Interaction of an Electron Beam with a Periodic Circuit

A field theory of a space-harmonic traveling wave tube is developed using a stationary field matching procedure. The circuit is the circularly symmetric disc loaded waveguide. Two cases are studied: a solid low cur- rent electron beam which completely fills the openings between sections, and a hollow beam of arbitrary radius. The latter analysis can be extended to the solid beam case through the use of Fletcher's equivalent hollow beam method. Particular attention is paid to the difference between forward space harmonics and backward space harmonics, and a comparison is made with Pierce's traveling wave tube parameters K and Q for both types of space harmonics. One result is to show that the sign of K is negative for back- ward space harmonics, while the sign of QC is positive. The principle value of the work may be in its use in "admittance-wall" or complete field theory analyses of forward and backward wave devices