Interaction between a sheet electron beam and an in-phase mode in coupled combs

Abstract

The sheet electron beam (EB) interaction with an in-phase mode excited in opposing combs, the period of which is much smaller than the slow-wave length, is discussed. The dispersion equation for arguments involving a transverse constant that is “perturbed” by the slow-wave interaction with the EB is derived. The dispersion equation is transformed to the so-called characteristic equation of a traveling-wave tube under the condition that its functions are expanded into a Taylor series near the arguments at the zero current. The variations in the coupling and depression coefficients of the dispersion equation versus the frequency-proportional parameter are found. The obtained results are employed to generalize the efficiency of the sheet EB interaction with the in-phase mode formed between flat impedance electrodes.