Table of contents

The neoclassical transport theory is developed for an axisymmetric toroidal plasma containing highly energetic α-particles as produced by fusion events. It is shown that the α-particle fluxes in this case have a weaker dependence on the aspect ratio than at lower energies since the prevailing collisional effect is a drag. The bootstrap current results to be reduced by the presence of fusion α-particles.

An analysis of the propagation of a laser beam in a cylindrical magnetically confined plasma with parabolic density profile is presented. The normal modes which are self-trapped are given. It is found that the largest mode that can be trapped by the plasma is given by (1/2) where R₀ is the radius of the plasma column and w is the fundamental mode width. It is found that all the trapped modes in a finite plasma can easily propagate distances of the order of one kilometer. An exact solution for the amplitude of the electric field for an incident Gaussian beam has been obtained. The solution exhibits alternate focusing and de-focusing of the beam. The effect of this on the plasma heating is discussed.

A multi-group diffusion method is derived for the slowing down and spatial transport of energetic positive ions in a hot plasma. A diffusion coefficient which is "flux-limited" is used to provide better accuracy when slowing-down is dominated by Coulomb collisions with electrons and the mean free path is long. This results in a fast, flexible, small-memory computer program for calculating the behaviour of energetic charged particles. Calculated results are presented for 3.5-MeV alpha-particles slowing down in a 50-keV deuterium-tritium plasma of uniform density. Various spatial distributions of the alpha-particle source were tested in spherical geometry and compared with the results of suitable Monte-Carlo calculations. Generally, fair to good agreement was obtained for the energy deposition in space and time with as few as ten energy groups, and good to excellent agreement was obtained with 100 groups. It was found that the multi-group method using 100 groups was appreciably faster than the Monte-Carlo method, while for only 10 groups it was at least an order of magnitude faster. This method is expected to give good results for temperature, density, and charged-particle source distributions which are typical of laser fusion reactors, and may also be applicable to certain astrophysical problems.

The influence of mismatch on a coherent, stimulated scattering process including the effect of pump depletion is studied. The efficiency of the non-linear three-wave interaction exhibits marked threshold behaviour for increasing mismatch, a result which is a generalization of the corresponding behaviour of parametric processes. The analysis is applied to the stimulated scattering processes (notably stimulated Brillouin scattering) occurring in laser-plasma interactions, where severe mismatch may be caused by plasma inhomogeneity and/or differential Doppler shifts. By means of a simple physical model we obtain thresholds for stimulated scattering in inhomogeneous and differentially expanding plasmas, results which are in good agreement with those recently given by an alternative approach. In addition, expressions predicting the rise of the reflectivity above threshold are given.

This paper reports the results of a numerical-analytical study of current penetration in tokamak-type discharges. Results presented include: (1) A survey of microinstabilities proposed as relevant to tokamak start-up; (2) an examination of the energy transport equations with toroidally enhanced classical thermal conduction to argue resistive penetration and scaling properties; (3) tabular and graphical data from a 1-D MHD code applied to cylindrical geometry for a variety of assumed start-up conditions. The transport included is classical resistance and toroidal classical thermal conduction radially. The results show that current penetration properties of fast-rise, low-density devices, such as ST, Doublet II and ORMAK, differ from those of slow-rise, high-density devices such as the planned PLT and Doublet III experiments. In the latter case, the electrons and ions can remain collisionally well coupled throughout the rise of the driving field, and ion thermal conductivity can frustrate the tendency of Joule heating near the plasma boundary to cause skin formation. It is further concluded that most of the micro-instabilities proposed to explain "anomalous" current penetration will in practice never occur.

A simple model of a toroidal, high- β quasi-uniform current model of a tokamak with elliptic cross-section is investigated for stability against uniform vertical displacements. On the basis of asymptotic theory, it is shown that for high- β/toroidal effects to be important β must be of order the equilibrium limit. For a given β and ellipticity the mode can always be stabilized by a conducting wall placed sufficiently close to the plasma. Although the plasma is displaced rigidly the toroidicity leads to both m = 1 and m = 2 harmonics in the perturbed vacuum field.

The non-relativistic theory of a plasma in an electric field E predicts that there will always be runaway electrons, although their number will be exponentially small for fields less than the Dreicer field E_D. However, when E/E_D ∼ kT/m_ec², the ratio of the electron thermal energy to the rest mass energy, relativistic effects become important. After comparing earlier non-relativistic calculations we extend the approach of Kruskal and Bernstein to take account of relativistic effects and also to investigate the influence of impurities. It is found that below the critical electric field E_R = E_D (kT/m_ec²) absolutely no runaways are generated. In addition, the number of runaway electrons produced by electric fields in excess of E_R is calculated and we find significant modifications to the non-relativistic estimates when (E_D/E)² (kT/m_ec²) > 1.

