Stability Analysis of VE Amplifiers Based on Determinant Equations

A general method for calculating self-excitation thresholds for a large class of standing and traveling wave structures used in klystrons, traveling wave tubes, and other vacuum-electronic devices is presented. We determine circuit parameters of RF structures that are changed due to the presence of electron beam, and analyze stability of the obtained matrices. Determinant equations defined by such stability matrices are derived. The use of the method for structures with round and arbitrary geometry beam tunnels is discussed. Analytical stability evaluation described here greatly complements the large signal beam-wave interaction CHRISTINE and TESLA family codes as well as EM PIC codes such as NEPTUNE.