Electron-beam Matching to Solenoid Magnetic Field in a Klystron

High-power klystrons for particle accelerators employ high-perveance electron guns which are usually focused by Solenoid magnets. The electron beam should be optically matched to the downstream magnetic field to prevent the beam from scalloping. The task usually requires a series of computer simulations with many design parameters, and therefore requires extensive(sometimes exhaustive) efforts if not aided by a priori experiences. In order to alleviate the difficulties we have developed a matching procedure which is systematic and reliable. In this article we describe the procedure with an example design of a 400-kV 500-A electron beam with radius 8 - 11 mm.