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When the working frequency of vacuum electronic device reaches the terahertz frequency, the ohmic loss has a significant impact on the vacuum electronic device. To study the effect of the ohmic loss on the working characteristic of the vacuum electronic terahertz devices, this paper implements the frequency-dependent surface impedance boundary condition (SIBC) in the 3 dimensional particle in cell code UNIPIC-3D. Conformal mesh is adopted in the code to overcome the staircase error in traditional particle in cell method. By using the surface impedance boundary, we eliminate the need to study the field inside the lossy dielectric objects which require extremely small grid cells for numerical stability. In comparison with constant parameter SIBC, the dispersive SIBC is applicable over a very large frequency bandwidth and over a large range of conductivities. The correctness of the implementation is verified by simulating the lossy resonant cavity and circular waveguide, the simulated power loss is comparable with the theoretical predication. High power vacuum electronic devices of terahertz regime are attracting extensive interests due to their potential applications in science and technologies. The impulse-wave relativistic surface wave oscillator (SWO) and low-voltage continuous-wave planar grating backward wave oscillator (BWO) both made of copper are numerically studied by using UNIPIC-3D and dispersive surface impedance boundary condition. Numerical results show that the strongest field is very close to the slow wave structure where the beam-wave interaction occurs and that terahertz wave generates both in these two devices. The distributed wall loss has a considerable effect on the devices: the output power has a significant decrease and the startup time becomes longer, but the working frequencies of the two devices keep unchanged. To improve the efficiency of relativistic SWO, a resonant reflector is proposed between the diode and the slow wave structure. Numerical results show that the working frequency of the device with a resonant reflector keeps unchanged as the original one, but the output power increases to 60 MW from 41 MW of the original one when the ohmic loss is considered.
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Keywords:
- surface impedance boundary /
- Ohmic loss /
- particle in cell /
- terahertz device /
- surface wave oscillator /
- BWO
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图 1 FDTD网格示意图
Figure 1. Schematic of FDTD cell.
图 2 局部共形网格
Figure 2. Local conformal grid.
图 3 谐振腔内诊断点处电场时间波形
Figure 3. Time history of electric field inside a resonator.
图 4 表面波振荡器示意图
Figure 4. Schematic of a surface wave oscillator.
图 5 SWO内z方向电场分布云图
Figure 5. Contour of the Ez inside the SWO.
图 6 理想导体SWO中 (a)电场时间波形; 电场频谱(b)
Figure 6. Time history of the electric field (a) inside the SWO with PEC and its spectrum (b).
图 7 有损耗铜材料SWO中 (a)电场时间波形; (b)电场频谱
Figure 7. Time history of the electric field (a) inside the SWO with lossy copper and its spectrum (b).
图 8 SWO输出功率
Figure 8. Output power from the SWO.
图 9 平板BWO结构示意图(外围波导尺寸: 宽a = 7.2 mm, 高b = 1.8 mm; 格栅尺寸: 周期l = 0.1 mm, 宽w = 2.5 mm, 高h = 0.16 mm, 间距d = 0.058 mm; 格栅周期数140)
Figure 9. BWO with planar structure.(a = 7.2 mm, b = 1.8 mm; l = 0.1 mm, w = 2.5 mm, h = 0.16 mm, d = 0.058 mm)
图 10 BWO中电子相空间图
Figure 10. Phase space of electrons in the BWO
图 11 BWO中电场波形 (a)无损耗; (b)有损耗
Figure 11. Time history of electric field in the BWO with PEC (a) and lossy copper (b).
图 12 BWO输出功率 (a) PEC边界的结果; (b)有耗金属边界的结果
Figure 12. Output power from the BWO: (a) PEC ; (b) lossy copper.
表 1 圆波导中模拟Poynting通量与理论解的对比
Table 1. Comparison of simulated and analytic Poynting flux in a circular waveguide.
