Table of contents

The steady-state collisional distribution function of a mirror-confined plasma which is known from Fokker-Planck calculations, implies a unique relationship between the plasma pressure and the magnetic field strength at any point within the plasma. Using this relationship it is possible to deduce the maximum β consistent with macroscopic stability in a mirror machine with given mirror ratio. This β limitation is found to impose a rather mild restriction upon reactor designs. For fields which satisfy this β limitation, the profile of the magnetic field along its axis is restricted but not fully determined, by the minimum-B requirement, and the remaining freedom can be used to optimize the magnet design by maximizing the ratio of the thermonuclear power produced to the cost of the magnetic field windings. It is found that even when the profile has been optimized in this way, the plasma density and pressure profiles are rather peaked towards the centre of the reactor, and the ratio of the thermonuclear power produced in such an optimized minimum-B reactor to the power which would be produced in a reactor of the same dimensions but with a square well profile (if it were stable) is approximately 1/4.

The role of azimuthal electric fields in toroidal transport is studied. A consistent kinetic theory for the collision-dominated regime is given and compared with a fluid calculation. The weakly collisional and intermediate regimes are also discussed.

The authors study, in a quasi-linear approximation, the absorption of oscillations excited by an electron beam in a non-uniform plasma. They find the change in the plasma electron distribution function with heating for two limiting cases: a plasma in a strong magnetic field, and a plasma without any field.

The particle distribution in phase space near the loss cone of a stable mirror machine is determined by an asymptotic analysis based on the smallness of λ, the ratio of transit time between mirrors to mean collision time. Away from the loss cone, the solution is obtained by averaging over a bounce motion. Near the loss Cone, i.e., within a distance scaling as λ^1/2, the governing equations are converted into a Wiener-Hopf equation along a boundary line in phase space whose solution yields the desired distribution. It is found that the ratio of plasma density in the mirror throat to central density scales as λ^3/4 while the ratio of external density to central density scales as λ. For typical reactor conditions, these ratios correspond to densities of 10¹¹ cm⁻³ and 10⁸, respectively. Since the distance over which this drop occurs scales as λ^1/2 times the local magnetic scale length, it is necessary to re-examine the reflection of unstable plasma waves in the neighbourhood of the mirrors.

High-frequency (ω ⪆ ω_ci) electrostatic instabilities driven by an electron-ion relative drift velocity across an external magnetic field are discussed for an inhomogeneous plasma. The presence of a density gradient perpendicular to the magnetic field has been found to greatly reduce critical velocities for the onset of several instabilities such as lower hybrid oscillations and ion cyclotron harmonic waves. It has been also shown that the lower hybrid instability can be caused by some positive dissipation mechanism such as Landau damping due to thermal ions and a finite electron collision rate. Some applications have been made to turbulent heating experiments in plasmas in which cross-field currents are present.

When a pellet of solid deuterium is heated in vacuum by convergent laser beams, the laser light is absorbed in a tenuous plasma corona surrounding a dense plasma core. If an attempt is made to heat the plasma too quickly, the corona electron temperature can decouple from that of the core, rising to a high value while the core temperature increases very little. This decoupling effect is examined quantitatively, and it is concluded that the effect may be severe for laser light whose wavelength much exceeds one micron.

The dispersion relation for longitudinal plasma waves in the presence of an external high-frequency electric field is solved in terms of the dielectric function and its derivatives. Particular emphasis is placed on the case of short-wavelength ion acoustic waves (ω <̃ ω_pi), electron plasma waves ω <̃ ω_ce), and cyclotron harmonic waves (ω_ce <̃ ω). which propagate obliquely to the magnetic field. It is found that these modes are unstable with respect to: (i) the purely growing mode; (ii) the overstable acoustic mode; (iii) the dissipative-kinetic instability. The hot-plasma dispersion relation is solved numerically, and thresholds and growth rates are given for a large range of parameters. It is concluded that both the extraordinary mode and the whistler mode may be used to excite the foregoing instabilities, and thus may provide a means for enhanced heating of plasmas. Possible applications for heating of fusion plasmas are discussed.

Computer studies based on the empirical transport coefficients of present-day tokamaks predict strong skin effect in larger, hotter tokamak models. If the skin effect is suppressed by further anomalous enhancement of thermal transport in the skin layer, the resultant energy, loss and associated limiter heat load are inevitably very large. Suppression of the skin effect by a moving limiter is investigated.

