Cold-Beam-Plasma Interaction Theory for Finite Transverse Dimensions and Finite Magnetic Fields

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Abstract
The dispersion relation for interaction between a cold electron beam and the electrons of a cold, uniform density plasma of a circular cylindrical cross section and of a radius equal to that of the beam inside a conducting pipe of a larger radius has been solved on a computer for a number of values of finite magnetic field, the ratio of plasma density to beam density, and beam perveance. Complete ω‐k diagrams are given for various cases along with more extensive data on the growing wave gain that occurs below the plasma frequency and the cyclotron frequency. A comparison with experimental data on a beam‐generated plasma is given and the theory is shown to provide a satisfactory explanation for the onset of oscillations in such a system with a finite length.

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