Table of contents

Conditions for the stability of the dissipative trapped ion mode in axisymmetric toroidal confinement systems are investigated, and the ranges of temperature and magnetic field for which the plasma is expected to be unstable are calculated numerically for several proposed Tokamaks. The collisional damping is studied as a boundary layer problem in the velocity space of the trapped ions. The Fokker-Planck equation is solved by means of a variational form with the ordering ν_iR/r ≪ ω ≪2π/τ_i, where R/r is the aspect ratio, ν_iR/r is the effective collision frequency, and τ_i is the bounce time. The relative damping rate is found to be proportional to (ν_iR/rω) ^1/2 [In (rω/ν_iR)^1/2]^−3/2 rather than ν_iR/rω. This damping term is compared with the electron driving term, which is proportional to rω/Rν_e, and with the Landau damping caused by resonant untrapped ions. The presence of a temperature gradient is found to be destabilizing. The Landau term provides relatively strong damping when dT/dr=0 but changes sign when d ln T/d In n > 2/3. In the latter case it is concluded that ion collisions are insufficient to stabilize the mode under typical operating conditions of the proposed machines. Finally, if d ln T/d In n > 1.75 the ion collisional damping itself changes to growth, and the mode cannot be stabilized.

A general expression is derived for the heat flux from a plasma column due to Coulomb collisions of electrons trapped in an electrostatic potential wave. In a particular case, when the electrons are trapped in drift waves, the calculated coefficient of electron thermal diffusivity is in qualitative agreement with the coefficient obtained by processing experimental data from a Tokamak system.

A hot electron plasma is established by ECR (6.4 GHz) in a simple cusped magnetic field. The plasma thus generated consists of hot electrons, cold electrons and helium ions. The hot-electron temperature is determined from X-ray spectra to be about 30 keV and the density of the hot electrons is of the order of 10¹⁰ cm⁻³, which is about 10% of the cold-electron density. The effect of the cusp field is particularly noticeable in the electron-density distribution, which has a void at the centre. Plasma decay times (10 – 60 ms) are observed to increase with the field current. There are several collision processes which cause the loss of hot electrons. The authors derive a simple equation which determines the confinement time of hot-electron plasma and study the confinement of hot electrons by ECR-wrapping. With a wrapping microwave power of 150 W, the decay time is observed to increase to more than three times that without the wrapping power.

The author studies the growth rate and boundary of a drift-dissipative instability in a plasma in which the value of the parameter 3 is finite (β = 8πp₀/B₀², p₀ being the pressure of the plasma and B₀ the magnetic field inside it). It is shown that the growth rate becomes small compared to the frequency at β > ν_e/ω_Be, where ν_e is the electron-ion collision frequency, and ω_Be is the electron cyclotron frequency. The development of this instability proves impossible at β > max[(m_e/m_i) ν_e/ω_*, ρ_i/a], where me and m_i are the masses of the electron and ion, ω_*-is the drift frequency, ρ_i is the ion Larmor radius, and a is a dimension characterizing the inhomogeneity of the plasma. This is in agreement with the results of experiments conducted by Bodin and Newton on the diffusion of a plasma in a linear theta pinch.

An equilibrium solution to the Vlasov equation for a high-6 plasma column with an applied uniform magnetic field B_z is the Maxwellian-like anisotropie distribution, f ∝ exp {−[U+(mv_θ + qA_θ)²r²/2mr₀²]/T}. where the radius r₀ characterizes the excess radial pressure compared to the azimuthal pressure. This is the sort of distribution that might result from the rapid expansion and trapping of a plasma following a sudden heating by a laser or an intense electron beam, before the ions relax by collisions. The weak anisotropy permits the existence of a large, nearly field-free interior bounded by a thinner interface of a thickness of the order of a few ion Larmor radii with only a weak electron-ion streaming. Approximate analytical expressions are obtained for the interface thickness and the plasma radius, and they are compared against numerically calculated plasma-density profiles.

