Space-Charge Wave Excitation in Solid-Cylindrical Brillouin Beams

When a beam only partly fills the space within a concentric drift tube, the field patterns of the modes derived by small-signal slow-wave analysis are not orthogonal to one another. This makes it difficult to find the amplitude of any single mode excited by an arbitrary initial disturbance. The cases of ion-neutralized beams in the absence of a magnetic field and of Brillouin flow are even more difficult, for in these cases infinite groups of modes assume the same phase velocity and degenerate into a wave of arbitrary transverse distribution, which, we shall show, cannot be excited at all. In treating the excitation of a confined-flow beam, Scotto and Parzen 1 have circumvented such difficulties by means of a Laplace transform procedure. More recently, Bresler, Joshi and Marcuvitz 2 have succeeded in formulating a complete set of orthogonal modes for such unidirectional electron beams, at the cost of some increased complexity in description. In this paper, a technique similar to that of Scotto and Parzen will be employed to solve several problems in the excitation of a solid-cylin99