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The research on a Smith-Purcell device becomes active since it holds promise in developing a high power, tunable, and compact terahertz radiation source. In this paper, a dielectric loaded grating for Smith-Purcell device is proposed. By investigating the interaction between the sheet electron beam and surface wave above the grating, the dispersion equation with electron beam is derived, in which the electron beam has a finite thickness. And then the growth rate of the beam-wave interaction is numerically calculated from the dispersion equation. In addition, the current threshold for oscillators, known as a start current, is carefully estimated from the dispersion equation by considering the boundary conditions of electromagnetic field. The effects of structure length, electron beam parameters and dielectric constant on start current are analyzed at length. The results reveal that the start current decreases as the structure length increases. This is because as the structure length becomes greater, the distance of the beam-wave interaction becomes longer, which can strengthen the beam-wave interaction. And with increasing beam thickness and beam-grating distance, the start current increases. Because the electric field of the surface wave decreases exponentially with the increase of distance from the grating, the electron beam far from the grating cannot be bunched by the field, which makes it harder for Smith-Purcell device to oscillate. However, as the beam voltage becomes greater, the start current decreases first quickly and then slightly. Compared with the case of metal grating, it can be seen that the use of dielectric can improve the growth rate and reduce the start current for the operation of a Smith-Purcell backward wave oscillator. The start current decreases quickly when the dielectric constant is greater than 1. Then it increases slightly when dielectric constant is between 2 and 3, and finally the start current continues to decrease. But it cannot be helpful to choose a very big value of dielectric in order to obtain a low start current, because the operation frequency decreases as dielectric constant increases. It is more appropriate to choose a dielectric constant in a required frequency range. The predictions of our theory and the results from the particle-in-cell simulation are consistent with each other, which verifies the validity and accuracy of the theory in this paper.
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Keywords:
- dielectric loaded grating /
- dispersion equation /
- growth rate /
- start current
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[2] Bakhtyari A, Walsh J E, Brownell J H 2002 Phys. Rev. E 65 066503
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[5] Andrews H L, Boulware C H, Brau C A, Jarvis J D 2005 Phys. Rev. ST Accel. Beams 8 050703
[6] Andrews H L, Boulware C H, Brau C A, Donohue J T, Gardelle J, Jarvis J D 2006 New J. Phys. 8 289
[7] Kim K J, Kumar V 2007 Phys. Rev. ST Accel. Beams 10 080702
[8] Li D Z, Hangyo M, Tsunawaki Y, Yang Z, Wei Y 2012 Appl. Phys. Lett. 100 191101
[9] Doucas G, Kimmitt M F, Kormann T, Korschinek G, Wallner C 2003 Int. J. Infrared. Milli. Waves. 24 829
[10] Xiong P F, Wang Y T 1996 High Power Laser and Particle Beams 8 1 (in Chinese) [熊平凡, 王友棠 1996 强激光与粒子束 8 1]
[11] Lu Z G, Gong Y B, Wei Y Y, Wang W X 2007 Acta Phys. Sin. 56 6931 (in Chinese) [路志刚, 宫玉彬, 魏彦玉, 王文祥 2007 56 6931]
[12] Zhang P, Zhang Y X, Zhou J, Liu W H, Zhong R B, Liu S G 2012 Chin. Phys. B 21 104102
[13] Donohue J T, Gardelle J 2006 Phys. Rev. ST Accel. Beams 9 060701
[14] Li D Z, Imasaki K, Gao X, Yang Z, Park G S 2007 Appl. Phys. Lett. 91 221506
[15] Kumar V, Kim K J 2006 Phys. Rev. E 73 026501
