Table of contents

The linear Boltzmann equation for the uansport of neuual atoms in highly ionized plasmas is compared with the neutron transport equation. It is shown that, when the plasma is isotropic, the neutral transport equation can be solved with neutron uansport methods. Two formulations of the neutral transport equation that are amenable to solution by existing multigroup neutron uansport codes are given – the multigroup formulation and the multispecies approximation. In the first, the solution provides the neuttal energy (as well as spatial and angular) disuibution, whereas in the latter, the specuum of each neutral species is assumed to be known and fixed. As an illustration, a problem of neutral penetration to and interaction with the plasma of the ST Tokamak is solved. The solution is obtained for a two-species model using the discrete ordinates code ANISN.

Measurements have been made of electron temperatures in the Oak Ridge Tokamak, ORMAK, using Thomsonscattered light from a Q-switched ruby laser. The measurements described were made during spring 1973. The measured electron temperature ranges from 0.20 keV to 1.2 keV for average electron densities of 1 × 10¹³ to 3 × 10¹³ cm⁻³. The radial electron temperature profiles observed in stable discharges are broad (flat over about 1/2 the limiter radius), while a tendency towards sharpened profiles appears when the discharges become unstable at low safety factor. In these measurements β_p (plasma kinetic pressure/poloidal magnetic field pressure) is observed to vary as _e/I, and the resistivity enhancement (experimental resistivity/Spitzer resistivity) as, at a constant current, 1/_e. An empirical expression for the energy confinement time is discussed.

Ion-cylotron resonance heating experiments in the toroidal plasma of the Heliotron-D are described. The magnetic configuration used has a fairly strong helical inhomogeneity with a large rotational transform angle and shear. An appreciable ion temperature increase is observed from measurements of the Doppler line width of He-II at a 100 kW r.f. power level. A comparison study with other devices is described for a scaling of the ion-cyclotron resonance heating in present toroidal plasma.

Exact solutions are given for an axisymmettic toroidal plasma equilibrium with rectangular cross-section. The equilibrium configuration in which the current and the plasma pressure are zero at the boundary is examined by using the criterion of local stability. The equilibrium exists for large β, but its maximum value is limited by local instability.

The optical power P_L required to achieve a given measure of inertial confinement ρR of a laser-compressed DT pellet is found to be approximately proportional to (ρR)². This result is based on a model of self-regulating pellet ablation by hot electrons of the pellet corona that is relatively insensitive to the details of the pellet ablation process. To achieve values of ρR believed necessary in the application of laser fusion to commercial power production, 3 × 10¹⁵ W of optical power is found to be required, implying a total laser output aperture of 30 m². (The same power requirement would appear to apply to pellet compression by charged-particle beams.) An estimate of the required laser-pulse energy W_L, assuming corona-core decoupling to be the controlling limitation, is also given. In the application to commercial power production the required pulse energy is found to range from 70 kJ at 0.265 μm to 3 MJ at 10.6 μm.

Some results on the properties and solutions of the steady-state form of the neoclassical transport equations are presented for regimes of interest to feasibility experiments and reactors. An analytical solution is obtained for the special case dT/dr = 0. For dT/dr ≠0, an analytic solution is found for the particle density n(r) in terms of the current j(r) and the temperature T(r). For a prescribed j(r), a single differential equation remains to find the temperature profile. The numerical results suggest that neoclassical scaling does not admit self-sustained fusion plasma operation (n ∼ 10¹⁴/cm³, T ∼ 10 keV) except in plasmas of uninterestingly small sizes (I_p <500 kA).

The stability of m = 1 long-wavelength kink modes in diffuse high-β ℓ = 0 and ℓ = 1 systems has been investigated. For ℓ = 0 it is found that new modes exist with potentially dangerous growth rates and mode structure but which degenerate into zero growth-rate modes in the sharp boundary limit. The existence of such modes provides an explanation to an apparent paradox in the literature concerning ℓ = 0 wall stabilization. For ℓ = 1, it is found that the sharp boundary wall stabilization of the gross m = 1 mode remains essentially unchanged for diffuse profiles. This is favourable for the Scyllac programme.

The plasma shape and location of a sharp boundary belt pinch is determined by the dimensions of the surrounding conducting shell and by thermodynamic parameters. It is shown that, except for simple scaling, there exists a one-parameter family of equilibria. The plasma shape is uniquely determined by initial parameters and wall current. The variation of the plasma shape during an adiabatic compression is calculated, as are plasma current, temperature, field strength, etc. As the compression ratio of the plasma is increased beyond two, the ratio of plasma height/width decreases to unity. For high compression ratios, the column cross-section becomes circular. Explicit solutions are obtained by conformal mapping.

The neoclassical transport theory of a toroidal plasma in the presence of ion impurities is investigated. In particular, referring to situations with hydrogen ions and electrons in the banana regime, the two possibilities, of the impurity ions being in the banana or in the plateau regime, are considered. It is found that, in the small aspect ratio limit and for practical values of impurity concentrations, the hydrogen ion diffusion across the magnetic field does not depend on the neoclassical regime of the impurities.

Experiments are reported on helical plasma equilibrium and stability in the Scyllac toroidal θ-pinch sectors (120°) which have major radii of 2.375 and 4.0 m with coil arc lengths of 5.0 and 8.4 m, respectively. In these experiments the outward toroidal drift force was compensated by a combination of ℓ = 1 helical and ℓ = 0 bumpy fields which are generated by shaping the inner surface of the compression coil or by driven ℓ = 1 windings. Time-resolved measurements were made of the gross plasma-column motion, the plasma radius, the magnetic flux excluded by the plasma, the external magnetic field, the plasma density, the electron and ion temperatures, and the plasma β at axial locations of minimum and maximum plasma radius. These data are used to study the approach to the theoretically predicted toroidal equilibrium (including axial pressure equilibrium). The plasma column remained in stable equilibrium for 7 – 10 μs in the 8-m sector compared with 4 – 7 μs in the 5-m experiment, at which times the onset of a terminating m = 1, k ≈ 0 sideways motion occurred. The results show that the plasma achieved axial pressure equilibrium (nkT = const) in 4 – 6 μs, while maintaining equilibrium in the toroidal plane for 10 μs or longer. The measurements of the plasma radius, β and magnetic field in the various experiments have confirmed in detail the stable toroidal equilibrium observed in the streak photographs during the first 4-10 μs of the discharge. The observed toroidal equilibria of the high-β, θ-pinch plasma are in quantitative agreement with MHD sharp-boundary theory and confirm the theoretical scaling of the equilibrium field between the 5-m and the 8-m sector experiments.

The non-linear evolution of drift-cyclotron and drift-cone oscillations close to the stability limit is considered. It is shown that non-linearity has the effect of stabilizing drift-cyclotron instability and intensifying drift-cone instability.

The possibility of using intense relativistic electron beams (REBs) for heating plasmas in open systems is discussed. Within this context the following three sets of problems are discussed:

1. REB transport in a vacuum with a strong magnetic field; beam equilibrium, stability and critical currents in a vacuum.

2. Beam transport in a plasma; charge and current neutralization of the beam; reverse-current heating of the plasma, and macroscopic REB instabilities in the plasma.

3. The theory of collective relaxation of REBs in a plasma, including quasi-linear and non-linear relaxation models; the role of plasma non-uniformity, and macroscopic effects during REB relaxation.

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