Table of contents

Experimental results from the Adiabatic Toroidal Compressor (ATC) tokamak are used to obtain empirical scaling laws for the average electron temperature and electron energy confinement time as functions of the average electron density, the effective ion charge, and the plasma current. These scaling laws are extended to include dependence upon minor and major plasma radius and toroidal field strength through a comparison of the various tokamaks described in the literature. Electron thermal conductivity is the dominant loss process for the ATC tokamak. The parametric dependences of the observed electron thermal conductivity are not explained by present theoretical considerations. The electron temperature obtained with Ohmic heating is shown to be a function of current density – which will not be increased in the next generation of large tokamaks. However, the temperature dependence of the electron energy confinement time suggests that significant improvement in confinement time will be obtained with supplementary electron heating.

The use of relativistic electron beams for supplementary heating of tokamaks to ignition temperatures is discussed, under the assumption that they can be successfully injected. It is shown that if an electron beam with present-state-of-the-art power, but longer pulse length, can be injected into an Ohmically pre-heated tokamak plasma, it transfers its energy to the plasma on a time-scale short enough for synchrotron radiation to be an unimportant beam energy loss mechanism, while the turbulence generated does not affect the energy confinement. Beam energy and pulse characteristics required for an extension of the ideas to a reactor-size tokamak are presented.

Experimental evidence of the effectiveness of a magnetic limiter has been obtained in the Heliotron-D. The fundamental properties of a built-in divertor are studied. In a divertor-like magnetic-field configuration, the plasma is observed to be isolated stably from the helical conductor. It is observed that the plasma diffuses through the divertor layer, whose thickness is estimated experimentally.

The generalized distribution function is used to investigate the effects of loss-cone and temperature anisotropy on the cross-field-current-driven electrostatic instabilities, i.e. the modified two-stream instability, the ion-acoustic instability and the electron cyclotron drift instability. These effects are important only when (k is the wave number and ρ_e the electron gyroradius). It is seen that non-Maxwellian plasmas with distribution index J≥1, can sustain fast-growing waves even in the region of k-space which is stable for a Maxwellian plasma. Moreover, when λ ∼ 1, the temperature anisotropy is found to have a destabilizing effect on.the modified-two-stream instability and on the ion acoustic instability.

The effect of adiabaticity and superadiabaticity limitations on the use of radio-frequency-augmented magnetic-mirror confinement is examined. It is shown that the scaling of the region over which the r. f. fields are applied to maintain a given level of adiabaticity is such that, although the fields decrease as resonance is approached, the total r. f. energy stored in the resonance region remains constant. Assuming that the dissipation is proportional to the energy stored, we conclude that the external energy supplied is not reduced from the energy requirements of non-resonant r. f. containment. In fact, the weak additional scaling required to maintain containment by superadiabaticity implies that resonant r. f. containment requires more applied power. The stochastic heating, resulting from the small-phase uncorrelated energy changes occurring on each pass through resonance, when superadiabaticity is not satisfied, is such that only a small improvement in the field strength required for containment can be made by operating in this mode.

The stability of kink modes in a cylindrical plasma column under the influence of an oscillating magnetic field applied in the azimuthal direction is studied. The frequency of the applied field is chosen close to the ion-acoustic frequency. It is found that coupling to damped ion-acoustic waves induces a small real frequency to the kink modes which can significantly affect their growth rates. Conditions for parametrically suppressing (or exciting) these modified kink modes are specified.

The conditions and consequence of the onset of ion cyclotron instabilities in tokamaks that can be induced by the finite amplitude level of the trapped-ion mode are studied. It is found that such oscillations are likely to be present but are not likely to alter the diffusion rates originally predicted by Kadomtsev and Pogutse.

The stability of helically symmetric finite-β, ℓ = 1 magnetohydrostatic equilibria with arbitrary pressure profile and vanishing longitudinal current is investigated by means of Mercier's criterion, a sufficient criterion by Lortz, Rebhan and Spies, and Shafranov's condition for a high–β magnetic well. The new finite–β effects are that (1) a magnetic well is created throughout the plasma region for 0.2 ≲ β ≲ 0.95 and 0.3 ≤ aτ ≤ 0.6 (a is the plasma radius, τ the torsion of the magnetic axis); (2) the mean magnetic well extends out into the vacuum region for 0.75 ≲ β and bτ ≲ 0.6 (b is the wall radius); (3) with the exception of a very narrow region (< 0.1 aτ) around the magnetic axis, the Mercier criterion is satisfied for 0.75 ≲ β ≲ 0.95 and 0.12 ≲ aτ ≲ 0.3.

Calculational results are presented from an extensive study of the hydro-burn response of bare DT shells, inert shells, and DT-filled micro-balloons to ramp-like, Gaussian, and square laser pulses. Scaling laws are determined for the best pulse energy and time scale for shells, as functions of their mass, aspect ratio and initial density. The advantages of DT ice over DT gas in the microballoons are demonstrated. An equivalence rule is established between linear ramp pulses and Gaussians, and a connection is drawn between the ramps and square pulses. Projections are made, via the scaling rules, to breakeven-plus pellet designs. The scaling rules are used to recommend pulses for pellets recently imploded at LASL and KMSF. The calculated performance of these targets is shown to agree, after adjustments, with the laboratory findings. Attention is drawn to practical problem areas in structured pellet design.

