A klystron study: Intermodulation suppression and beam loading of cavities.

Abstract

Beam loading, or the change in resonant frequency and quality factor of a cavity due to an electron beam, plays an important role in klystron operation. Klystrons are high power microwave amplifiers which transfer the kinetic energy of a DC electron beam to electromagnetic radiation through a series of resonant cavities. The change in the cavity parameters (resonant frequency and quality factor) has been studied nearly since the invention of the klystron, but is still restricted to very simple models. The fundamental process of energy exchange between the beam and the electromagnetic fields of the cavity is usually modeled by a ballistic analysis, where the AC space charge effects are ignored, and by assuming an infinite magnetic field to guide the electron beam. This thesis extends the ballistic theory to finite values of magnetic field, by calculating the real and imaginary parts of the complex energy transfer between the electron's radial velocity and the radial electric field. The effect of radial motion is shown to be small compared to the energy transfer between the electron's axial motion and the axial electric field, which remains the same for a general magnetic field. The effect of a finite magnetic field leads to less than a 5% change in quality factor and less than a 1% change in resonant frequency for a low perveance klystron. The ballistic theory and standard space AC charge wave theories are extended to include the space charge waves of all ranks and all higher order vacuum modes of the cavity. Previous space charge wave theories considered only the fundamental space charge waves, and used an effective space charge wave interaction with the dominant cavity mode. The analysis presented here contains a complete treatment of space charge waves, and their interaction with all vacuum modes of the cavity-drift tube assembly. The effects of AC space charge are shown to be small, typically modifying the beam loading conductance by less than 5% and the beam loading susceptance by less than 1%, even for high values of perveance (3 micropervs). In addition, results of intermodulation suppression theory and experiments are presented. The klystron intermodulation theory recently developed by Lau and Wilsen, which is capable of calculating all intermodulation products produced in a klystron with high accuracy and spectral resolution, including the effects of charge overtaking, is used. In this thesis, it is compared with results of an intermodulation suppression experiment conducted at the University of Wisconsin, in which a weak signal is injected at the frequency of the third order intermodulation product in order to cancel the intermodulation product produced by the klystron. The theory is shown to accurately predict the suppression. With the proper choice of amplitude and phase of the injected signal, the intermodulation product can be suppressed by 30 dB at the output of the klystron.