Vi. Microwave Electronics * A. Theory of Mode Coupling: a Summary

Studies reported in the last Quarterly Progress Report (1) have been modified and extended. The purpose of these studies is to find a formal basis and justification for Pierce's coupling-of-modes formalism (2) as it applies to uniform slowwave structures containing two or more subsystems that individually propagate slow waves (e.g., traveling-wave tubes). If it can be assumed that the coupling is weak, approximations that lead to simple coupling equations like those discussed by Pierce can be made. Specific expressions have been found for the coupling coefficients for example, for Pierce's K for a traveling-wave tube with a thick beam, which was given in reference 1. We found that the expressions previously derived (1) are not valid at strong coupling; therefore second-order terms must be considered in the coupling coefficients. Expressions that are valid at strong coupling can be obtained if a different approach is taken. As before, we recognize that the coupling-of-modes formalism discussed by Pierce is, in principle, an expansion of the actual fields in terms of the modes of two (or more) (sub)systems. In the neighborhood of a particular (sub)system, the field expansion in terms of the modes of that particular (sub)system is used to represent the actual field. Expressions were obtained that differ at strong coupling from those given in reference 1. The method for obtaining them was discussed at the URSI May 1957 meeting in Washington, D.C. A paper on this subject is in preparation.