Table of contents

A normal mode treatment is proposed for the solution of boundary value problems in plasma oscillations. The plasma distribution function and electric field are expanded in terms of the solutions of the coupled Vlasov and Maxwell equations. These normal mode solutions are somewhat unusual in that they are singular functions of the velocity variable, and, in fact, the expansion theorem is proved by means of a direct solution of an associated singular integral equation. As an application of the method we obtain the impedance of a plasma-filled parallel plate condenser.

The moderation and thermalization of ions by a hot plasma is treated by a method which is a generalization of the age theory of continuous slowing down. Formulas are given for the slowing down coefficients of an ion in a hot plasma. The method is illustrated by calculating the thermalization of a monoenergetic pulse of ions injected into a plasma and by a calculation of the T-D reaction probability when high-energy tritons are injected into a deuterium plasma.

A capacitor bank of 9-20 μF, charged to 5-7 kV was suddenly connected to a short coaxial gap, having an electrode separation of 4 cm, filled with N₂ at pressures between 4 and 4 × 10^-2 torr. It was observed that in spite of gap and external electric circuit symmetry, the discharge with a peak current of 10,000 A to 60,000 A always developed initially in one or more radial columns and never in a continuous luminous ring, and that the development of each radial column occurred in three distinct stages.

When the switch was closed, the gap and cables were first charged and, when the gap broke down, discharged in a period of some 200 nanoseconds with an estimated peak current of 2000 A. A `dark' period of 600 nanoseconds followed during which the discharge current of the capacitor bank built-up to a comparable value. An analysis of the discharge development was made by means of current and voltage oscillograms, streak photographs, microwave transmission measurements and spectrograms. It was found that the copper electrodes ablated strongly, but no emission of Cu lines was observed. Thus the discharge occurred essentially in nitrogen, despite the formation of both anode and cathode spots.

It is suggested that discharges supplied by locally stored energy may precede the main flow of current in many experimental arrangements in which the electrodes, the connexions, and the storage capacitance do not constitute a transmission line and therefore have more than one naturaldis charge frequency.

Measurements are described of the behaviour of 100-200 kA discharges in a variety of configurations of the general pinch and hard-core type. The systems were studied using a variety of internal and external magnetic probes, by electrostatic double probes and by fast photography. Correlation of the magnetic field fluctuations measured by the various coils enabled the axial wave number k and azimuthal mode number m of the perturbation to be deduced. In both pinch and hard-core cases the predominant mode number was m = 1 and the sign and magnitude of k were such that the perturbation was helical with a direction parallel to that of the mean magnetic field. Framing camera pictures of the discharge supported these results. Increasing the azimuthal magnetic field at all radii in the hard-core case was found to reduce the amplitude of the magnetic fluctuations and a discharge stable on this basis was achieved. By contrast, increasing the axial field at all radii had a slight de-stabilizing effect. Programming the axial field so as to have a null at some radius made the discharge violently unstable. Electric field measurements in stable and unstable hard-core discharges showed irreproducible fluctuations in the latter case of similar 10 V/cm and frequencies 500 kc/s - 1 Mc/s. Langmuir probe measurements of the plasma density in pinch and hard-core discharges showed a well-confined plasma only in the hard-core case.

These results are shown to be in good agreement with the theory of hydromagnetic stability when, and only when, the effect of finite electric conductivity is included.

It has previously been demonstrated theoretically and experimentally that a hollow cylindrical plasma possesses two main resonance frequencies. When the two cylinders limiting the plasma are not centred on the same axes, it is shown theoretically that each resonance splits into a couple of cross-polarized resonances. These results are in very good agreement with the experimental data.

The possibility is considered of using a microtron as an external injector for a synchrotron. The design is described and the results of starting up a microtron at an energy of 6.5 MeV are given.