Two-Stream Cyclotron and Plasma Wave Interactions

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Abstract
Cyclotron and plasma wave interactions between drifting electron streams in a steady axial magnetic field are studied for configurations of finite transverse cross section. It is shown for the case of equal and opposite drift velocities, that there exists an instability at approximately one‐half the cyclotron frequency. This instability is a consequence of the coupling between the slow space‐charge wave on one stream and backward cyclotron wave on the other stream. This coupling can occur whenever the streams are of finite transverse cross section. In order to verify some of the features of this instability, experiments in which two coaxial oppositely directed electron beams were passed between two planes, were carried out for a limited range of electron drift velocity and magnetic field values. These experiments demonstrated the existence of an instability at one‐half the cyclotron frequency, in agreement with the theory. It was found experimentally that at a particular stream velocity the instability could exist over a small range of magnetic field values. The upper limit of magnetic field can be explained by the assumption that nonlinearities result in a thermalization which causes the velocity spread on the electron beam to become comparable to its mean velocity. The lower limit is a consequence of the finite length of the interaction region. Although the measured signal level was much less than that expected on the basis of converting a reasonable fraction of the beam energy to rf energy, it was found that the signals observed had a narrow frequency spread (−3 dB width was 10 kc/sec at 50 Mc/sec).

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