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Recently, a new mechanism of secondary electron multipaction, termed “long-term” multicarrier multipactor, was found in wideband high-power systems used in vacuum environments. Due to the long-term accumulation of secondary electrons between consecutive periods of the multicarrier signal, the long-term multicarrier multipactor has relatively low discharge threshold and is difficult to predict, thus causes potential reliability problems in space and accelerator applications. In this paper, we propose a stochastic approach to the analytical analysis of the multicarrier multipactor discharge occurring in inhomogeneous electric fields. By introducing the random walk and Levy walk theory, the probabilistic model of the lateral diffusion of secondary electrons in the process of a multipactor discharge is derived. Based on the derived probability density, the purely theoretical calculation of the accumulation of secondary electrons of a multicarrier multipactor in a rectangular waveguide supporting TE10 mode is given. The theoretical results comply well with the results achieved by the time-consuming particle simulation, with reducing computational time by about one- order of magnitude. The presented probability density of the lateral diffusion of secondary electrons can have applications in high-power electronics and electromagnetism.
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Keywords:
- multicarrier multipactor /
- secondary electrons /
- random walk /
- probability density
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[11] Anza S, Mattes M, Vicente C, Gil J, Raboso D, Boria V E, Gimeno B 2011 Phys. Plasmas 18 032105
[12] Anza S, Vicente C, Gil J, Boria V E, Gimeno B, Raboso D 2010 Phys. Plasmas 17 062110
[13] Semenov V E, Zharova N, Udiljak R, Anderson D, Lisak M, Puech J 2007 Phys. Plasmas 14 033509
[14] Li Y, Cui W Z, Zhang N, Wang X B, Wang H G, Li Y D, Zhang J F 2014 Chin. Phys. B 23 048402
[15] Bouchaud J, Georges A 1990 Phys. Reports 195 127
[16] Edwards A M 2007 Nature 449 1044
[17] Humphries N 2010 Nature 465 1066
[18] Shlesinger M F, Klafter J, Zumofen G 1999 Am. J. Phys. 67 1253
[19] Gnedenko B V, Kolmogorov A N 1968 Limit Distributions for Sums of In-dependent Random Variables (Massachusetts: Addison-Wesley, Reading)
[20] Lin F, Bao J D 2011 Chin. Phys. B 20 040502
[21] Mussawisade K, Santos J E, Schutz G M 1998 J. Phys. A: Math. Gen. 31 4381
[22] Furman M A, Pivi M T F 2002 Phys. Rev. ST Accel. 5 124404
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[1] Farnsworth P T 1934 Franklin Inst. 218 411
[2] Vaughan J R M 1988 IEEE Trans. Electron. Dev. 35 1172
[3] Kishek R A, Lau Y Y, Ang L K, Valfells A, Gilgenbach R M 1998 Phys. Plasmas 5 2120
[4] Li Y D, Yan Y J, Lin S, Wang H G, Liu C L 2014 Acta Phys. Sin. 63 047902 (in Chinese) [李永东, 闫杨娇, 林舒, 王洪广, 刘纯亮 2014 物理学报 63 047902]
[5] Gill E W B, von Engel A 1948 Proc. R. Soc. London, Ser. A 192 446
[6] Semenov V, Kryazhev A 2001 Phys. Plasmas 8 5034
[7] Rozario N, Lenzing H F, Reardon F, Zarro M S, Baran C G 1994 IEEE Trans. Microwave Theory Tech. 42 558
[8] Geisser K H, Wolk D 1996 Proceedings of the Second International Workshop on Multipactor, RF and DC Corona and Passive Intermodulation in Space RF Hardware ESTEC Noordwijk
[9] Sazontov A, Vdovicheva N, Buyanova M, Semenov V, Anderson D, Puech J, Lisak M, Lapierre L 2003 Proceedings of the Fourth International Workshop on Multipactor, RF and DC Corona and Passive Intermodulation in Space RF Hardware ESTEC Noordwijk
[10] Anza S, Vicente C, Gimeno B, Boria V E, Armendáriz J 2007 Phys. Plasmas 14 082112
[11] Anza S, Mattes M, Vicente C, Gil J, Raboso D, Boria V E, Gimeno B 2011 Phys. Plasmas 18 032105
[12] Anza S, Vicente C, Gil J, Boria V E, Gimeno B, Raboso D 2010 Phys. Plasmas 17 062110
[13] Semenov V E, Zharova N, Udiljak R, Anderson D, Lisak M, Puech J 2007 Phys. Plasmas 14 033509
[14] Li Y, Cui W Z, Zhang N, Wang X B, Wang H G, Li Y D, Zhang J F 2014 Chin. Phys. B 23 048402
[15] Bouchaud J, Georges A 1990 Phys. Reports 195 127
[16] Edwards A M 2007 Nature 449 1044
[17] Humphries N 2010 Nature 465 1066
[18] Shlesinger M F, Klafter J, Zumofen G 1999 Am. J. Phys. 67 1253
[19] Gnedenko B V, Kolmogorov A N 1968 Limit Distributions for Sums of In-dependent Random Variables (Massachusetts: Addison-Wesley, Reading)
[20] Lin F, Bao J D 2011 Chin. Phys. B 20 040502
[21] Mussawisade K, Santos J E, Schutz G M 1998 J. Phys. A: Math. Gen. 31 4381
[22] Furman M A, Pivi M T F 2002 Phys. Rev. ST Accel. 5 124404
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