volume | PIER Journals

Abstract

In this paper, we propose a stochastic approach for the analytical analysis of the multicarrier multipactor discharge occurring in high-power vacuum microwave devices, in which electric fields are not homogeneously distributed. We indicate that the statistical behavior of large amount of secondary electrons in the process of a multipactor discharge can be well described by the probabilistic random walk and Levy walk theory. Based on the derived probability density of the lateral diffusion of secondary electrons in homogeneous fields, the multicarrier multipaction in inhomogeneous fields can be analytically computed with significantly enhanced efficiency. As a demonstration, the accumulation of secondary electrons of a multicarrier multipaction in a rectangular waveguide supporting TE₁₀ mode is given. The theoretical results comply well with the results achieved by the time-consuming particle simulation, the slope difference of which is less than 0.8%, while only costs one-order less computational time. To the best of our knowledge, this is the first time that the probability density of the lateral diffusion of secondary electrons during a multipaction is theoretically derived. This density depicts the physical picture of the statistical movement of secondary electrons during the process of a multicarrier multipactor, which can be widely used in the areas of high-power electronics and electromagnetism.

1. Farnsworth, P. T., "Television by electron image scanning," Journal of the Franklin Institute, Vol. 218, 411, 1934.
doi:10.1016/S0016-0032(34)90415-4 Google Scholar

2. Vaughan, J. R. M., "Multipactor," IEEE Trans. Electron. Dev., Vol. 35, 1172, 1988.
doi:10.1109/16.3387 Google Scholar

3. Kishek, R. A., Y. Y. Lau, L. K. Ang, A. Valfells, and R. M. Gilgenbach, "Multipactor discharge on metals and dielectrics: Historical review and recent theories," Phys. Plasmas, Vol. 5, 2120, 1998.
doi:10.1063/1.872883 Google Scholar

4. ECSS "Space engineering: Multipacting design and test,", ESA Publication Division, Noordwijk, 2003. Google Scholar

5. Gill, E. W. B. and A. von Engel, "Starting potentials of high-frequency gas discharges at low pressure," Proc. R. Soc. London, Ser. A, Vol. 192, 446, 1948.
doi:10.1098/rspa.1948.0018 Google Scholar

6. Semenov, V. and A. Kryazhev, "Multipactor suppression in amplitude modulated radio frequency fields," Phys. Plasmas, Vol. 8, 5034, 2001.
doi:10.1063/1.1410980 Google Scholar

7. Rozario, N., H. F. Lenzing, F. Reardon, M. S. Zarro, and C. G. Baran, "Investigation of Telstar 4 spacecraft Ku-band and C-band antenna component for multipaction breakdown," IEEE Trans. Microwave Theory Tech., Vol. 42, 558, 1994.
doi:10.1109/22.285060 Google Scholar

8. Geisser, K. H. and D. Wolk, "Proceedings of the Second International Workshop on Multipactor, RF and DC Corona and Passive Intermodulation in Space RF Hardware," ., ESTEC, Noordwijk, 1996. Google Scholar

9. Sazontov, A., N. Vdovicheva, M. Buyanova, V. Semenov, D. Anderson, J. Puech, M. Lisak, and L. Lapierre, "Proceedings of the Fourth International Workshop on Multipactor, RF and DC Corona and Passive Intermodulation in Space RF Hardware," ESTEC, Noordwijk, 2003.
doi:10.1063/1.2768019 Google Scholar

10. Anza, S., C. Vicente, B. Gimeno, V. E. Boria, and J. Armendariz, "Long-term multipactor discharge in multicarrier systems," Phys. Plasmas, Vol. 14, 082112, 2007.
doi:10.1063/1.3561821 Google Scholar

11. Anza, S., M. Mattes, C. Vicente, J. Gil, D. Raboso, V. E. Boria, and B. Gimeno, "Multipactor theory for multicarrier signals," Phys. Plasmas, Vol. 18, 032105, 2011.
doi:10.1063/1.3443128 Google Scholar

12. Anza, S., C. Vicente, J. Gil, V. E. Boria, B. Gimeno, and D. Raboso, "Nonstationary statistical theory for multipactor," Phys. Plasmas, Vol. 17, 062110, 2010.
doi:10.1016/0370-1573(90)90099-N Google Scholar

13. Bouchaud, J. and A. Georges, "Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications," Physics Reports, Vol. 195, 127-293, 1990.
doi:10.1038/nature06199 Google Scholar

14. Edwards, A. M., et al. "Revisiting Levy flight search patterns of wandering albatrosses, bumblebees and deer," Nature, Vol. 449, 1044-1049, 2007.
doi:10.1038/nature09116 Google Scholar

15. Humphries, N., et al. "Environmental context explains Levy and Brownian movement patterns of marine predator," Nature, Vol. 465, 1066-1069, 2010. Google Scholar

16. Shlesinger, M. F., J. Klafter, and G. Zumofen, "Above, below and beyond Brownian motion American Journal of Physics,", Vol. 67, 1253-1259, 1999. Google Scholar

17. Gnedenko, B. V. and A. N. Kolmogorov, Limit Distributions for Sums of In-dependent Random Variables, Addison-Wesley, Reading, Massachusetts, 1968.
doi:10.1088/0305-4470/31/19/006

18. Mussawisade, K., J. E. Santos, and G. M. Schutz, "Branching-annihilating random walks in one dimension: Some exact results," J. Phys. A: Math. Gen., Vol. 31, 4381-4394, 1998.
doi:10.1103/PhysRevSTAB.5.124404 Google Scholar

19. Furman, M. A. and M. T. F. Pivi, "Probabilistic model for the simulation of secondary electron emission," Phys. Rev. ST Accel., Vol. 5, 124404, 2002. Google Scholar

Dr. Qingqing Song

Dr. Xinbo Wang

Dr. Wan-Zhao Cui

Dr. Zhiyu Wang

Dr. Yichen Shen

Professor Li-Xin Ran