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A plane parallel model of multipactor is studied in detail using both an analytical approach and numerical simulations. The analytical analysis is carried out within a widely exploited approximation, which assumes a fixed value for the initial velocity of secondary electrons. It is shown that the commonly accepted picture of the multipactor zones is not quite complete and should be modified by taking into account the existence of hybrid resonance modes and the important consequences of a secondary emission yield that significantly exceeds unity. Numerical simulations demonstrate that the chart of the multipactor zones is also very sensitive to a spread of the initial velocity of the electrons. In particular, the full effect of initial electron velocities cannot accurately be modeled by using a single fixed value only.

This paper presents a novel theory for describing the initial stage of a single-surface multipactor discharge on a dielectric surface in the presence of a dc electric field, which returns secondary emitted electrons to the surface. The calculations employ a statistical method based on an exact analytical solution for the probability density of the arrival times of the secondary electrons. A general integral equation determining the steady-state distribution of the emission phases of the secondary electrons and the threshold of the multipactor growth is formulated. A computer program has been developed to implement this theory for realistic secondary yield curves and arbitrary, nonuniform, distributions for velocities and angles of emitted electrons. Susceptibility diagrams, applicable to a wide range of materials, are obtained in terms of the rf and dc electric fields and are found to be relatively independent of the emission distribution of the electrons.

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Detailed numerical simulations of the two-sided multipactor have been carried out within a plane-parallel model. The main aim of the simulations is to clarify the uncertainty that still exists in the literature concerning the overlapping of multipactor zones. Three different codes (Monte Carlo, particle-in-cell, and statistical) were used to calculate the multipactor charts within a wide range of parameters such as spread of initial velocities of the secondary electrons and maximum value of the secondary emission yield. It was found that an increase in the spread of initial velocities results in overlapping of the multipactor zones, provided the secondary emission is high enough. In the opposite case, an increase in the spread of initial velocities leads to a suppression of the higher multipactor zones.