Energy losses occurring in high-temperature plasma in contact with a rapidly moving wall are studied. It is found that thermal-conduction and radiation losses prevent reaching thermonuclear temperatures unless the wall moves at a very high speed. On the other hand, re-absorption in high-density systems and relatively weak magnetic fields reduce these losses. A thermonuclear regime can be reached with wall velocities of 25 km/s, attainable by electromagnetic techniques.

A simple technique for reducing the re-cycling rate and impurity concentration in a tokamak plasma is described. An active metal coating, in this case titanium, evaporated onto the surface of the vacuum vessel, provides a trap for neutral hydrogen and impurity atoms which would otherwise freely penetrate the plasma. With this treatment, the plasma density decays with time after the ionization of the initial filling gas is completed, in contrast to typical standard discharges which have a rising density throughout the entire period of the discharge, indicating a large gas influx. These discharges are observed to have resistances close to that of a pure hydrogen plasma, Z_eff ≃ 1.0. There is a corresponding reduction in the intensity of highly ionized spectral lines of oxygen and iron as evidence of reduced impurity concentrations. The value of the effective ion charge, Z_eff, can be varied, by pulsing controlled amounts of impurity gases into the hydrogen plasma.

A powerful beam of neutral hydrogen is injected tangentially into the plasma produced in the Cleo-Tokamak apparatus. The effect on the macroscopic parameters of the plasma and on the equilibrium are found to be small. The energy spectrum of the resulting fast ions contained in the plasma is deduced from measurements of tangentially emitted charge-exchange neutrals. The results for injection parallel and anti-parallel to the plasma current are compared with a classical theoretical model, and good agreement is obtained. Measurements of the perpendicular energy spectrum of 'plasma ions' show that the bulk of the ions are heated by about 10%, and that the low-energy ion distribution has a 'tail', which is consistent with the spectrum of decelerated injected ions.

Fusion power density P_f is a critical parameter for certain fusion reactor applications such as fissile breeding. This paper considers the optimal plasma conditions for maximizing P_f in a beam-driven D-T tokamak reactor. Given T_e=T_i and fixed total plasma pressure, there is an optimal n_eτ_E for maximizing P_f, i.e. n_eτ_E = 4 × 10¹² to 2 × 10¹³ cm⁻³ · s for T_e = 3 – 15 keV and 200-keV D beams. The corresponding = (beam pressure/bulk-plasma pressure) is 0.96 to 0.70. P_fmax increases as T_e is reduced and can be an order of magnitude larger than the maximum P_f of a thermal reactor of the same beta, at any temperature. A lower practical limit to T_e may be set by requiring a minimum beam power multiplication Q_b. For the purpose of fissile breeding, the minimum Q_b ∼ 0.8, requiring T_e⪆ 4 keV if Z = 1.

The optimal operating conditions for obtaining P_fmax in a beam-driven reactor are considerably different from those for enhancing Q_b. Maximizing P_f requires restricting both T_e and n_eτ_E, maintaining a bulk plasma markedly enriched in tritium, and spoiling confinement of fusion alphas. Provided that beam penetration is satisfactory, considerable impurity content can be tolerated without seriously degrading P_fmax.

Variations in the peak electron density and in the impurity concentrations cause significant shifts in the location of the lower hybrid resonance in a hydrogen plasma for a given incident wave frequency. Moreover, small variations in the impurity concentration can resuit in violation of the accessibility condition. Numerical results are presented which indicate these phenomena.

The general characteristics of the implosion of glass shells are described and analytic estimates given. The problems of implosion symmetry are enumerated. The results of the analyses are correlated with computer simulation of the implosions. The diagnosis of pellet behaviour using X-ray pinhole imaging is described and the characteristics of the implosion signature are given. Comparison with experiment shows that the implosions obtained closely agree with the theoretical and computational predictions.

Progress in tokamak research is reviewed for the period 1971–74. The theories of MHD-stability, classical transport and anomalous transport have been refined. The tokamak device population has increased by about an order of magnitude. Non-Ohmic heating methods have been developed successfully. The severity of the problem of plasma impurity has been recognized, and technological countermeasures are being developed. The experimental results on energy confinement are not yet well understood theoretically and cannot be fitted by any simple empirical transport coefficient; the general empirical trend, however, is favourable to the achievement of reactor plasma conditions in large future tokamak devices.

The overall subject of the Conference, – plasma waves and instabilities – allowed the conference activities to be more or less evenly divided between quite different areas of research and application, e.g. fundamental and/or applied theory of waves and turbulence, including numerical models and methods, small laboratory experiments, plasma waves in space, and fusion-oriented work including tokamaks, pinches, heating and diagnostic experiments. Actually, it seemed that nuclear fusion work was less emphasized than at the first Conference in 1973, a fact that was documented, for instance, by the near-absence of MHD-stability theory. One could also note a certain shift of emphasis from short communications to survey lectures.