Effects of Plasma Boundaries in Plasma Oscillations

The discussion of electron plasma oscillations is extended to include some of the effects of boundaries. It is first shown that an electron taking part in a traveling plasma oscillation will be reflected at a sheath of infinitesimal thickness with velocity appropriate to the oscillation traveling in the reverse direction. This means that standing waves may be built up without loss at the sheaths. This approach is extended to sheaths where a finite time of penetration is necessary before reflection occurs and also to the case of reflection at metallic electrodes. In both cases expressions for the damping are derived and it is concluded that for low pressure discharges damping resulting from imperfect reflection from electrode sheaths may be comparable with collision damping but that damping arising from conducting electrodes is unimportant.

The excitation of the plasma by sharp beams is considered briefly and expressions are derived for the energy transfer of a beam to growing and of stationary amplitudes. It is pointed out that beams should excite oscillations only when a regular geometry exists. With irregular geometry bunching pulses are to be expected, of the type observed by Merrill and Webb. A detailed analysis is given of the bunching and of the Merrill and Webb experiments. Good agreement is obtained if one assumes that the pulses are maintained because high harmonic waves in the pulse cannot be shielded out by the plasma. These feed back energy towards the cathode and continuously modulate the beam.