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Vacuum diode is a critical component of the apparatus which is the source of electron beams, the emitted electrons from the cathode of the diode have strong space charge limited effects. Based on Coulomb's law, the distributions of electric field in cathode-anode gap for different values of the ratio of radius to gap distance, R/D, are calculated numerically with the model of space charge limited effects in a planar vacuum diode. This method can avoid solving a non-linear differential equation which is used to yield the Child-Langmuir law from Poisson's equation. The results demonstrate that the only difference between the results from Coulomb's law and Child-Langmuir law is a modification factor, which is shown to be related to the potential difference across the gap. The results also show that one-dimensional space charge limited law will be a good approximation for the practical planar diode if the parameter R/D is beyond 10, but it can present a large error if the parameter R/D is small. Therefore it should be cautiously used.
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Keywords:
- vacuum diode /
- space charge limited effects /
- Child-Langmuir law /
- Coulomb's law
[1] Barker R J, Schamiloglu E (translated by Zhou C M, Liu G Z et al.) 2005 High-Power Microwave Sources and Technologies (Beijing: Tsinghua University Press) p284 (in Chinese) [Barker R J, Schamiloglu E著 (周传明, 刘国治等译) 2005 高功率微波源与技术 (北京: 清华大学出版社) 第284页]
[2] Han M, Zou X B, Zhang G X 2010 Fundamental of Pulsed Power Technology (Beijing: Tsinghua University Press) p124 (in Chinese) [韩旻,邹晓兵,张贵新 2010 脉冲功率技术基础 (北京:清华大学出版社)第124页]
[3] Xia L S, Wang M, Huang Z P, Zhang K Z, Shi J S, Zhang L W, Deng J J 2004 Acta Phys. Sin. 53 3435 (in Chinese) [夏连胜, 王勐, 黄子平, 张开志, 石金水, 章林文, 邓建军 2004 53 3435]
[4] Lin M C 2005 J. Vac. Sci. Technol. B 23 636
[5] Litvinov E A 1985 IEEE Trans. Electr. Insul. 20 683
[6] 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]
[7] Liu X S 2007 Intense Particle Beams and its Applications (Beijing: National Defense Industry Press) p25 (in Chinese) [刘锡三 2007 强流粒子束及其应用(北京:国防工业出版社) 第25页]
[8] Anderson W A 1993 J. Vac. Sci. Technol. B 11 383
[9] Child C D 1911 Phys. Rev. 32 492
[10] Langmuir I 1913 Phys. Rev. 2 450
[11] Feng Y, Verboncoeur J P, Lin M C 2008 Phys. Plasmas 15 043301
[12] Luginsland J W, Lau Y Y, Umstattd R J, Watrous J J 2002 Phys. Plasmas 9 2371
[13] Zhang Y H, Chang A B, Xiang F, Song F L, Kang Q, Luo M, Li M J, Gong S G 2007 Acta Phys. Sin. 56 5754 (in Chinese) [张永辉, 常安碧, 向飞, 宋法伦, 康强, 罗敏, 李名加, 龚胜刚 2007 56 5754]
[14] Birdsall C K, Bridges W B 1966 Electron Dynamics of Diode Regions (New York: Academic Press) p239
[15] Lau Y Y 2001 Phys. Rev. Lett. 87 278301
[16] Luginsland J W, Lau Y Y, Gilgenbach R M 1996 Phys. Rev. Lett. 77 4668
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[1] Barker R J, Schamiloglu E (translated by Zhou C M, Liu G Z et al.) 2005 High-Power Microwave Sources and Technologies (Beijing: Tsinghua University Press) p284 (in Chinese) [Barker R J, Schamiloglu E著 (周传明, 刘国治等译) 2005 高功率微波源与技术 (北京: 清华大学出版社) 第284页]
[2] Han M, Zou X B, Zhang G X 2010 Fundamental of Pulsed Power Technology (Beijing: Tsinghua University Press) p124 (in Chinese) [韩旻,邹晓兵,张贵新 2010 脉冲功率技术基础 (北京:清华大学出版社)第124页]
[3] Xia L S, Wang M, Huang Z P, Zhang K Z, Shi J S, Zhang L W, Deng J J 2004 Acta Phys. Sin. 53 3435 (in Chinese) [夏连胜, 王勐, 黄子平, 张开志, 石金水, 章林文, 邓建军 2004 53 3435]
[4] Lin M C 2005 J. Vac. Sci. Technol. B 23 636
[5] Litvinov E A 1985 IEEE Trans. Electr. Insul. 20 683
[6] 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]
[7] Liu X S 2007 Intense Particle Beams and its Applications (Beijing: National Defense Industry Press) p25 (in Chinese) [刘锡三 2007 强流粒子束及其应用(北京:国防工业出版社) 第25页]
[8] Anderson W A 1993 J. Vac. Sci. Technol. B 11 383
[9] Child C D 1911 Phys. Rev. 32 492
[10] Langmuir I 1913 Phys. Rev. 2 450
[11] Feng Y, Verboncoeur J P, Lin M C 2008 Phys. Plasmas 15 043301
[12] Luginsland J W, Lau Y Y, Umstattd R J, Watrous J J 2002 Phys. Plasmas 9 2371
[13] Zhang Y H, Chang A B, Xiang F, Song F L, Kang Q, Luo M, Li M J, Gong S G 2007 Acta Phys. Sin. 56 5754 (in Chinese) [张永辉, 常安碧, 向飞, 宋法伦, 康强, 罗敏, 李名加, 龚胜刚 2007 56 5754]
[14] Birdsall C K, Bridges W B 1966 Electron Dynamics of Diode Regions (New York: Academic Press) p239
[15] Lau Y Y 2001 Phys. Rev. Lett. 87 278301
[16] Luginsland J W, Lau Y Y, Gilgenbach R M 1996 Phys. Rev. Lett. 77 4668
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