Multipactor is a resonant, low-to-medium rf voltage breakdown phenomenon in microwave cavities, windows, and accelerator structures. A simple model is used to study the temporal evolution of a first-order, two-surface multipactor discharge and its interaction with the surrounding rf structure. The model assumes an infinitesimally thin sheet of electrons released with monoenergetic velocities in a parallel plate geometry.; The loading of the structure by the changing multipactor current, a combination of de-tuning and of reducing the quality factor of the resonant structure, is found to cause saturation. The steady state multipactor current has been derived analytically, and compares favorably with the computational results of the model. This current, properly normalized, is found to depend only on the magnitude of the drive current and the first cross-over point of the wall material's secondary yield curve (as well as the initial velocity of secondaries).; Transiently, the behavior of the multipactor depends on the quality factor of the rf structure. Non-resonant structures experience a fairly steady growth of the discharge towards the steady state level predicted by the theory. Highly-resonant structures, on the other hand, experience large oscillatory transients in the level of the discharge before it settles to the steady state. During these oscillations, the discharge feeds from the significant energy stored in the structure, and can be very damaging to the structure itself.; Simulations performed with two electron sheets instead of one reveal a novel phase-focusing mechanism in which one sheet grows at the expense of the other. This "cannibalism" results from the different impact energies, hence different yields, encountered by the different sheets (parts of the bunch). This mechanism may result in the multipactor electrons being very tightly bunched. However, this cannibalism operates on a relatively long time scale.; A multipactor discharge can take place during the "fill-time" of an rf structure, even if the operating voltage is above the multipactor region, provided the rise time of the voltage is sufficiently long. The conventional susceptibility diagram is modified to include the effects of surface materials. This is the first attempt where the dynamics of a multipactor discharge are linked to the material properties. Comparison with published experimental data is given.
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