High power microwave systems operating in vacuum or near vacuum run the risk of multipactor breakdown. In order to avoid multipactor, it is necessary to make theoretical predictions of critical parameter combinations. These treatments are generally based on the assumption of electrons moving in resonance with the electric field while traversing the gap between critical surfaces. Through comparison with experiments, it has been found that only for small system dimensions will the resonant approach give correct predictions. Apparently, the resonance is destroyed due to the statistical spread in electron emission velocity, and for a more valid description it is necessary to resort to rather complicated statistical treatments of the electron population, and extensive simulations. However, in the limit where resonance is completely destroyed it is possible to use a much simpler treatment, here called non-resonant theory. In this paper, we develop the formalism for this theory, use it to calculate universal curves for the existence of multipactor, and compare with previous results. Two important effects that leads to an increase in the multipactor threshold in comparison with the resonant prediction are identified. These are the statistical spread of impact speed, which leads to a lower average electron impact speed, and the impact of electrons in phase regions where the secondary electrons are immediately reabsorbed, leading to an effective removal of electrons from the discharge.

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