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In order to compute the multipactor thresholds of microwave devices with high efficiency and precision,a novel fast particle-in-cell (PIC) method is proposed,which takes advantage of the frequency-domain (FD) electromagnetic field solver of CST Microwave Studio (MWS).At the initial stage of multipactor (when there are not many electrons in the device),the self-consistent field generated by the electrons is much smaller than the applied electromagnetic field. Therefore it can be ignored in calculating the multipactor threshold and this will significantly reduce the computation burden.During simulations of multipactor process,the FD field pre-calculated by CST MWS is converted into timedomain (TD) scaling with the square root of the input power.Then the electron motion is investigated by Boris algorithm.When the electrons hit the boundaries of the simulation region,where triangular facets from CST are used for discretization,the secondary electrons will be emitted.After a series of simulations with variable input powers,the multipactor threshold is determined according to time evolution of the electron number.The multipactor thresholds in a parallel plate and a coaxial transmission line are investigated,and used as relevant verifications.Compared with the CST Particle Studio (PS),the fast method obtains almost the same thresholds,while the computational efficiency is improved by more than one order of magnitude.Since the self-consistent field generated by the electrons is ignored in the fast method and it is considered in CST PS,the results validate that the self-consistent field can be ignored in calculating the multipactor threshold.Finally,taking for example a parallel plate transmission line and a stepped impedance transformer,we study the effect of the number of initial macro-particles on the calculation precision.When the initial particles are so few that they can hardly reflect the randomness of the multipactor process,a higher calculated value will be resulted in.With the increase of the number of initial macro-particles,the calculated multipactor threshold is lower and more accurate.It is convergent when the number reaches about 2000 for the parallel plate transmission line and 4000 for the stepped impedance transformer,respectively.Taking into account other microwave devices with more complex electromagnetic field distribution,in order to ensure precision,it is recommended to select the number of initial macro-particles to be 8000.In addition,although CST MWS is used to obtain the electromagnetic field and boundary information in this paper,of course,other electromagnetic softwares (such as HFSS) can also be adopted as an alternative.
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Keywords:
- multipactor threshold /
- Boris algorithm /
- particle-in-cell simulation /
- secondary electron emission
[1] Vaughan J R M 1988 IEEE Trans. Electron Dev. 35 1172
[2] Kishek R A, Lau Y Y, Ang L K, Valfells A, Gilgenbach R M 1998 Phys. Plasmas 5 2120
[3] Ang L K, Lau Y Y, Kishek R A, Gilgenbach R M 1998 IEEE Trans. Plasma Sci. 26 290
[4] Nieter C, Stoltz P H, Roark C, Mahalingam S 2010 AIP Conf. Proc. 1299 399
[5] Gill E W B, Engel A V 1948 Proc. Roy. Soc. London A 192 446
[6] Vdovicheva N K, Sazontov A G, Semenov V E 2004 Radiophys. Quantum Electron. 47 580
[7] Anza S, Vicente C, Gil J, Boria V E, Gimeno B, Raboso D 2010 Phys. Plasmas 17 062110
[8] Sazontov A G, Sazontov V A, Vdovicheva N K 2008 Contrib. Plasma Phys. 48 331
[9] Udiljak R, Anderson D, Lisak M, Semenov V E, Puech J 2007 Phys. Plasmas 14 033508
[10] Lin S, Wang H G, Li Y, Liu C L, Zhang N, Cui W Z, Neuber A 2015 Phys. Plasmas 22 082114
