Table of contents

The present paper is a coherent account of various aspects of longitudinal oscillations in one and two component plasmas. A discussion is offered of dispersion equations, conditions necessary for the growth or decay of oscillations, the physical mechanisms of growing or damping, and the possibility of arbitrary steady-state solutions. The physical situation is described in terms of Poisson's equation and the Boltzmann equation, while the mathematical description is in terms of solutions of an initial-value problem in the small amplitude (linearized) approximation. Some general results are derived for an arbitrary unperturbed velocity distribution of electrons and ions. From these expressions the customary results for a stationary plasma in thermal equilibrium can readily be obtained. For simplicity, one dimensional motion of a simple one component plasma is treated in detail; appropriate generalizations for two or more component plasmas (electrons and ions) are, however, indicated in text. Collisions between particles and non-linear effects are not considered, nor are the effects of external electric or magnetic fields.

The properties of longitudinal plasma oscillations in an external electric field are investigated. In a completely linear approximation, it is found that the direct-current electric field introduces essentially no new effects. A quasi-linear approximation is also considered, in which couplings between different plasma modes are neglected while the space-averaged distribution functions are assumed to be approximately independent of time. In this case, a Maxwellian distribution function is found to be always unstable against the growth of very long wavelength oscillations.

The motion of a one dimensional oscillator with time dependent restoring force is investigated. We consider ω(t) having one singularity for finite t and such that

lim_|t|->∞|d/dtω^-1(t)| = 0

and consider the asymptotic behaviour of ω times the square of the amplitude. The ratio of this quantity evaluated at two times, t₁ and t₂ averaged over an ensemble is, in the limit |t₁|, |t₂| → ∞, an adiabatic invariant in the sense that this quantity is not changed by multiplication of ω by a slowly varying function of t. This permits replacement of the actual ω(t) by a, presumably simpler, ω₀(t) if their ratio, ω₀/ω is non-singular.

Since the orbit equation for a charge in a time-dependent axisymmetric magnetic field is reducible to that of a one-dimensional oscillator it possesses such an invariant. This problem is examined in some detail, particularly for the model field ω(t) = ωt. These solutions provide explicit estimates for the energy gained by a charge under a reversal of the magnetic field.

This paper describes the neutron emission observed during an investigation of the characteristics of fast linear Z-pinches using a low-inductance condenser bank. The neutron production is compared with the results obtained elsewhere and is shown to be different in several respects from that obtained with low-power banks, but is quite similar to that reported in more recent, high-power experiments. It is shown that much of the yield is non-thermonuclear, and a number of existing theories for the production of neutrons by acceleration processes in a plasma are discussed. A process of neutron production in fast linear pinches is suggested, which qualitatively accounts for many recently reported results; the proposed mechanism becomes the well-known Colgate process in discharges where m = 0 instabilities lead to narrow necks in the plasma. Reasons are given to account for the absence of appreciable thermonuclear yields which might be expected from theoretical considerations.

A complete algebraic analysis has been obtained for the variation of the steady-state ion density n₊ with injected current I in an OGRA-type fusion device (i.e. a device based on trapping of ions by break-up of energetic molecular ions on collision with either the background gas or trapped ions). The most general variation of n₊ with I is shown to be an S-curve with at most three roots of n₊ for a given input I. A physical interpretation of these three roots is given. In addition algebraic expressions are obtained for the two currents at which the bends in the S-curve occur. It will be necessary to attain the larger current in order to build up a high-density plasma when the density is being increased from below. On the other hand, once the high density has been achieved, it may be maintained by steady injection of a current larger than the lower value. Parameters corresponding roughly to the specifications of OGRA are used to obtain some numerical results. In the final appendix, the previously published formulas for burn-out in DCX are extended to include effects of neutral backstreaming from the input beam and `ion-pumping.'

The positive column of a gas discharge is shown to become unstable when a sufficiently large longitudinal magnetic field is superimposed. This instability causes oscillations which lead to an increase in the flux of charged particles striking the walls; that is, in agreement with the experimental results, there is an increase in the effective diffusion.

The feasibility of filling up a magnetic trap with plasma has been investigated by injecting accelerated plasmoids into a trap formed by a magnetic field which increases towards the periphery. It is shown that in such a system the lifetime of the plasma is several tens of microseconds under the conditions of these experiments.

The motion of tritium β-particles in an adiabatic trap is considered. It is shown that under some conditions the β-particles may be reflected from the strong field region (the magnetic mirror) more than 10⁷ times. The lifetime of the particle has been studied as a function of the gas pressure and of the configuration and uniformity of the magnetic field.

Consideration is given to resonances between the Larmor rotation of charged particles and their slow oscillations along the lines of force. Under certain conditions these resonances can result in a complete exchange of energy among the degrees of freedom of the particle, so that the particle escapes from the trap. The influence of resonances on adiabatic processes associated with a time variation of the magnetic field is also examined.

Possible designs for a cyclotron with a radially travelling magnetic field wave are considered and relations between the parameters are deduced. One or more radially travelling waves can be produced in the magnet gap by using separate ring windings fed from an a.c. source. Two possible systems are proposed. In the first, the travelling wave is responsible for accelerating the particles; in the second, a travelling field is superimposed on the normal fixed field and the particles are accelerated in the resulting total field. A region of stability (1 > n > 0) can be obtained and this must move outwards at the radial velocity of the particles. Stability is possible if the absolute field strength increases sharply from the inside to the outside of the acceleration zone. In principle, the system would allow the production of particles with energies as high as desired. In spite of the cyclic nature of the action, the mean beam intensity could well be better than that from a synchrocyclotron because of better focusing. Some approximate calculations are presented for accelerators of this type designed to produce various energies. It is shown that for a given energy the weight and size can be substantially less than for other types of accelerator.

Preliminary results from a study of the effect of a magnetic field on electron diffusion in a plasma are described. A stepwise increase in the ratio of the electron current to the ion current to a probe has been found for a certain critical magnetic field strength. According to the preliminary results, this critical magnetic field is proportional to the gas pressure. These facts seem to indicate that there are two qualitatively different mechanisms of the transverse movement of electrons, one of these being diffusion by collisions.

Experimental data concerning the anomalously high mobility of electrons across a magnetic field are discussed. It is shown that the concentration distribution of the secondary plasma of a hot-cathode discharge is almost independent of the transverse diffusion coefficient of the electrons, and so cannot be used to elucidate the mechanism of diffusion. The electron diffusion coefficient is estimated from the density of the electron current to the anode; the result confirms that the transverse mobility is anomalously high.