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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.

This paper analyzes the effects of the rf magnetic field and partial reflection of the circularly polarized electromagnetic wave on multipactor discharge on a dielectric. A statistical theory ͑taking into account the velocity spread of injected electrons͒ is constructed to evaluate the multipactor induced breakdown and saturation level. It is concluded that the spread of initial velocities considerably changes the condition for multipactor initiation in comparison with the dynamic approach. This effect is especially strong for the case of relatively low rf electric field amplitude ͑when the transit time essentially exceeds the rf period͒ and leads to the oscillation suppression of effective electron yield and to an increase in the threshold of multipactor growth. It is established that the rf magnetic field eliminates the upper boundary of the susceptibility diagram, while the low boundary almost remains unchanged. It is also found that the presence of partial reflection causes degradation of the saturation level ͑in comparison with the nonreflecting case͒ and results in decreasing of the characteristic time required to achieve the steady state.

A particular software ‘MuSLi’ has been developed and applied for simulations of the multipactor effect in shielded microstrip lines with cross-sections that are partially filled with dielectric material. The software combines an electromagnetic field solver, determining the electric field structure in the microstrip line, and a Monte Carlo algorithm, calculating the corresponding electron trajectories taking into account a spread of the electron initial velocity and different secondary emission properties of the metal and dielectric surfaces. The simulations were carried out for a number of structures of interest for communication systems, currently being discussed for application in coming space missions. The microstrip line system is shown to be strongly resistant to multipactor growth and the main reason for this is identified as the ponderomotive (or Miller) force, which governs the average electron motion in non-uniform rf fields and which tends to push the electrons out of regions with strong rf fields.

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