The electron multiplication on surfaces exposed to an oscillating electromagnetic field causes the phenomenon of multipacting, which can degrade significantly the performance of vacuum RF devices, especially accelerating cavities. It is a serious obstacle to be avoided for normal operation of particle accelerator and their RF components. Many types of room temperature and superconducting accelerating cavities are designed and produced at Fermilab for different projects. The extensive simulations of multipacting in the cavities with updated material properties and comparison of the simulation results with experimental data are routinely performed during electromagnetic design of the cavities. The new advanced computing capabilities made it possible to take the space charge effect into account in the multipacting simulations. The basic new features of multipacting process that appear due to the space charge effect are shown for the classic case of the parallel plates and discussed. As the first practical application of the multipacting simulations with space charge effect the study of multipacting in the low-beta and high-beta 650 MHz elliptical superconducting cavities is also presented.
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