The dispersion relation is derived for parametric instabilities caused by an intense ion sound wave which couples high- and low-frequency electrostatic modes of a non-isothermal unmagnetized homogeneous plasma. The phase velocity of the pump wave is between the ion and the electron thermal speed. The dispersion relation contains filamentational, modulational, and stimulated scattering instabilities. Growth rates as a function of the pump and plasma characteristics are given. For a given amplitude of the pump, |ϕ₀|, the largest growth rate is found in the case of filamentation instability. The particular physical situation studied in this paper is related only loosely to any actual R. F. heating experiment. However, it allows some new basic parametric processes occurring during R. F. heating below and around the ion gyrofrequency to be clarified. Finally, the relevance of this and other more generalparametric instabilities, from the point of view of plasma heating and confinement, is briefly discussed.

Line radiation in the vísible and ultraviolet (100–1300 Å) spectral regions has been studied on TFR for a 140-kA, 26-kG plasma. The emission is integrated along the line of sight, except for neutral-deuterium visible radiation, which has been spatially resolved. From the measured absolute signals, the initial (in the first ten milliseconds) amount of impurities has been determined. Subsequently, the observed signals can be interpreted in terms of an impurity-recycling flux. It has been deduced from power balance considerations that this flux is confined to an external plasma shell, a small part only diffusing towards the centre to account for the independently inferred Z_eff. The power radiated by the observed lines corresponds to an important fraction of the injected Ohmic power (∼ 30-40%). Two lines ascribed to Mo XXXI and Mo XXXII (and therefore originating in the central hot plasma core) have been detected for electron temperatures greater than 1.5 keV.

As part of a study for a mirror fusion-fission hybrid reactor, a preliminary design for a 225-MW neutral beam injector of fast deuteriu m atoms at 100 kV and fast tritium atoms at 150 kV was prepared. The injector layout consists of four assemblies, each comprising 70 ion-sourc e modules mounted in a converging array. An efficient, long-lifetime cathode for the plasma sources is proposed. The requirements for ion extraction and acceleration are satisfied by a two-stage accel -decel-accel-decel grid system designed to operate within th e limitations imposed by beam space charge, beam optics, voltage breakdown, and grid bombardment by secondary ions and electrons. A low-temperature neutralizing cell followed by a system for recovery of the energy of the unneutralized fraction of the beam has been designed to provide an overall injector power efficiency greater than 70%. To maintain required pressures within th e acceleration assemblies, the neutralizers, the beam energy recovery systems, and the beam line itself, pumping systems capable of handling a total gas flow of 2400 Torr·litre·s⁻¹ are required. Problems associated with magnetic shielding of the ion source assemblies from the reactor fringing field as well as the mounting of the accel-decel grids at high voltage and high temperature are evaluated.

The variational principle of irreversible entropy production as formulated by Rosenbluth, Hazeltine and Hinton is used to evaluate the electron thermal diffusion coefficient. Starting from an equal-temperature plasma kinetic equation using the drift approximation and assuming that a small periodic electrostatic non-uniformity exists within the plasma we derive an expression for the electron heat flux. In this derivation the full Fokker-Planck collision operator is employed and the effect of both like and unlike particles is included. The coefficient of electron thermal diffusion deduced from the electron heat flux expression is identical with the one deduced by Pogutse (up to a multiplicative factor), and is in qualitative agreement with the pseudoclassical result.

The excitation of a current in a plasma by injection of an ion beam is considered. It is shown that a current ca n be maintained in a plasma not only i n the case where the plasma and beam ion charges are different but also in the case where they are the same . The current density is calculated for the latter case. In addition, the relaxation of an ion beam in a Maxwellian plasma is considered and the distribution function of the beam ions in a plasma is obtained in the form of a Legendre polynomial series. This function is used for calculating a number of quantities important for the problem of maintaining the current.

Analytic expressions are obtained for particle and heat fluxes in the Pfirsch-Schlüter regime for tokamak plasmas with elliptical cross-section flux surfaces, allowing for outward toroidal equilibrium shifts. The results are then used in an elliptical metric 1D transport code, and rather striking differences in the plasma profiles are found to result from cross-section shaping for the comparative example of tokamak start-up. The Pfirsch-Schlüter diffusion flux of heavy impurities is then compared analytically for elliptical and circular cross-sections, and quantitative estimates are made of the extent to which ellipticity can retard impurity accumulation in a device such as Doublet II-A.

A study was made of the influence of ion viscosity and ion hea t conductivity on the drift instability of a weakly collisional plasma of finite pressure in a magnetic field. Drift oscillations, whose phase velocities in the direction of the magnetic field are of the order of the ion thermal velocity, were considered. Instability region boundaries and growth rate s were determined. The influence of ion viscosity and heat conductivity leads to a widening of the instability regions. In the stability regions, the given effects result in damping of the oscillations. The corresponding damping rates were determined.

