Table of contents

In the paper, the decay instabilities of the hydromagnetic oscillations in a plasma cylinder placed in the field of a direct magneto-sonic wave H_z = ₀I₀(k₀r)cosΩ₀t (I₀ is the Bessel function, k₀ is the radial wave number, ) and ₀ is the amplitude of the high-frequency field) are studied. Instability growth rates were derived for decay in cases where the result is the excitation of short-wave Alfvén and slow magneto-sonic oscillations. Calculations were carried out for various distributions of the field of the background wave over the cylinder cross-section: k₀a ≪ 1; k₀a = 2.405; a is the radius of the cylinder. The growth-rates are determined by formulae of the type γ = Ω₀A₀/H₀, where H₀ is the strength of the static field, A is a coefficient less than or of the order of unity, depending on the type of decay, the plasma parameters and the wave numbers for the excited waves. Formulae are presented for the determination of the threshold amplitudes for excitation of the instabilities. The possibility of using these instabilities for plasma heating is briefly discussed.

The general expression of the ℓ = 2 straight helical heliotron field is obtained by integrating Biot-Savart's formula after expanding the integrand. Solving the differential equation of the line of force, a general expression for the magnetic surfaces, which is in good agreement with the results of a computer calculation up to the separatrix, is obtained. The rotational transform and the shear of this field are calculated as functions of the average radius of the magnetic surface. For a certain range of α*, the ratio of the longitudinal field produced by the B_z–coil to the longitudinal component of the field produced by the helical coil, the field cannot form a closed magnetic surface. The width of this range, the forbidden zone, is a function of γ = 2πa/p, where a is the radius of the helical winding and p is the pitch. For small γ, the zone is wide and the closed magnetic surface has very small shear. For large γ, the zone is narrow and the magnetic surface has very small rotational transform and shear. Only for intermediate γ, the zone is narrow and rotational transform and shear are both large. These values of γ could be considered to be optimum values for plasma confinement.

It is demonstrated that the allowance for "axial" and "radial" — with respect to the direction of surface-wave propagation — inhomogeneities of plasma density, first, results in a variation of the spatial distribution of the electric field amplitude and, secondly, the frequencies of the propagating surface waves turned out to be local functions of the co-ordinates. The latter point is important in the interaction of charged-particle beams with surface waves. Indeed, the function ω_sw() gives rise to a dependence of the phase velocity (v_pn = ω_sw/k) on the co-ordinates. Since the most intensive energy exchange between the beam and the surface wave occurs under Cherenkov resonance (v_ph = v₀, where v₀ is the beam velocity) the density inhomogeneity affects the conditions of resonance. For this reason, the growth rate of the unstable oscillations decreases.

The dependence of the cross-section and the current distribution on an applied magnetic field in translationally symmetric hybrid systems, in which the magnetic field is produced by external conductors and plasma currents, is considered. If the flux function and the plasma boundary are expanded in Fourier series, this dependence is obtained as relationships between Fourier coefficients. In a first approximation, the cross-section and the current distribution are determined by the applied magnetic field, and for some cases a conducting wall is necessary.

The radial profiles of density, temperature and current of an axisymmetric toroidal plasma in the banana regime are calculated for the case where the rotational transform is produced by a seed current and the radial heat losses are balanced by a heat source. The seed current and heat source are localized in a finite region around the magnetic axis.

A simple global-balance model shows the possibility of reaching the ignition of a low-density (3 − 4 × 10¹³ cm⁻³) tokamak reactor. This requires the use of fast-neutral injection at already achievable energy (100 keV). With the help of their complete cylindrical code, the authors have found for a typical reactor (q = 1.5) that the total injected power has to be about 25 MW. To increase the density up to about 10¹⁴ cm⁻³, the authors propose the use of a moving limiter, the plasma radius being increased from 90 to 300 cm during about 10 s. Plasma ignition is still possible with fast-neutral injection of similar energy. The total injected power for a reactor with q = 3 has been found to be about 80 MW. This power decreases if during expansion q changes from q = 3 (a = 90 cm) to q = 2 (a = 300 cm).

A high-β hot-electron plasma was studied in an asymmetric magnetic mirror device with a variable cant angle. The plasma was produced by microwave heating at a frequency corresponding to cold-electron-cyclotron resonance together with a higher frequency suitable for upper-off-resonance heating. The position of the high-β plasma annulus was studied as a function of cant angle and was found to correspond approximately to the position of a midplane modulus-B contour. High-β effects did modify the spatial location of the losses of energetic electrons into the loss cone but had little effect on the cold-plasma losses. Destabilization was not observed when the line-tying of the plasma centre was reduced with glass end plates. An asymmetry of the cold-plasma loss with respect to the equatorial plane was observed at small cant angles and an electric field model was conjectured to explain this behaviour.

The high-speed ballistic injection of a solid spherical pellet of deuterium into a thermonuclear reactor plasma is studied to determine the feasibility of this technique for controlled thermonuclear reactor fuelling. An evaporation wave front is driven into the solid by the ambient particle energy flux which evaporates the surface of the solid. This evaporated pellet material is an ionized plasma the temperature of which is initially of the order of 10⁴ °K. About one half of the input power to the pellet is convected away by the expanding warm plasma cloud. This evaporated plasma cloud then helps shield the pellet surface from the incident reactor electrons. The dynamics of this pellet evaporation, the expanding plasma cloud, and its shielding effect are studied in detail.

The trajectory of the pellet and the deposition of the evaporated material are analysed for the case of high-speed injection into a fusion plasma having a density profile which is characteristic of a large reactor. Sufficient pellet penetration can be achieved by this means at relatively small power expenditure, but very-high-voltage particle acceleration is required to achieve the needed input velocity.

The authors consider the instability of an electron beam in a plasma with a hot electron component. The presence of the beam means that waves with negative energy may be propagated through the plasma. If the pair collision frequency or the collisionless Landau damping decrement is greater than the beam growth rate, a dissipative instability is created in the plasma/cold beam system.

They indicate the conditions under which the dissipative ion-acoustic instability originates, together with its growth rate and threshold excitation current. On the basis of quasi-linear theory equations, they derive the noise level created by development of the instability and also the distribution of the energy lost by the beam in terms of degrees of freedom (increase in the effective beam temperature and heat-up of electrons and plasma ions).

A review is given of recent developments in collisionless-shock-wave research. Theoretical concepts are compared with both numerical simulation results and experimental observations. Particular emphasis is put on the analysis of collisionless dissipation processes, anomalous resistivity and viscosity.

The Third International Symposium on Toroidal Plasma Confinement was held at the Max-Planck-Institut für Plasmaphysik at Garching near Munich in the Federal Republic of Germany from 26 to 30 March 1973. This Symposium, which was sponsored by the European Physical Society, was the third of a series, the first of which was held at Princeton in 1966 and the second at Dubna in 1969.

The Plasma Physics and Quantum Electronics Groups of the Institute of Physics held a two-day conference on "Laser-Produced Plasmas" on 17–18 April, 1973, at Ferens Hall, The University of Hull. The conference was attended by 120 people, including 16 foreign participants, reflecting the considerable interest in this subject.

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