Single-transit E-type Travelling-wave Devices†

Abstract

A small-signal analysis is presented for single-transit E-type traveling- wave devices in which a bunched electron beam follows a circular path and interacts with an azimuthally propagating electromagnetic wave. The ribbonshaped beam is maintained on the proper trajectory, without the use of focusing magnets, by balancing the electron centrifugal force against a steady radial electric- field force. The present investigation differs from earlier studies in a number of important respects: (1) The solutions apply to electron ribbons having all values of centerof-the-beam radius; (2) the origin of azimuthally directed electromagnetic field components in inhomogeneously loaded coaxial-cylindrical transmission systems is more closely examined; (3) the effect of the radial r-f spacecharge field on the interaction process, and its importance relative to the aximuthal field, receives attention; and (4) both unperturbed and slipping-stream motion for ribbon beams undergoing helical motion are treated in order to demonstrate the close relationships existing between electron streams possessing helical and plane circular motion. Numerical solutions are carried out for two limiting situations: One single-transit E-type tube is chosen to have a center-of- the-beam radius of 0.100 in. while another has a beam radius of 11.8 in. These results show that the small-signal solutions of large-radius E-typemore » devices closely resemble those of O-type tubes. The rate-ofchange of gain (with spatial angle), which is shown to be an increasing function of the radius of curvature of the beam, is bounded between two definite limits: (1) The gain rate approaches zero as the radius of beam curvature vanishes; (2) the gain rate approaches that of O-type tubes as the radius of beam curvature becomes infinite. For beam radii of 1 in. or more, practical E-type devices possess gain rates closely approaching those of O-type tubes. The practicability of single-transit E-type tubes is contingent upon finding means to substantially improve beam stiffness.« less