Statistical multipactor theories are critical prediction approaches for multipactor breakdown determination. However, these approaches still require a negotiation between the calculation efficiency and accuracy. This paper presents an improved stationary statistical theory for efficient threshold analysis of two-surface multipactor. A general integral equation over the distribution function of the electron emission phase with both the single-sided and double-sided impacts considered is formulated. The modeling results indicate that the improved stationary statistical theory can not only obtain equally good accuracy of multipactor threshold calculation as the nonstationary statistical theory, but also achieve high calculation efficiency concurrently. By using this improved stationary statistical theory, the total time consumption in calculating full multipactor susceptibility zones of parallel plates can be decreased by as much as a factor of four relative to the nonstationary statistical theory. It also shows that the effect of single-sided impacts is indispensable for accurate multipactor prediction of coaxial lines and also more significant for the high order multipactor. Finally, the influence of secondary emission yield (SEY) properties on the multipactor threshold is further investigated. It is observed that the first cross energy and the energy range between the first cross and the SEY maximum both play a significant role in determining the multipactor threshold, which agrees with the numerical simulation results in the literature.
Multipactor occurrence essentially depends on the secondary emission property of the surface material, which is, thus, the requisite input for multipactor threshold prediction using the numerical and theoretical approaches. However, secondary emission yield (SEY) deviation in experimental measurements inevitably leads to uncertainty error in multipactor threshold prediction. Therefore, this paper presents a thorough quantitative analysis of multipactor threshold sensitivity to SEY including the effect of the device geometry, the multipactor mode, and the material type. Based on the statistical modeling, multipactor threshold voltages with respect to the SEY variation in critical SEY regions are calculated for both the parallel plates and coaxial lines with different multipactor orders and typical materials. Furthermore, the distribution of electron impact energy is also obtained to elucidate the underlying mechanism for the relevant sensitivity discrepancy. The result reveals that multipactor threshold is generally most sensitive to the energy region below the first crossover energy ( E1), and this is changed to higher energies below the corresponding energy to the SEY maximum ( Em) with a change in the device geometry, multipactor mode, or coating material. It is also found that the magnitude relation of the threshold sensitivity between different regions is radically determined with the distribution of electron impact energy, and the SEY variation close to Em merely affects the threshold result with a high multipactor order. This research provides useful reference for properly determining the threshold margin from the measurement error of SEY, thus promoting the performance optimization with multipactor prevention in the practical application of microwave devices.
Multipactor breakdown is a detrimental electromagnetic phenomenon caused by resonant secondary electron emissions synchronizing with field oscillation, which frequently takes place in powerful microwave devices and accelerating structures. Regarded as the principal failure mode of space microwave systems, multipactor may cause the performance to degenerate or even hardware operation to deteriorate catastrophically, thus multipactor becomes a major limitation in promoting the further development of space communication technology. Meanwhile, higher power capacity and volume integration accordingly lead to continuously growing multipactor hazard. In order to prevent multipactor from occurring, the accurate predictive technique to determine multipactor susceptibility has become a key issue for the mechanical design and performance optimization of microwave devices in the ground stage. Compared with the existing approaches to investigating the multipactor, statistical theories are able to conduct multipactor threshold calculation and mechanism analysis, with the stochastic nature of secondary emission fully considered from the probabilistic perspective. Currently, stationary statistical theory of multipactor has been developed for efficient multipactor threshold analysis of the parallel-plate geometry. However, it has not been further extended to the coaxial geometry which is commonly involved in radio frequency (RF) systems. For this reason, the stationary statistical modeling of the coaxial multipactor with all influencing factors considered is detailed in this paper. Due to the field nonuniformity and the secondary emission randomness, analytic equation of electron trajectories in the coaxial geometry is approximately derived by using the perturbation approach. Based on the implicit correlation between electron emission velocity and transit time, the joint probability density function is constructed for the calculation of the probability density distribution of electron transit time. Afterwards, a system of integral equations for depicting electron multiplication process in the coaxial geometry is formulated and solved with a novel and general iteration method. Finally, this stationary statistical theory is applied to the full multipactor susceptibility chart of coaxial transmission lines with typical coating materials in space engineering, such as silver, copper, alumina and alodine. A comparison shows that the calculation results are in reasonable agreement with the experimental measurements provided by the Europe Space Agent. What is more, there exists significant difference between multipactor susceptibility curves of the parallel-plate geometry and the coaxial geometry. This research is of great significance for optimizing the mechanism design and material selection of multipactor-free microwave devices.
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