[16] Jarvis J D, Andrews H L, Brau C A 2010 Phys. Rev. ST Accel. Beams 13 020701
[17] Liu W X, Yang Z Q, Liang Z, Li D Z, Imasaki K, Shi Z J, Lan F, Park G S 2007 Nucl. Instrum. Meth. Phys. Res. A 580 1552
[18] Cao M M, Liu W X, Wang Y, Li K 2014 Acta Phys. Sin. 63 024101 (in Chinese) [曹苗苗, 刘文鑫, 王勇, 李科 2014 63 024101]
[19] Di J, Zhu D J, Liu S G 2005 J. UEST China 34 4 (in Chinese) [狄隽, 祝大军, 刘盛纲 2005 电子科技大学学报 34 4]
[20] Zhang K Q, Li D J 2001 Electromagnetic Theory for Microwaves and Optoelectronics (Beijing: Publishing House of Electronics Industry) p382 (in Chinese) [张克潜, 李德杰 2001 微波与光电子学中的电磁理论(北京:电子工业出版社) 第382页]
[21] Yasumoto K, Tanaka T, Aramaki T 1990 IEEE Trans. Plasma Sci. 18 699
[22] Mechrany K, Rshidaian B 2003 IEEE Trans. Electron Dev. 50 1562
[23] Chang S F R, Scharer J E, Booske J H 1992 IEEE Trans. Plasma Sci. 20 293
[24] Tan H Q, Tian S Q 2007 Fortran Language: Fortran 77 Structured Programming (Beijing: Tsinghua University Press) pp177-183 (in Chinese) [谭浩强, 田淑清 2007 Fortran语言: Fortran 77结构化程序设计(北京: 清华大学出版社) 第177183页]
[25] Liu W X, Yang Z Q, Zhang Z C, Lan F, Shi Z J, Liang Z, Liu S G 2008 J. Infrared Millim. Waves 27 152 (in Chinese) [刘文鑫, 杨梓强, 张祖存, 兰峰, 史宗君, 梁正, 刘盛纲 2008 红外与毫米波学报 27 152]
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[1] Smith S J, Purcell E M 1953 Phys. Rev. 92 4
[2] Bakhtyari A, Walsh J E, Brownell J H 2002 Phys. Rev. E 65 066503
[3] Urata J, Goldstein M, Kimmitt M F, Naumov A, Platt C, Walsh J E 1998 Phys. Rev. Lett. 80 516
[4] Andrews H L, Boulware C H, Brau C A, Jarvis J D 2004 Phys. Rev. ST Accel. Beams 7 070701
[5] Andrews H L, Boulware C H, Brau C A, Jarvis J D 2005 Phys. Rev. ST Accel. Beams 8 050703
[6] Andrews H L, Boulware C H, Brau C A, Donohue J T, Gardelle J, Jarvis J D 2006 New J. Phys. 8 289
[7] Kim K J, Kumar V 2007 Phys. Rev. ST Accel. Beams 10 080702
[8] Li D Z, Hangyo M, Tsunawaki Y, Yang Z, Wei Y 2012 Appl. Phys. Lett. 100 191101
[9] Doucas G, Kimmitt M F, Kormann T, Korschinek G, Wallner C 2003 Int. J. Infrared. Milli. Waves. 24 829
[10] Xiong P F, Wang Y T 1996 High Power Laser and Particle Beams 8 1 (in Chinese) [熊平凡, 王友棠 1996 强激光与粒子束 8 1]
[11] Lu Z G, Gong Y B, Wei Y Y, Wang W X 2007 Acta Phys. Sin. 56 6931 (in Chinese) [路志刚, 宫玉彬, 魏彦玉, 王文祥 2007 56 6931]
[12] Zhang P, Zhang Y X, Zhou J, Liu W H, Zhong R B, Liu S G 2012 Chin. Phys. B 21 104102
[13] Donohue J T, Gardelle J 2006 Phys. Rev. ST Accel. Beams 9 060701
[14] Li D Z, Imasaki K, Gao X, Yang Z, Park G S 2007 Appl. Phys. Lett. 91 221506
[15] Kumar V, Kim K J 2006 Phys. Rev. E 73 026501
[16] Jarvis J D, Andrews H L, Brau C A 2010 Phys. Rev. ST Accel. Beams 13 020701
[17] Liu W X, Yang Z Q, Liang Z, Li D Z, Imasaki K, Shi Z J, Lan F, Park G S 2007 Nucl. Instrum. Meth. Phys. Res. A 580 1552
[18] Cao M M, Liu W X, Wang Y, Li K 2014 Acta Phys. Sin. 63 024101 (in Chinese) [曹苗苗, 刘文鑫, 王勇, 李科 2014 63 024101]
[19] Di J, Zhu D J, Liu S G 2005 J. UEST China 34 4 (in Chinese) [狄隽, 祝大军, 刘盛纲 2005 电子科技大学学报 34 4]
[20] Zhang K Q, Li D J 2001 Electromagnetic Theory for Microwaves and Optoelectronics (Beijing: Publishing House of Electronics Industry) p382 (in Chinese) [张克潜, 李德杰 2001 微波与光电子学中的电磁理论(北京:电子工业出版社) 第382页]
[21] Yasumoto K, Tanaka T, Aramaki T 1990 IEEE Trans. Plasma Sci. 18 699
[22] Mechrany K, Rshidaian B 2003 IEEE Trans. Electron Dev. 50 1562
[23] Chang S F R, Scharer J E, Booske J H 1992 IEEE Trans. Plasma Sci. 20 293
[24] Tan H Q, Tian S Q 2007 Fortran Language: Fortran 77 Structured Programming (Beijing: Tsinghua University Press) pp177-183 (in Chinese) [谭浩强, 田淑清 2007 Fortran语言: Fortran 77结构化程序设计(北京: 清华大学出版社) 第177183页]
[25] Liu W X, Yang Z Q, Zhang Z C, Lan F, Shi Z J, Liang Z, Liu S G 2008 J. Infrared Millim. Waves 27 152 (in Chinese) [刘文鑫, 杨梓强, 张祖存, 兰峰, 史宗君, 梁正, 刘盛纲 2008 红外与毫米波学报 27 152]
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