Linear beam tube theory

This paper presents the basic theories underlying the principles of operation of linear beam tubes. These theories are more general than the previous ones because they can be applied equally well to all types of tubes using linear electron beams. The tube types will differ only in the rf circuits that are being used. Emphasis of the theories is placed on the fundamental equations involved rather than the analytic solutions of these equations. The concept of electromagnetic and hydrodynamic power flow is emphasized in the treatments. The purpose is to leave the details of the solution to the electronic computer that is now being adapted to this type of problem. To this end, the equations are only developed in such a way as to facilitate programming in the computer. To illustrate the use of the theory, the special cases of the traveling-wave tube in which a waveguide mode is continuously interacting with the beam, and the klystron tube in which the interaction takes place in a limited space, will be developed in more detail. To further avoid mathematical complexities, electron motion, limited to the longitudinal direction, will be emphasized, and only the small-signal case will be treated. However, sufficient fundamental ideas will be presented so that the extension to the cases involving transverse electron motions and the large signal operation can be easily accomplished.