[11] Kishek R A, Lau Y Y 1998 Phy. Rev. Lett. 80 193
[12] Birdsall C K, Langdon A B 1984 Plasma Physics via Computer Simulation (New York:McGraw Hill Higher Education) pp1-400
[13] Goplen B, Ludeking L, Smithe D, Warren G 1995 Comput. Phys. Commun. 87 54
[14] Nieter C, Cary J R 2004 J. Comput. Phys. 196 448
[15] Computer Simulation Technology (CST) Center 2012 Framingham M A 2009 High Power Laser and Particle Beams 21 1866 (in Chinese)[李永东, 王洪广, 刘纯亮,张殿辉,王建国,王玥2009强激光与粒子束21 1866]
[16] Li Y, Cui W Z, Wang H G 2015 Phys. Plasmas 22 053108
[17] You J W, Wang H G, Zhang J F, Tan S R, Cui T J 2014 IEEE Trans. Electron Dev. 61 1546
[18] Dong Y, Dong Z W, Yang W Y 2011 High Power Laser and Particle Beams 23 454 (in Chinese)[董烨, 董志伟, 杨文渊2011强激光与粒子束23 454]
[19] Liu L Q, Liu D G, Wang X Q, Peng K, Yang C 2012 High Power Laser and Particle Beams 24 1980 (in Chinese)[刘腊群, 刘大刚, 王学琼, 彭凯, 杨超2012强激光与粒子束24 1980]
[20] Boris J P 1970 Proceedings of the Fourth Conference on Numerical Simulation of Plasmas Washington, USA, November 2-3, 1970 p3
[21] Möller T, Trumbore B 1997 J. Graph. Tool. 2 21
[22] Vaughan J R M 1989 IEEE Trans. Electron Dev. 36 1963
[23] Furman M A, Pivi M T F 2002 Phys. Rev. ST Accel. 5 124404
[24] 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]
[25] Liu L, Li Y D, Wang R, Cui W Z, Liu C L 2013 Acta Phys. Sin. 62 025201 (in Chinese)[刘雷, 李永东, 王瑞, 崔万照, 刘纯亮2013物理学报62 025201]
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[1] Vaughan J R M 1988 IEEE Trans. Electron Dev. 35 1172
[2] Kishek R A, Lau Y Y, Ang L K, Valfells A, Gilgenbach R M 1998 Phys. Plasmas 5 2120
[3] Ang L K, Lau Y Y, Kishek R A, Gilgenbach R M 1998 IEEE Trans. Plasma Sci. 26 290
[4] Nieter C, Stoltz P H, Roark C, Mahalingam S 2010 AIP Conf. Proc. 1299 399
[5] Gill E W B, Engel A V 1948 Proc. Roy. Soc. London A 192 446
[6] Vdovicheva N K, Sazontov A G, Semenov V E 2004 Radiophys. Quantum Electron. 47 580
[7] Anza S, Vicente C, Gil J, Boria V E, Gimeno B, Raboso D 2010 Phys. Plasmas 17 062110
[8] Sazontov A G, Sazontov V A, Vdovicheva N K 2008 Contrib. Plasma Phys. 48 331
[9] Udiljak R, Anderson D, Lisak M, Semenov V E, Puech J 2007 Phys. Plasmas 14 033508
[10] Lin S, Wang H G, Li Y, Liu C L, Zhang N, Cui W Z, Neuber A 2015 Phys. Plasmas 22 082114
[11] Kishek R A, Lau Y Y 1998 Phy. Rev. Lett. 80 193
[12] Birdsall C K, Langdon A B 1984 Plasma Physics via Computer Simulation (New York:McGraw Hill Higher Education) pp1-400
[13] Goplen B, Ludeking L, Smithe D, Warren G 1995 Comput. Phys. Commun. 87 54
[14] Nieter C, Cary J R 2004 J. Comput. Phys. 196 448
[15] Computer Simulation Technology (CST) Center 2012 Framingham M A 2009 High Power Laser and Particle Beams 21 1866 (in Chinese)[李永东, 王洪广, 刘纯亮,张殿辉,王建国,王玥2009强激光与粒子束21 1866]
[16] Li Y, Cui W Z, Wang H G 2015 Phys. Plasmas 22 053108
[17] You J W, Wang H G, Zhang J F, Tan S R, Cui T J 2014 IEEE Trans. Electron Dev. 61 1546
[18] Dong Y, Dong Z W, Yang W Y 2011 High Power Laser and Particle Beams 23 454 (in Chinese)[董烨, 董志伟, 杨文渊2011强激光与粒子束23 454]
[19] Liu L Q, Liu D G, Wang X Q, Peng K, Yang C 2012 High Power Laser and Particle Beams 24 1980 (in Chinese)[刘腊群, 刘大刚, 王学琼, 彭凯, 杨超2012强激光与粒子束24 1980]
[20] Boris J P 1970 Proceedings of the Fourth Conference on Numerical Simulation of Plasmas Washington, USA, November 2-3, 1970 p3
[21] Möller T, Trumbore B 1997 J. Graph. Tool. 2 21
[22] Vaughan J R M 1989 IEEE Trans. Electron Dev. 36 1963
[23] Furman M A, Pivi M T F 2002 Phys. Rev. ST Accel. 5 124404
[24] 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]
[25] Liu L, Li Y D, Wang R, Cui W Z, Liu C L 2013 Acta Phys. Sin. 62 025201 (in Chinese)[刘雷, 李永东, 王瑞, 崔万照, 刘纯亮2013物理学报62 025201]
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