Table of contents

For a plasma body of density n and characteristic macroscopic dimension L_cthere exists a critical ion density n_c = 1/σ_cmL_cwhere σ_cm ≃ 3 × 10⁻¹⁹ m² for hydrogen. When n ⪅ n_c the plasma is permeable to neutral gas, whereas it becomes impermeable to the same gas when n ≫ n_c. Permeable and impermeable plasmas have different equilibrium and stability properties. So far, tokamak experiments have been performed in the range of permeable plasmas, whereas full-scale steadystate fusion reactors are likely to operate in the impermeable range.

The effects of plasma-neutral-gas interaction, finite resistivity, and viscosity on the gravitational instability modes of a magnetized plasma have been investigated:

1. There are both direct and indirect neutral-gas effects on the ballooning and flute modes. The direct effects are due to frictional forces from collisions, and the indirect ones to the influence of the plasma-neutral-gas balance on the unperturbed pressure and density distributions.

2. In an impermeable plasma, the driving mechanism of the ballooning and flute instabilities can be localized to a narrow, dense and cool, partially ionized boundary region, in which plasma-neutral-gas collisions and viscosity strongly reduce the instability growth rates. Further reductions of these rates are expected to arise in more advanced and non-linear approaches.

3. In tokamaks, resistive ballooning modes should be practically unaffected by neutral-gas collisions. However, when n approaches n_c from below, a collisionless ballooning mode is expected to arise from an increase of the gradients in the boundary region. This behaviour is consistent with observations, including adiabatic-compression experiments.

For a stable Tokamak plasma and given Z-value, it is shown that there is a universal relationship for the toroidal current density which is satisfied in all collisional regimes to within an accuracy of 6%. With Z = 1, the relationship is j_ϕ=σ_||s (E_ϕ + V_rB_θ + [0.32_rB_θ/nT_e]). The only exception occurs for Pfirsch-Schlüter transport where the coefficient of the electron heat flux _r changes from 0.32 to 0.28. This universal relationship is derived from published transport equations and also directly. It is an extra relationship between the fluxes which results because the first-order Larmor radius perturbation to the electron distribution function has approximately only two moments.

The authors consider a theory for the scattering of high-frequency electromagnetic waves in a strongly turbulent plasma in an external magnetic field. In constructing the theory, they do not assume any definite connection between the frequency ω₁ and the wave vectors ₁ of the turbulent plasma oscillations, which is in keeping with strong turbulence.

High-frequency electromagnetic waves interacting with uncorrelated turbulent oscillations change their correlation functions. There arises a certain indeterminacy in the relationship between the frequencies and wave numbers of the high-frequency electromagnetic waves. The theory constructed by the authors makes it possible to consider the correlations of high-frequency waves in a turbulent plasma. The results can be used in the diagnosis of strong turbulence. Examples of strong drift instability and Buneman instability are considered.

Stability properties of large-amplitude, relativistic non-linear plasma waves are investigated by solving the Cauchy problem for the motion of a relativistic electron fluid with uniform stationary ion background. The development of a stationary large-amplitude relativistic wave is studied under the influence of initial perturbations of electric field and particle velocities. Stochastic initial perturbations are slightly damped with time; in the case of parametric initial perturbations, a perturbation growth is followed by non-linear saturation and decay. Under some conditions, particle interstreaming can develop but it does not significantly influence the large potential wells in the wave.

It is shown that the energy variation can be estimated by an integral containing only quantities constant on a magnetic surface. This one-dimensional problem is treated like the cylindrically symmetric case. The result is a sufficient stability criterion which admits a decreasing pressure profile and a non-vanishing current density on the magnetic axis. Unlike the sufficient criteria known so far the new criterion is applicable to axisymmetric configurations without interior conductors.

