Space-Charge Waves in an Accelerated Parallel-Flow Electron Beam in a Constant Magnetic Field

摘要

This report considers the small-perturbed electron motions in an accelerated (space charge limited) cylindrical parallel flow electron beam to establish whether noise fluctuations will grow or decay as a function of distance and magnetic field. Approximate solutions of the resulting second order differential equations are presented in the form of both first order WKB solutions and asymptotic series, the WKB form having the advantage of being a fairly good normal mode representation. Solutions show magnitude of perturbed radial electron displacement will increase indefinitely for no magnetic field and will reach an asymptotic value at a certain distance from the cathode, with magnetic field, the stronger of the field, the shorter this distance. The transverse and quasi-static electric fields decay in both cases. (Author)