| A self-consistent numerical analysis of klystrons is presented. The analysis is detailed enough to include all the significant physical effects of the device, but also simple enough that it can be used as a viable design tool.; There are four parts to the analysis. First, the continuous beam-cavity standing wave interaction equations are studied. In particular, the space-charge forces, the mechanism of how the beam induces fields in cavities, and the cavities' effects on the beam motion is outlined. Second, these equations are shown in discrete form and the scheme of following representative electrons in the beam is described. The concept of tracking a dynamic rf wavelength of particles is presented. The third part consists of several test cases to determine in which regimes the analysis is valid. The tests include uniform DC flow, universal beam spread, ballistic and space-charge beam bunching, calculating beam-loaded admittances, and checking the self-consistency of the space-charge forces. The final part discusses detailed simulations of an actual klystron, Litton Industries model L-5021 which is used in the LAMPF accelerator at the Los Alamos National Laboratory. Studies were made of the tube's performance while varying the penultimate cavity tuning, second harmonic cavity tuning, the solenoidal magnetic field profile at the output cavity, the initial beam-current-density cross section, and the external load impedance seen by the tube. In addition, situations in which the cavity spacing, the external load impedance, and the beam preveance were varied in a two cavity klystron were simulated. Finally in this part, the LAMPF klystron is optimally redesigned by changing cavity placements, yielding an electron efficiency increase to about 64%. A short summary follows which lists points learned about klystron behavior from the earlier simulations.; Three appendices are included. First, Ramo's theorem, which relates the cavity induced current to the beam, is shown to be accurate to lowest order by using a normal mode field expansion. The next appendix outlines the formulation of the particle pusher routine used in the code. The last appendix contains a complete listing of the simulation code. |