A new sufficient criterion for the stability of magnetohydrostatic equilibria and Mercier's criterion are compared for axially symmetric equilibria. For simplicity, the analysis is restricted to the neighbourhood of the magnetic axis. The stability conditions lead to the existence of critical values of the rotational transform in the neighbourhood of the magnetic axis which depend on three parameters: the ellipticity and triangularity of the plasma cross-section and the poloidal current. The dependences are qualitatively similar for both criteria. In particular, the case of stationary resistive equilibria without material sources is investigated. Also, rough estimates for the critical values of the plasma β are given. D-shaped plasma cross-sections with a diamagnetic poloidal current appear to be favourable.

The interaction between time-tailored, high-intensity laser radiation and spherical light-element targets is investigated. Simultaneous measurements of the laser plasma electron temperature, charged-particle distribution, absorbed energy, neutron yields and backscattered light intensity and spectra were made. For 100 ps, wide laser pulses focused to intensities ranging between 3 × 10¹⁵ and 2 × 10¹⁶ W/cm² on 150-200μm-diameter LiD and C₃₆D₇₄ targets, plasmas with electron temperatures up to 1.2 keV and target-generated yields of up to 4 × 10⁴ neutrons are produced. The absorption can be accounted for by inverse bremsstrahlung and no.significant contributions due to parametric instabilities are observed. No more than 10⁻¹ of the incident laser energy is back-reflected into spectral components at ω_L, (3/2,)ω_L, and 2ω_L.

The existing theories of transit-time magnetic pumping are based either on the motion of the guiding centre or on the dielectric properties of the plasma and give the ion heating rate and the R.F. power absorbed by the plasma, respectively. It is shown here that the two theories produce identical results if the flux of ion kinetic energy within the plasma is taken into account and that this flux is not accompanied by any mass transport.

A point model of particle densities and temperatures within a CTR is formulated, and equilibrium solutions are obtained for different plausible operating regimes of a D-T reactor of commercial interest. The stability of these equilibrium points against excursions in the overall particle densities and temperatures is determined by linear analysis and confirmed by dynamic simulation – certain regimes are found to be unstable. Control of a CTR about an unstable equilibrium point by varying the injected ion intensity and D-T mixture is investigated and found to be difficult when the ion containment time is not large with respect to the delay time between consecutive changes in the injected ion beam.

A systematic study has been carried out varying the parameters of the Yin-Yang configuration in order to obtain the maximum mirror ratio, , for the last closed nested isobar of the magnetic well. It has been found that the maximum values of obtained are about 2.5, even when the mirror ratio along a line of force attains a large value (≃ 5). Optimization of the access for fast neutral injection is included.

A linear hard-core configuration is used in a study of shear stabilization of drift dissipative instabilities. A neutral-collision-dominated hydrogen plasma with n_e = 10¹¹ cm⁻³, T_e = 10 eV and T_i ≃ 1 eV with a neutral gas pressure between 10⁻³ and 3 × 10⁻³ torr is produced. The spatial mode structure and dependence of the stabilization upon axial magnetic field, pressure and shear are investigated by using correlation techniques. It is found that in the presence of shear the waves retain a drift wave structure (k_|| ≃ 0), while the radial mode is essentially the lowest-order normal mode. A theory is developed which takes into account the collisional mechanism as well as axial ion motion. The stabilizing effect of the magnetic field is in quantitative agreement with the theory. A derived stabilization law which depends upon neutral pressure explains the experimental observation of either a normal-mode structure or a convective-noise-like pattern.

The energy flow per pulse of a D-T reactor is considered, including effects of radial and temporal variations of plasma density and temperature. The overall "efficiency" of the cycle will probably be less than twenty per cent, because of the inefficiency of coupling electrical energy into plasma thermal energy. This low overall efficiency and the spatial and temporal effects lead to required products of density and confinement time which are significantly higher than those obtained ignoring these effects.

It is found that the pattern of plasma changes in its structure when hard X-rays are emitted from a plasma focus and that the sources of the hard X-rays and the fast accelerated deuterons are located in the same region. It is shown that the character of the deuteron spectrum is directly related to the pattern of the plasma focus.

