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The analytical expressions of the beam-wave coupling coefficients and the beam-loaded conductance in an N-gap coupled cavity are derived based on space-charge wave theory. Through calculating the relations of the beam-wave coupling coefficient and the normalized beam-loaded conductance to the gap number, beam voltage and perveance for 2π mode, the mechanism of the beam-wave synchronization and coupling in the multi-gap coupled cavity are discussed. The results show that, with the increase of N(≥2), the beam-wave coupling efficiency and the normalized beam-loaded conductance vary with beam voltage more rapidly and there is a maximum value for the absolute squared value of the coupling coefficient |MN|2 and a maximum value and a minimum value for the normalized beam-loaded conductance gb. The magnitudes of these extrema increase with the increase of gap number N, and the corresponding voltage is close to the synchronization voltage. The increase of the perveance could make the voltage difference between two extremums of gb increase, the magnitudes of these extrema decrease, and the beam-wave coupling efficiency fall.
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Keywords:
- multi-gap coupled cavity /
- coupling coefficient /
- beam-loaded conductance /
- synchronization and coupling
[1] Wessel-Berg T 1957 Microwave Lab Stanford Univ. Tech. Rep. 376
[2] Chodorow M, Wessel-Berg T 1961 IRE Trans. ED 8 44
[3] 30
[4] Shin Y M, Park G S 2004 J. Korean Phys. Soc. 44 1239
[5] Roitman A, Horoyski P, Hyttinen M, Berry D, Steer B 2006 Proc. IEEE International Vacuum Electronics Conference 191
[6] Roitman A, Berry D, Steer B 2005 IEEE Trans. ED 52 895
[7] Huang H, Luo X, Lei L R, Luo G Y, Zhang B Z, Jin X, Tan J 2010 Acta Phys. Sin. 59 1907 (in Chinese) [黄 华、 罗 雄、 雷禄容、 罗光耀、 张北镇、 金 晓、 谭 杰 2010 59 1907] [7] Zhang K C, Wu Z H,Liu S G 2008 Chin. Phys. B 17 3402
[8] Nguyen K T, Pershing D E, Abe D K, Levush B 2006 IEEE Trans. Plasma Sci. 34 576
[9] Quan Y, Ding Y, Wang S 2009 IEEE Trans. Plasma Sci. 137
[10] Chodorow M, Susskind C 1964 Fundamentals of Microwave Electronics (New York: McGraw-Hill Book Co. ) p158
[11] Kantrowitz F, Tammaru I 1988 IEEE Trans. ED 35 2018
[12] Haikov A Z (translated by Huang G N) 1980 Klystron Amplifiers (Beijing: National Defense Industry Press) p93 (in Chinese) [哈依柯夫 А З 著 黄高年译 1980速调管放大器(北京:国防工业出版社)第93页]
[13] Pierce J R, Shepherd W G 1947 J. Bell System Tech. 26 663
[14] Branch G M 1961 IRE Trans. ED 8 193
[15] Xie J L, Zhao Y X 1966 Bunching Theory of Klystrons (Beijing: Science Press) p31 (in Chinese) [谢家麐、赵永翔 1966速调管群聚理论(北京:科学出版杜)第31页]
[16] Branch G M, Mihran T G 1955 IRE Trans. ED 2 3
[17] Chodorow M, Kulke B 1966 IEEE Trans. ED 13 439
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[1] Wessel-Berg T 1957 Microwave Lab Stanford Univ. Tech. Rep. 376
[2] Chodorow M, Wessel-Berg T 1961 IRE Trans. ED 8 44
[3] 30
[4] Shin Y M, Park G S 2004 J. Korean Phys. Soc. 44 1239
[5] Roitman A, Horoyski P, Hyttinen M, Berry D, Steer B 2006 Proc. IEEE International Vacuum Electronics Conference 191
[6] Roitman A, Berry D, Steer B 2005 IEEE Trans. ED 52 895
[7] Huang H, Luo X, Lei L R, Luo G Y, Zhang B Z, Jin X, Tan J 2010 Acta Phys. Sin. 59 1907 (in Chinese) [黄 华、 罗 雄、 雷禄容、 罗光耀、 张北镇、 金 晓、 谭 杰 2010 59 1907] [7] Zhang K C, Wu Z H,Liu S G 2008 Chin. Phys. B 17 3402
[8] Nguyen K T, Pershing D E, Abe D K, Levush B 2006 IEEE Trans. Plasma Sci. 34 576
[9] Quan Y, Ding Y, Wang S 2009 IEEE Trans. Plasma Sci. 137
[10] Chodorow M, Susskind C 1964 Fundamentals of Microwave Electronics (New York: McGraw-Hill Book Co. ) p158
[11] Kantrowitz F, Tammaru I 1988 IEEE Trans. ED 35 2018
[12] Haikov A Z (translated by Huang G N) 1980 Klystron Amplifiers (Beijing: National Defense Industry Press) p93 (in Chinese) [哈依柯夫 А З 著 黄高年译 1980速调管放大器(北京:国防工业出版社)第93页]
[13] Pierce J R, Shepherd W G 1947 J. Bell System Tech. 26 663
[14] Branch G M 1961 IRE Trans. ED 8 193
[15] Xie J L, Zhao Y X 1966 Bunching Theory of Klystrons (Beijing: Science Press) p31 (in Chinese) [谢家麐、赵永翔 1966速调管群聚理论(北京:科学出版杜)第31页]
[16] Branch G M, Mihran T G 1955 IRE Trans. ED 2 3
[17] Chodorow M, Kulke B 1966 IEEE Trans. ED 13 439
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