. An initially collisionless neutral gas is separated from the vacuum region by the first wall, and at time t = 0 the wall becomes transparent to these neutrals so that half of them move freely into the boundary layer where they react with a plasma whose parameters are those given in the RTPR (Reference Theta-Pinch Reactor) design after quench. Initial neutrals react with the low-density edge of the plasma, and succeeding neutrals therefore react with the edge of a cooler plasma, removing less energy from the plasma by charge exchange. Also less energetic charge-ex change neutrals hit the wall, causing less damage as time progresses. A steady-state profile is quickly established. Essentially all the energy reaching the wall arrives in the initial pulse (about 11 μs long), and this amount of energy is insufficient to cause wall damage.

Experimental studies of plasma heating due to microwave irradiation of the magnetically confined plasma column in the Princeton L-3 device is presented. X-band (10.4 GHz) microwave power, both in the ordinary and the extraordinary modes of propagation, is used in these experiments. Plasma heating is observed to occur simultaneously with the occurrence of parametric decay instabilities. The mode structure of the pump wave and the decay ion wave dispersion have been measured with high frequency probes. Detailed measurements of electron heating rates are presented and compared with collisional heating rates. In addition, production of suprathermal electrons and ions is also observed and measured. A comparison is made with recent laser-pellet interaction experiments.

Measurements of the TFR plasma ion temperature over a wide range (300 eV ≤T_i≤ 1000 eV) have shown that the ion energy balance could be explained by losses following a 'plateau' dependence, the ion-ion collision frequency being increased by the presence of impurities. No 'banana'-like conduction loss has been found even for a 1 keV ion temperature plasma.

The transient time history of the energy distribution function of alpha-particles in the D-T fusion reactors is obtained by numerically solving a Fokker-Planck equation, by taking into consideration the possible alpha-particle loss from the core-plasma volume. On the basis of the results obtained, the total amount of energy transfer to background plasma and the efficiency of the alpha-particle heating, together with the partition of energy transfer to electrons and to ions, are calculated. In addition, a new fact has been found, i. e. the effect of an 'inertial' property of the alpha-particle distribution function on the transient response of the total amount of energy transfer for a temporal perturbation of the parameters of background D-T plasma, which is important in connection with stability and control problems of D-T reactor-core plasmas.

The energy-dependent equation for the slowing-down of energetic ions in fully ionized plasma is cast into a multigroup form. The resulting multigroup equation is a linear equation for the flux of the energetic ions and is easy to solve. It can take into account large-energy-transfer reactions preserving their discrete nature. The sensitivity of the multigroup approximation to the group width and weighting function used for generating group constants is investigated. It is found that few groups with simple, problem-independent weighting functions can yield results of reasonable accuracy. The relation between the multigroup and other methods for the solution of the slowing-down equation is discussed.

Feedback suppression of trapped-particle instabilities of the magnetic type by modulated neutral-beam injection is studied. The neutral beam acts both as a particle source and a momentum source and it is found that the potentially dangerous dissipative trapped-particle modes may be effectively quenched by means of a negative feedback at −90° phase.

The evolution of the electron distribution function, when an electric field that is not too small in comparison with the critical electron runaway field is applied along the confining magnetic field of a high temperature plasma, is analysed. In the regimes considered, a finite fraction of the electron population has magnetically trapped orbits, and is not appreciably affected by the applied electric field, while the distribution of circulating electrons tends to "slide away" as a whole. Then the Spitzer-Härm model for the current-carrying electron distribution is inadequate, and the role that collective modes, in particular current-driven microinstabilities, and collisions can play in producing a stationary electron distribution is analysed. Modes at the ion plasma frequency, ω_pi, that are driven by the positive slope of the current-carrying electron distribution, can be excited, when the average electron drift velocity is a finite fraction of the electron thermal velocity, and transfer transverse energy to the main body of the electron distribution. These features are consistent with the experimental observations performed on the Alcator device. Modes at the "reduced" electron plasma frequency (k_||/k)ω_pe can also be excited both in connection with the modes at ω_pi and independently. Modes at the electron gyrofrequency Ω_e associated with the loss-cone feature that the electron distribution tends to develop are considered, among others, as a factor for the strongly enhanced electron cyclotron emission experimentally observed in regimes where non-thermal electron distributions have been realized.

The non-local theory of the dissipative trapped-electron instability, including magnetic shear, is extended to higher electron collisionality. In regions sufficiently close to a rational magnetic surface the trapped-electron mode becomes a 'collisionless' drift mode, which is Landau-damped (where η ≡ ∂ ln T_e/∂ ln n_e > 0). The collisional broadening of the untrapped electron Landau resonance makes this an effective stabilization mechanism, even when the parallel phase velocity lies in the trapped-particle region of parallel velocities. For the normal temperature gradient (η > 0) and for large aspect ratio (⁻¹ > 1) a sufficient condition for stability is obtained that is independent of shear: ^½ η^1/3 < 1. For the inverted gradient case (η < 0) a shear stabilization criterion is derived.

Over 580 participants from nine different countries attended the Sixth Symposium on Engineering Problems of Fusion Research held 18-21 November in San Diego. This represents about a two-fold increase in the number of participants and more than a two-fold increase in the number of technical papers over those at the Fifth Symposium at Princeton two years previously. The Symposium was jointly sponsored by the Institute of Electrical and Electronics Engineers (Nuclear and Plasma Physics Society) and the American Nuclear Society (Division of Controlled Nuclear Fusion) along with the assistance of the General Atomic Company and the United States Energy Research and Development Administration. A. A. Schupp of the General Atomic Company was General Chairman.

The importance of reducing the impurity concentration in future confinement experiments and ultimately in fusion reactors brought together a group of 120 plasma physicists and surface physicists from 10 countries to the Second International Conference on Surface Effects in Controlled Fusion Devices. Over 80 papers were presented on subjects ranging from the investigation of surface interactions of importance in fusion devices to descriptions of the behaviour of impurities in plasma confinement experiments. A major success of the Conference was in bringing about effective communication between the plasma physicists and the surface physicists concerned with the fundamental processes.

Work is currently underway in the field of fusion reactor design on problems associated with (D-T)- burning tokamak devices such as TFTR, JET and T-10. Additional related programmes have been outlined for the longer-range development of experimental power reactors (EPRs) designed to produce several hundred megawatts of thermal power. The design requirements for still larger (> 500 MW(e)), electric- or fission fuel-producing reactors that might appear near the turn of the century have also been studied by several groups, and more than ten such designs have already been proposed.