Abstract: A simple model is constructed to analyze the temporal evolution of a multipactor discharge in an rf cavity. The multipactor current may, transiently, reach a level comparable to the wall current that is needed to sustain the rf field. It saturates at a much lower level in the steady state, primarily by its loading of the cavity; the space charge force associated with the multipactor electrons plays a relatively minor role. At saturation, the electron impact energy equals the lowest value that gives unity in the secondary electron yield curve. We also discovered a new phase focusing mechanism, whereby the leading edge of the multipactor discharge grows at the expense of the trailing edge, in spite of the mutual repulsion among the electrons. This phase focusing mechanism may shape the steady state multipactor discharge in the form of a very tight bunch of electrons.!8
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