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In high-power microwave diode design, the space-charge-limited current is important because of its relation to the diode property and the formation of the virtual cathode. Although the Langmuir–Blodgett law, as a numerical solution, is helpful, a simple functional expression is more convenient for practical research and can avoide the divergence of the series for large R\-c/R\-a. First principle is used to generalize two-dimensional space-charge-limited current for planar plane capacitor and coaxial cylinders, and its reliability has been examined adequately. In this paper we obtain the functional expression of space-charge-limited current for concentric sphere, and the space-charge field factor in this expression by comparing the classical Langmuir current with the current from concentric sphere.
[1] Zhang Y H, Jiang J S, Chang A B 2003 Acta Phys. Sin. 52 1676 (in Chinese) [张永辉、江金生、常安碧 2003 52 1676]
[2] Liu G Z, Yang Z F 2010 Chin. Phys. B 19 075207
[3] Shi L, Zhang J S, Qiu A C, He X P 2001 High Power Laser And Particle Beams. 13 357 (in Chinese)[石 磊、张嘉生、邱爱慈、何小平 2001 强激光与粒子束 13 357]
[4] Xia L S, Wang M, Huang Z P 2004 Acta Phys. Sin. 53 3453 (in Chinese) [夏连胜、王 勐、黄子平 2004 53 3453]
[5] Liu J, Shu T, Li Z Q 2010 Acta Phys. Sin. 59 2622 (in Chinese) [刘 静、舒 挺、李志强 2010 59 2622]
[6] Liu G Z, Shao H 2003 Chin. Phys. 12 204
[7] Liu G Z, Huang W H, Shao H, Xiao R Z 2006 Chin. Phys. 15 600
[8] Langmuir I, Blodgett K 1924 Phys. Rev. 24 49
[9] Page L, Adams I 1945 Phys. Rev. 68 126
[10] Degond P, Jaffard S, Poupaud F, Raviart P A 1996 Math. Methods Appl. Sci. 19 287
[11] Luginsland J W, Lau Y Y, Gilgenbach R M 1996 Phys. Rev. Lett. 77 4668
[12] Jeli Dc＇ N, Schrittwieser R, Kuhn S 1998 Physics Letters A 246 318
[13] Lau Y Y 2001 Phys. Rev. Lett. 87 278301-1
[14] Xu P C, James Dickens, Hatfield L L 2004 Phys. Plasmas 11 3278
[15] Electron tube design handbook compiling committees 1981 A handbook for design of electron optics system in microwave tube (First edition)(Beijing: National defense industry press) P340—357 (in Chinese)[电子管设计手册编辑委员会 1981 微波管电子光学系统设计手册 (第一版) (北京: 国防工业出版社) 第340—357页]
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[1] Zhang Y H, Jiang J S, Chang A B 2003 Acta Phys. Sin. 52 1676 (in Chinese) [张永辉、江金生、常安碧 2003 52 1676]
[2] Liu G Z, Yang Z F 2010 Chin. Phys. B 19 075207
[3] Shi L, Zhang J S, Qiu A C, He X P 2001 High Power Laser And Particle Beams. 13 357 (in Chinese)[石 磊、张嘉生、邱爱慈、何小平 2001 强激光与粒子束 13 357]
[4] Xia L S, Wang M, Huang Z P 2004 Acta Phys. Sin. 53 3453 (in Chinese) [夏连胜、王 勐、黄子平 2004 53 3453]
[5] Liu J, Shu T, Li Z Q 2010 Acta Phys. Sin. 59 2622 (in Chinese) [刘 静、舒 挺、李志强 2010 59 2622]
[6] Liu G Z, Shao H 2003 Chin. Phys. 12 204
[7] Liu G Z, Huang W H, Shao H, Xiao R Z 2006 Chin. Phys. 15 600
[8] Langmuir I, Blodgett K 1924 Phys. Rev. 24 49
[9] Page L, Adams I 1945 Phys. Rev. 68 126
[10] Degond P, Jaffard S, Poupaud F, Raviart P A 1996 Math. Methods Appl. Sci. 19 287
[11] Luginsland J W, Lau Y Y, Gilgenbach R M 1996 Phys. Rev. Lett. 77 4668
[12] Jeli Dc＇ N, Schrittwieser R, Kuhn S 1998 Physics Letters A 246 318
[13] Lau Y Y 2001 Phys. Rev. Lett. 87 278301-1
[14] Xu P C, James Dickens, Hatfield L L 2004 Phys. Plasmas 11 3278
[15] Electron tube design handbook compiling committees 1981 A handbook for design of electron optics system in microwave tube (First edition)(Beijing: National defense industry press) P340—357 (in Chinese)[电子管设计手册编辑委员会 1981 微波管电子光学系统设计手册 (第一版) (北京: 国防工业出版社) 第340—357页]
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