距离/cm 理论值/P0 模拟值/P0 相对误差/% 5 0.8964 0.8933 0.3 10 0.8035 0.7969 0.8 15 0.7203 0.7105 1.4 20 0.6457 0.6335 1.9 
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[1] Siegel P H 2002 IEEE Trans. Microw. Theory Techn. 50 910
Google Scholar
[2] Booske J H, Dobbs R J, Joye C D, Kory C L, Neil G R, Park G, Park J, Temkin R J 2011 IEEE Trans. Terahertz Sci. Techn. 1 54
Google Scholar
[3] Li X Z, Wang J G, Sun J, Song Z M, Ye H, Zhang Y C, Zhang L J, Zhang L G 2013 IEEE Trans. Electron Dev. 60 2931
Google Scholar
[4] 李爽, 王建国, 童长江, 王光强, 陆希成, 王雪峰 2013 62 120703
Google Scholar
Li S, Wang J G, Tong C J, Wang G Q, Lu X C, Wang X F 2013 Acta Phys. Sin. 62 120703
Google Scholar
[5] 王光强, 王建国, 李爽, 王雪峰, 陆希成, 宋志敏 2015 64 050703
Google Scholar
Wang G Q, Wang J G, Li S, Wang X F, Lu X C, Song Z M 2015 Acta Phys. Sin. 64 050703
Google Scholar
[6] Wang J G, Wang G Q, Wang D Y, Li S 2018 Scientific Report 8 6978
Google Scholar
[7] Shin Y M, Zhao J F, Barnett L R, Luhmann N C 2010 Phys. Plasmas 17 123105
Google Scholar
[8] Xi H Z, He Z C, Wang J G, Li R, Zhu G, Chen Z G, Liu J S, Liu L W, Wang H 2017 Phys. Plasmas 24 033105
Google Scholar
[9] Zhang K C, Qi Z K, Yang Z L 2015 Chin. Phys. B 24 079402
Google Scholar
[10] Xi H Z, Wang J G, He Z C, Zhu G, Wang Y, Wang H, Chen Z G, Li R, Liu L W 2018 Scientific Reports 8 348
Google Scholar
[11] Birdsall K, Langdon A B 1985 Plasma Physics via Computer Simulation (New York: McGraw-Hill) pp7–32
[12] Goplen B, Ludeking L, Smithe D, Warren G 1995 Comp. Phys. Comm. 87 54
Google Scholar
[13] Verboncoeur J P, Langdon A B, Gladd N T 1995 Comp. Phys. Comm. 87 199
Google Scholar
[14] Wang J G, Zhang D H, Liu C L, Li Y D, Wang Y, Wang H G, Qiao H L, Li X Z 2009 Phys. Plasmas 16 033108
Google Scholar
[15] Wang J, Chen Z, Wang Y, Zhang D, Liu C, Li Y, Wang H, Qiao H, Fu M, Yuan Y 2010 Phys. Plasmas 17 073107
Google Scholar
[16] Na D Y, Omelchenko Y A, Moon H, Borges B H, Teixeira F L 2017 J. Comput. Phys. 346 295
Google Scholar
[17] Wang G Q, Wang J G, Li S, Wang X F 2015 AIP Advances 5 097155
Google Scholar
[18] 杨利霞, 马辉, 施卫东, 施丽娟, 于萍 2013 62 034102
Google Scholar
Yang L X, Ma H, Shi W D, Shi L J, Yu P 2013 Acta Phys. Sin. 62 034102
Google Scholar
[19] 闫玉波, 葛德彪, 柴玫 2001 电波科学学报 16 484
Google Scholar
Yan Y B, Ge D B, Chai M 2001 Chin. J. Radio Sci. 16 484
Google Scholar
[20] Mak J C, Sarris C D 2013 IEEE International Symposium on Antennas and Propagation & Usnc/ursi National Radio Science Meeting Orlando, USA, July 7−13 2013 p902
[21] Taflove A, Hagness S 2000 Computational Electrodynamics: the Finite Difference Time Domain Method (Norwood: Artech House) p67
[22] Beggs J H, Luebbers R J, Yee K S, Kunz K S 1992 IEEE Trans. Ant. Propag. 40 49
Google Scholar
[23] Wang Y, Wang J, Chen Z, Cheng G, Wang P 2016 Comput. Phys. Commun. 205 1
Google Scholar
[24] Zagorodnov I A, Schuhmann R, Weiland T 2007 J. Comput. Phys. 225 1493
Google Scholar
[25] Chen J, Wang J G 2007 IEEE Trans. Ant. Propag. 55 3613
Google Scholar
[26] Chen J, Wang J G 2007 IEEE Trans. Ant. Propag. 55 3603
Google Scholar
[27] Maloney J G, Smith G S 1992 IEEE Trans. Ant. Propag. 40 38
Google Scholar
[28] Benford J 2006 High Power Microwave (New York: Taylor & Francis) p124
[29] Wang J G, Wang Y, Zhang D H 2006 IEEE Trans. Plasma Sci. 34 681
Google Scholar
[30] Li X, Wang J, Xiao R, Wang G, Zhang L, Zhang Y, Ye H 2013 Phys. Plasmas 20 083105
Google Scholar
[31] Chen C, Xiao R, Sun J, Song Z, Huo S, Bai X, Shi Y, Liu G 2013 Phys. Plasmas 20 113113
Google Scholar
[32] Moreland L D, Schamiloglu E, Lemke W, Korovin S D, Rostov V V, Roitman A M, Hendricks K J, Spencer T A 1994 IEEE Trans. Plasma Sci. 22 554
Google Scholar
[33] Xiao R, Tan W, Li X, Song Z, Sun J, Chen C 2012 Phys. Plasmas 19 093102
Google Scholar
[34] Xiao R, Chen C, Tan W, Teng Y 2014 IEEE Trans. Electron Dev. 61 611
Google Scholar
[35] Song W, Chen C, Zhang L G, Hu Y, Yang M, Zhang X 2011 Phys. Plasmas 18 063105
Google Scholar
[36] Song W, Teng Y, Zhang Z, Li J, Sun J, Chen C, Zhang L 2012 Phys. Plasmas 19 083105
Google Scholar
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