Field distribution in a centrally loaded circular cylindrical cavity

To accelerate protons in an Alvarez type linear accelerator or electrons in velocity modulated tubes, the cavity must be excited in the dominant TM010 mode. For proper understanding of beam dynamics and for purposes of design, the R. F. fields must be computed accurately for any specified dimensions of the drift space. In this paper the exact numerical solution for the fields in a drift tube loaded linear accelerator cavity with a beam guiding hole is presented. The eigenvalues, field distribution, transit time factor and the shunt impedance are formulated everywhere by boundary value techniques in the same manner as proposed by Bolle and Gluckstern in the absence of the beam guiding hole. The numerical results are obtained with the aid of a digital computer and are established by an excellent agreement with an experiment based on perturbation techniques.