A Vlasov description of the gridded gapelectron flow interaction
Abstract
Selfconsistent solutions of the system of Vlasov equations are found for the case when the electric field in the gap does not depend on the longitudinal coordinate. The solution is valid for an arbitrary nonrelativistic particle distribution in velocity and time at the gap entrance, for any gap length, for any beam current, and for a broad class of field dependences on time. In the region of applicability of the smallsignal approximation (small beam current, small transit angle of the gap), the solution derived reproduces the results of the smallsignal approximation. Numerical results for the input klystron cavity and for an idler cavity are given and compared with the calculations in smallsignal approximation. Possible applications of this formulation are discussed. In particular, we argue that the Vlasov description provides a suitable framework for developing onedimensional models of a multiplecavity klystron. These models will be valid for large signals, and are useful therefore for predicting the performance of highpower klystrons.
 Publication:

IEEE Transactions on Microwave Theory Techniques
 Pub Date:
 June 1985
 DOI:
 10.1109/TMTT.1985.1133101
 Bibcode:
 1985ITMTT..33..467K
 Keywords:

 Cavity Resonators;
 Electric Fields;
 Electron Beams;
 Klystrons;
 Particle Interactions;
 Vlasov Equations;
 Boundary Value Problems;
 Electromagnetic Interactions;
 Electron Distribution;
 Gaps;
 Maxwell Equation;
 Self Consistent Fields;
 Electronics and Electrical Engineering