An engineering study of r.f. heating of fusion reactors is described. The frequency range considered is below 100 MHz. Special consideration is given to r.f. structures located between the reactor wall and the plasma in the main fusion region. Possible arcing problems in this region are discussed and it is found that they may not be too serious for neutral pressures below 10⁻⁴ torr. It is proposed to feed the r.f. through a slanted vacuum port in order to reduce port area and to protect the voltage insulator from radiation and temperature damage. The cooling of an r.f. coil structure is considered in detail. It is proposed to use a split r.f. coil composed of heat pipes to carry the heat away. Curves are presented which give the maximum r.f. on-time for various coil currents, frequencies, and coil sizes before the coil surface reaches melting temperature. Other coupling schemes involving the use of the vacuum wall as a r.f. structure or locating a wave launcher in the high-field region of a mirror reactor are discussed. In the case of a mirror reactor it is found that this last scheme may be quite attractive since unidirectional couplers can be made and experimental results indicate that the wave reflections may not be too serious in the severe-density and field gradients. This scheme also offers a possible way of launching, for instance, ion-cyclotron waves into very dense plasmas. It is concluded that the engineering problems of fusion-reactor-r. f. heating, albeit formidable, are not impossible.

It has been shown previously that the ignition of thermonuclear micro-explosions ( micro-bombs) may become possible by bombarding a dense thermonuclear target with an intense relativistic electron beam. Although such a scheme is within the realm of technical feasibility, the energy requirements were shown to be considerable, amounting to a burst of relativistic electrons of several megajoules to be delivered within several nanoseconds. It is shown in this paper that the energy requirements can be greatly reduced by utilizing the strong self-magnetic field of intense electron beams. The strong self-magnetic field can reduce the electronic-heat-conduction losses and also greatly quench the range of the charged fusion products within the thermonuclear target. The reduction in the input energy in conjunction with the demand for a strong self-magnetic beam field directs the emphasis on beams of relatively low voltage but high current. The relatively low beam voltage also facilitates the beam energy dissipation in the target.

Because of the much greater ease and efficiency by which intense electron beams can be produced as compared to laser beams and because of the energy-reducing effect of the self-magnetic beam field the described method may have substantial advantages over the laser method of bombarding a thermonuclear target.

The paper presents theoretical calculations and the results of experimental studies of the behaviour of a plasma contained in a strong constant magnetic field when a rotating high-frequency field of dipole configuration with frequency Ω is superimposed upon it. It is shown that for υ_ei > Ω (where υ_ei is the frequency of collisions between electrons and ions) the high-frequency field excites an azimuthal electric current j_φ on the plasma surface. The interaction between the current j_φ and the constant magnetic field H_z generates a dynamic force, which forms the plasma into a column.

The plasma is compressed into a column when the vector of the angular velocity of rotation of the high-frequency field and that of the constant magnetic field ₀ coincide in direction. When the plasma is compressed into a column, there is no contact with the walls of the vacuum chamber and the degree of ionization is close to total. Probe and microwave measurements have shown that the time of compression of a plasma into a column for H_z = 8 × 10³ – 1 × 10⁴ Oe is ∼ 300 μs and the rate 6 × 10³ cm/s. The diameter of the column was of the order of 2–3 cm. The charged-particle concentration measured with the help of superhigh-frequency waves (λ = 2 mm, 8 mm and 32 mm) was greater than 2 × 10¹⁴ cm⁻³ and decreased by more than two orders at a distance of 1−1.5 cm from the column centre.

When the vectors and ₀ are opposite in direction, the force is directed away from the axis, and in this case, the plasma in the form of a hollow cylinder is situated at the vacuum-chamber walls.

The maximum strength of the rotating high-frequency field at 1.25 MHz was 100 Oe. The results obtained show good agreement with the theoretical calculations.

As a continuation of a previous study, the magnetic configuration of the torsatron with ℓ = 2 helical windings and no toroidal field coils is investigated. A useful volume with closed toroidal magnetic surfaces exists only for sufficiently large pitch angles of the helical windings (> 45°). With increasing pitch angle the rotational transform on the magnetic axis decreases, and high shear is obtained (Θ ∼ 1). In this case, the mirror ratio along the field lines is relatively high (B_max/B_min > 1.5). If we require low mirror ratio (B_max/B_min < 1.5) the ℓ = 2 configuration is limited to low shear, in contrast to the previously studied case ℓ = 3 which has considerable shear even when the mirror ratio is low.

Research on plasma physics occupies a prominent place in modern science. It is closely associated with the search for a solution to such extremely important scientific and technical problems as the achievement of controlled nuclear fusion, the development of a magneto-hydrodynamic method for the conversion of thermal energy into electric power, and the conquest of space. In view of the important tasks facing plasma physics and the enormous variety of phenomena with which it is concerned, the intensive development observed in that field during the last two decades was a foregone conclusion. From a branch of physics studying a narrow range of phenomena, plasma physics has turned into a broad, independent avenue of research which is now rapidly encroaching upon and penetrating other branches of physics. The interlinking and interpenetration that exists between plasma physics and related branches of physics is most evident in the realm of theory, since they are based on a common background of method and the inherent unity of fundamental physical laws.

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