The influence of longitudinal electron heat conductivity and finite heat exchange between electrons and ions on the drift instability in a strongly collisional plasma with finite pressure is investigated. Drift oscillations are considered whose phase velocities in the magnetic-field direction are of the order of the thermal velocity of the ions. The boundaries of the drift instability regions and the instability growth rates are determined. The dissipative effects considered result in broader regions of instability than those found when these effects are not taken into account.

The authors describe hybrid magnetic trap of the stellarator type (Unitron) employing a helical winding with four poles arranged in a certain way with respect to the minor azimuth . Combination of the helical conductors and current provides qualitatively different magnetic traps with spatial and plane magnetic axes. Analytical expression are derived for the various characteristics of the main types of Unitron trap. A study of the parameters of the Unitron shows that the system with the second and third harmonics of the helical field has better confinement properties.

The authors study the structure of the magnetic field in an ℓ = 1 toroidal torsatron. Experiments on the Vint-20 device and numerical calculations on a computer have shown that closed magnetic surfaces with high parameters exist in an ℓ = 1 torsatron. The forms of the magnetic surfaces are given together with graphs showing how their parameters vary within the working volume under different operating conditions. It has been established that the magnetic surface parameters can be adjusted within wide limits by changing the vertical field. It is shown that this type of system is characterized by high inhomogeneity of the magnetic field in the working volume and that this inhomogeneity can be substantially reduced by applying a vertical field or by changing some parameters of the helical winding.

An overall systems analysis of a fusion reactor scheme based on strong rings of high-energy ions generate d by adiabatic compression of low-energy rings is presented. Consideration of the reactor aspects of such a system reveals the potential for a number of technologically and economically interesting features; in particular, those associated with the expected high-β confinement characteristics of such minimum-B configurations. Although insufficient knowledge on some of the related physics questions exists, no insurmountable problems regarding th e feasibility of such a scheme can be discerned at this point. A preliminary design study for a N × 300-MW reactor (N being the number of simultaneously employed rings) is presented.

The authors consider the penetration of electromagnetic waves with a frequency of the order of the ion cyclotron frequencies and with a fixed longitudinal wave number k_||, so that N_|| = k_||cω ≫ 1 deep into an inhomogeneous plasma with two ion species. The propagation of two kinds of waves (fast and slow) with widely differing polarization and transverse refraction index is possible. For both types of waves there is an evanesence region at the plasma periphery.

The evanescence region is narrow for slow waves and the y easily penetrate the plasma. In a dense plasma they become electrostatic and can reach the ion-ion hybrid resonance region. However, the damping of these waves due to Cherenkov interaction with electrons in a high-temperature plasma is strong and therefore they are not suitable for heating plasma of large dimensions, as they are absorbed at the plasma periphery.

The fast waves have a wider evanescence region and can be excited effectively only if N² is not too high. These waves can be completely absorbed in the plasma (due to Cherenkov interaction with electrons) if where a is the plasma radius and . Fast waves can also reach the region where they are transformed into slow waves. In this region their damping increases considerably. It is shown that the transformation region in an inhomo-geneous plasma with two ion species in a non-uniform magnetic field may be at the centre of the plasma. Fast waves can be used effectively for heating plasma of large dimensions.

The Third Topical Conference on Pulsed High-Beta (β) Plasmas took place at Culham Laboratory (United Kingdom) from September 9 to 12 197 5. Approximately one hundred papers were read, covering theta-pinches, high-beta stellarators, reversed-field pinches, screw-pinches, high-beta tokamaks, plasma focus and related theory. Welcoming the delegates, the Director of Culham Laboratory (Dr Pease) stressed the quadratic dependence of the nuclear power density on β and the consequential advantage of high β. He also directed attention at the possible stabilizing influence of high β on drift-wave modes and at the importance of finding hydromagnetically stable high-β toroidal equilibria. He doubted the long-term value of basically unstable toroidal systems relying on feedback dynamic or finite-Larmor radius effects for satisfactory operation.

This Conference in Eindhoven represented the twentieth anniversary of similar conferences held every two years on the topics of gas discharge and plasma physics. The first of these conferences was also held in The Netherlands. Since then, plasma physics has evolved considerably. Basically the aim of the organizing committee was to divide up the conference as evenly as possible between contributions on gas-discharge physics and contributions on plasma physics. However, of a total of 397 contributed papers, only 131 referred to plasma physics. Of the thirteen invited papers, eight were concerned with plasma physics and controlled of fusion research.

Davidson and Schram (Nucl. Fusion8 (1968) 183) studied, using Lagrangian methods, the phenomena of nonlinear oscillations in a cold plasma. In particular, they conclude that their solution can never take the form of Bernstein-Greene-Kruskal waves. It is the purpose of this note to point out that this is not so and that for a particular choice of initial conditions, given explicitly below, B-G-K waves can be obtained.