This paper reviews the history of multipactor discharge theory, focusing on recent models of multipactor accessibility and saturation. Two cases are treated in detail: That of a first-order, two-surface multipactor, and that of a single-surface multipactor on a dielectric. In both cases, susceptibility curves are constructed to indicate the regions of external parameter space where multipactor is likely to occur, taking into account the dependence on surface materials, and the effects of space charge and cavity loading. In the case of a dielectric, multipactor is found to deliver about 1% of the rf power to the surface. The two cases are contrasted in light of experimental observations.

This paper proposes a novel theory of single-surface multipactor discharge on a dielectric, such as an rf window. Using a Monte Carlo simulation, we obtain the susceptibility diagram, applicable to a wide range of materials, in terms of the rf electric field and of the dc electric field that may result from dielectric charging. The electron multiplication mechanism assumes realistic yield curves of secondary electrons, including distributions of emission velocities and angles for these electrons. The susceptibility diagram thus constructed allows an immediate assessment of the range of rf power over which multipactor may be expected to occur. A simple analytic theory is constructed to explain the simulation results. [S0031-9007(97)04847-3] PACS numbers: 84.40.Zc

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 image space charge force associated with the multipactor electrons plays a relatively minor role. At saturation, the electron impact energy is equal the lowest value that gives unity in the secondary electron yield curve.

Space-charge modes similar to those observed in recent experiments appear in simulations of nonequilibrium charged particle beams with anisotropy. The modes couple degrees of freedom, causing energy transfer and equipartitioning without halo formation in just a few betatron wavelengths. The rate depends on a single free parameter quantifying the space-charge intensity of the final state. Traditional stability analyses are shown not to apply to high-intensity laboratory beams originating with a large perturbation from equilibrium.

Experiments and particle-in-cell simulations demonstrate the appearance of wavelike transverse density variations in a space-charge dominated electron beam. Simulations show how an aperture located near the source gives rise to a nonequilibrium phase-space distribution with strong force imbalance confined to a sheath near the beam edge. Tracking of particles in this sheath, starting near the aperture's edge, reproduces well the onset of the perturbation. The subsequent evolution of the perturbation over about one meter suggests the appearance of a transverse wave. For the parameters investigated, simulations further indicate that the perturbation damps out over a few plasma periods without causing any rms emittance growth. [S0031-9007(99)09152-8]