Stability criteria for the collisional trapped-particle instability in an axisymmetric, large-aspect-ratio tokamak with an elliptic cross-section are derived. Comparison with the circular configuration indicates that an increase in the vertical ellipticity can lead to a factor-of-two reduction in the critical density below which the mode is unstable. The improvement is a result of an enhancement of both ion Landau damping and ion collisional damping in the boundary layer of the trapped ions. Collisions are treated via the Fokker-Planck operator and the resulting problem is solved, as in earlier work, by a variational method. Unlike previous treatments of resonant effects, Landau damping by trapped rather than untrapped ions is considered, and the damping rate is found to be approximately the same in magnitude as the untrapped rate derived in earlier work. Results are applied to design parameters for Princeton's PLT (Princeton Large Torus) device and for a reactor, and stability conditions for several tokamaks presently in operation are also determined.

The effect of a large-amplitude, spatially uniform electric field at lower hybrid frequency, which is applied across the static magnetic field, on the dispersion relations for low-frequency drift waves (ω ≪ ω_ci) and drift cyclotron waves (ω ≃ ω_ci) in a collisionless plasma is investigated. It is found that the lower hybrid field can parametrically excite or suppress the drift waves. Expressions are derived for the threshold electric field required for such effects. A particularly interesting result is the possibility of exciting some new macroscopic instabilities when wave-particle resonances are ignored. The results of this investigation are likely to be relevant to some of the recently proposed schemes using lower hybrid waves for heating plasma ions up to fusion temperatures.

The electrostatic modified two-stream instability excited by transverse currents in an inhomogeneous magnetized plasma is studied in the domain where electromagnetic corrections become important . The effects due to ∇B, the distortion in the magnetic field caused by transverse currents, are also included. They are found to affect growth rates and instability conditions for both flute (k_|| = 0) and non-flute type modes significantly.

Rapid-scanning spectrometric techniques have permitted the determination of ion temperatures in ORMAK as a function of time during the discharge pulse for ORMAK plasma currents up to 180 kA. Emission spectra of hydrogen atoms are Doppler-broadened in the line wings, characteristic of the initial proton motions prior to charge exchange, and give ion "temperatures" generally less than kT₊ ∼ 300 eV. Impurity spectra of C III and O V, as well as the spectra of He II in helium discharges, lead to somewhat higher ion temperatures ranging up to a maximum of kT₊ ∼ 700 eV.

The authors make a theoretical study of the excitation of a monochromatic plasma wave by a modulated electron beam in an inhomogeneous plasma when synchronism is kept up between the beam and the excited wave. Results are also given of experimental studies on the interaction of a modulated beam with a homogeneous and an inhomogeneous plasma.

Satisfactory agreement has now been obtained between the MHD model and the experimental behaviour of a plasma focus. On the basis of this agreement and similarity theory, the authors formulate various sets of predictions relating to a device with a high energy content. The authors discuss the different sets of predictions and estimate the associated degree of uncertainty. The relationship, derived from extrapolation of the theoretical results, between neutron yield and capacitor bank energy is confirmed experimentally by increasing the latter several times.

The International Atomic Energy Agency organizes international conferences on controlled thermonuclear fusion and plasma physics every three years. It is, however, clear that intervals of three years are very long; for this reason, the European conferences on controlled fusion and plasma physics are held in between the IAEA Conferences and have recently also acquired international status.

The working group on the interaction of intense laser and electron beams with plasmas met at the International Centre for Theoretical Physics in Trieste from 13 to 31 August 1973. Nine countries were represented by 33 participants, who came principally from the USA (15) and the USSR (6). They were, of course, primarily theorists and hence dealt with problems of parametric instability and possible subsequent strong-turbulence effects, in laser and beam fusion applications. In particular, the questions as to whether Brillouin or Raman backscatter could become important in preventing laser absorption and whether adequately effective absorption mechanisms exist for electron beams were of great interest to the group.

Plasma physicists are becoming increasingly aware of the importance of obtaining an understanding of basic plasma phenomena which cannot be explained in terms of any linear theory of small-amplitude disturbances, and which, collectively, are described as turbulent or large-amplitude phenomena. The first theoretical attempts at describing finite-amplitude effects were made over a decade ago, in the various formulations with the generic title 'quasi-linear theory'.

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