Beam-Plasma Interaction in a Warm Plasma†

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Abstract
Theoretical studies of electron beam-plasma interactions have predicted the occurrence of amplifying waves having growth rates maximizing near to the electron plasma frequency. For the special case of an infinite beam interacting with a cold infinite plasma, an infinite growth rate is expected at the plasma frequency. In practice, the theoretical gain becomes finite if factors such as collisions or non-zero electron temperature are taken into account, or if the beam and plasma ore not both infinite. In this paper, beam-plasma interaction is investigated in planar geometry for both finite and infinite beams in an infinite, uniform, warm plasma. In the finite beam case, the question of appropriate boundary conditions to use at the beam edge arises. For cold plasmas, the Hahn approximation involving postulatian of an equivalent surface charge at the beam edge is usually applied. In the case of a warm plasma, it is unlikely that this approximation would describe accurately the plasma behaviour, though it may still be appropriate for the beam. Suitable boundary conditions are suggested, and computed curves are presented comparing the complex solutions of the resulting dispersion relation with the cold plasma solutions for the same geometry. For typical experimental conditions a substantial reduction of gain is indicated when non-zero electron temperature is taken into account.

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