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A simple model of vacuum/dielectric/vacuum interface breakdown initiation caused by high power microwave has been developed. In contrast to already existing models, a spatially varying electron density normal to the interface surface has been introduced. Geometry and parameter ranges have been chosen close to the conditions of previously carried out experiments. Hence, physical mechanisms have become identifiable through a comparison with the already known experimental results. It is revealed that the magnetic field component of the microwave plays an important role. The directional dependence introduced by the magnetic field leads to a 25% higher positive surface charge buildup for breakdown at the interface downstream side as compared to the upstream side. This and the fact that electrons are, in the underlying geometry, generally pulled downstream favors the development of a saturated secondary electron avalanche or a saturated multipactor at the upstream side of the dielectric interface. The previously observed emission of low energy x-ray radiation from the interface is explained by bremsstrahlung generated by impacting electrons having initially a higher energy than the average emission energy. Final breakdown is believed to be triggered by electron induced outgassing or evaporation, generating a considerable gas density above the dielectric surface and eventually leading to a gaseous breakdown.

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Dielectric surface flashover in vacuum is characterized by a three-phase development, as shown by current measurements covering the range from 10−4 to 100 A, assisted by x-ray emission measurements, high speed photography, and time-resolved spectroscopy. Further information is gained from a comparison of the flashover dynamics at 77 and 300 K. Phase one comprises a fast (several nanoseconds) buildup of a saturated secondary electron avalanche reaching current levels of 10 to 100 mA. Phase two is associated with a slow current amplification, with a duration on the order of 100 ns, reaching currents in the ampere level. The final phase three is characterized again by a fast (nanoseconds) current rise up to the impedance-limited current on the order of 100 A in this specific apparatus. The development during phase two and three is described by a zero-dimensional model, where electron-induced outgassing leads to a Townsend-like gas discharge above the surface. The feedback mechanism towards a self-sustained discharge is due to space charges leading to an enhanced field emission from the cathode. A priori unknown model parameters, such as field enhancement factors, outgassing rate, and the buildup of the gas density above the surface, are determined by fitting calculated results to experimental data.

In high-power microwave diode design, the space-charge-limited current is important because of its relation to the diode impedance, and the formation of the virtual cathode. Although the Langmuir–Blodgett law, as a numerical solution, is helpful, a simple functional expression would be more convenient for practical research. In this paper, a physical approximation has been introduced to analyze the nonlinear Poisson’s equation in a one-dimensional (1-D) cylindrical vacuum diode. With the help of this physical approximation, a solution for the space-charge-limited current for 1-D cylindrical diodes has been investigated and developed. In addition, a comparison between our approximate result and the Langmuir–Blodgett numerical solution shows that the physical approximation method is valid in nonlinear differential equation analyses. This physical approximation can be used to analyze similar nonlinear differential equations. Also, a correction for the space-charge-limited current in a two-dimensional cylindrical diode is obtained within a limitation.

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