A neutral spectrometer, consisting of a gas conversion cell and electrostatic energy analyser, has been designed, constructed, and calibrated to measure the energy dispersion of energetic H- or D-atoms escaping a plasma. For energies less than 300 to 500 eV the D-atom conversion to D⁺ was greater than that of H-atom conversion to H⁺. At a target density of 0.0125 Torr-cm the conversion efficiency of H in N₂ gas is 3.8 × 10⁻⁴ at 0.165 keV and increases to 3.3 × 10⁻² at 10 keV. Results for H₂ conversion gas were an order of magnitute less than that of N₂ at the lower energies.

This article is devoted to problems of stability in a plasma column which has a hybrid current (constant and variable in time) flowing through it. The variable component of the current is, generally speaking, a helical multipole with zero skin layer. The constant current component exhibits either a skin effect or a uniform distribution over the column cross-section. The perturbations considered here are of the surface-wave type, since it is known that this type of perturbation plays a major role in a current plasma with a free boundary.

Analysis of the dispersion equation obtained indicates that the application of high-frequency multipole fields reduces the critical q-value in current systems. From the physical point of view, stabilization is brought about by the presence of a time-averaged magnetic well and by the effect of dynamic shear. It was found that the effectiveness of stabilization increases as the multipolarity of the high-frequency field, a fact which is explained by increased depth (on average) of the magnetic well. This requires an increase in the radio-frequency circuit currents, however, which means that circuits with a high Q-factor must be used.

The authors also show to what extent the high-frequency circuit (helical conductors) can assume the role of a stabilizing sheath. In the model adopted here the circuit is taken to be an anisotropically conducting sheath and the helical pattern is reflected; perturbations are found on which the circuit exercises a stabilizing effect. These are perturbations whose helix coincides with that of the high-frequency circuit currents projected on a cylindrical plasma surface of radius "a". All other perturbations remain unaffected by the circuit: the perturbed currents do not form a circuit because the helices of the perturbation and the circuit are crossed.

In evaluating the conventional weak-turbulence equations for ion-sound turbulence somewhat more carefully, it is found that the theoretical value of the turbulent energy W = ⟨²⟩/4πnT_e is consistent with observations on collisionless shock waves. However, calculating the anomalous resistivity η using this value of W, η turns out to be too large, regardless of whether simple quasi-linear theory or the strong-trapping theory of Dupree is used.

The theoretical conditions for the applicability of the quasi-linear theory (QLT) are formulated and to investigate the importance of these conditions, numerical experiments are performed on two different types of weak one-dimensional plasma instabilities. It is found that the behaviour of the bump-in-tail instability is consistent with QLT (saturation field energy <²>/8π nT ∼ linear growth rate γ) if these conditions are satisfied, while in the opposite case trapping stabilization is important (trapped-particle bounce frequency ω_b∼γ). The weak symmetric two-stream instability never satisfies the criterion for QLT validity, since all particles that are supposed to diffuse are trapped (Δv_diff ∼ Δv_trap). Incidentally, the first saturation level predicted by QLT is the same as given by the condition for trapping stabilization, ω_b ∼ γ. However, the important deviation from the weakly turbulent behaviour is apparent from the coherent mode-coupling process, which becomes (relatively) the stronger, the weaker the instability.

It is well known that mechanical systems in an unstable equilibrium position can be stabilized by dynamic techniques. Dynamic stabilization has also been applied to unstable plasma equilibria. This review paper attempts to give a general introduction to these problems. A number of special cases within the framework of MHD are discussed.

The Conference was sponsored by the European Physical Society and by the Danish Atomic Energy Commission. The latter also gave financial support. The meeting was organized by members of the Q-machine group at Risø in collaboration with an international advisory committee consisting of Dr. N. D'Angelo, ESRIN, Italy, Professor H. Doucet, Ecole Polytechnique, Paris, and Dr. S. Hamberger, Culham, England. 60 scientists representing 12 countries were present at the meeting and 51 papers were presented.

The Symposium was sponsored by IUTAM (International Union of Theoretical and Applied Mechanics). The Scientific Committee of the Symposium consisted of M. J. Lighthill (Chairman) and eight other members from seven countries. The main topics of the Symposium were: (1) high-speed flow of ionized gas; (2) flow with solid boundaries; (3) shock waves; (4) instability and turbulence, and (5) experimental methods.

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