Interaction of a Cylindrical Beam with a Plasma. I. Theory

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Abstract
A linear analysis is given of the interaction of a homogeneous, monoenergetic cylindrical electron beam, of radius a, with a homogeneous, cold plasma for two cases: (A) the plasma is unbounded and (B) the plasma is bounded by a conductor at radius b(>a). The quasistatic approximation is compared with an exact treatment, and conditions for the validity of the former are stated. A stability analysis according to the method of Derfler and Briggs is carried out in terms of the mapping of ω into the complex k plane. It is shown that the system is always absolutely unstable and the dependence of the stability analysis on the system parameters is discussed. The absolute instability is, however, always sufficiently weak that in practice the stabilizing effect of collisions is sufficient to quench it, leaving a convective instability. The properties of the amplifying waves resulting from collisional stabilization are discussed for parameter values appropriate to the experimental conditions described in Pt. II.

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