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To investigate a complex physical phenomenon and its evolution law at the cathode surface at the initial stage of the explosive electron emission process in a high-power diode, in this paper we present a model of a planar vacuum diode with a field emission cathode. The model is one-dimensional and nonstationary. To study the space charge effect of the emitted electrons on the electric field at the cathode surface, Poisson's equation is solved numerically by using our developed code, and the time-dependences of the electric field at the cathode surface for different cases are obtained. The results show that the electric field at the cathode surface first oscillates and finally yields a steady state. The absolute value of the steady electric field at the cathode surface is higher for the higher field enhancement factor at a given applied electric field, and the applied electric field has the same effects on the steady value at a certain field enhancement factor. The electric field at the cathode surface completely determines the extracted field emission current density from the cathode, and at the same time, the electric field at the cathode surface is influenced by the emitting current density.
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Keywords:
- field emission /
- space charge /
- electric field /
- cathode surface
[1] Barker R J, Schamiloglu E 2005 High-Power Microwave Sources and Technologies (Beijing: Tsinghua University Press) p277-312 (in Chinese) [Barker R J, Schamiloglu E 2005 高功率微波源与技术(北京: 清华大学出版社) 第277-312页]
[2] Liao Q L, Zhang Y, Huang Y H, Qi J J, Gao Z J, Xia L S, Zhang H 2008 Acta Phys. Sin. 57 1778 (in Chinese) [廖庆亮, 张跃, 黄运华, 齐俊杰, 高战军, 夏连胜, 张篁 2008 57 1778]
[3] Child C D 1911 Phys. Rev. 32 492
[4] Langmuir I 1913 Phys. Rev. 2 450
[5] Goplen B, Ludeking L, Smithe D, Warren G 1995 Comput. Phys. Commun. 87 54
[6] Feng Y, Verboncoeur J P 2006 Phys. of Plasmas 13 073105
[7] Mesyats G A 1998 Explosive Electrons Emission (Ekaterinburg: URO-Press) p1-49
[8] Cai L B, Wang J G 2011 Acta Phys. Sin. 60 025217 (in Chinese) [蔡利兵, 王建国 2011 60 025217]
[9] Shi Y, Guo C B, Huang J K, Fan D 2011 Acta Phys. Sin. 60 048102 (in Chinese) [石玗, 郭朝博, 黄健康, 樊丁 2011 60 048102]
[10] Wang L D, Chen G D, Zhang J Q, Yang M, Wang Y J, An B 2009 Acta Phys. Sin. 58 7852 (in Chinese) [王六定, 陈国栋, 张教强, 杨敏, 王益军, 安博 2009 58 7852]
[11] Fowler R H, Nordheim L 1928 Proc. R. Soc. London, Ser. A 119 173
[12] Jonge N D, Allioux M, Doytcheva M, Kaiser M 2004 Appl. Phys. Lett. 85 1607
[13] Schwettman H A, Turneaure J P, Waites R F 1974 J. Appl. Phys. 45 914
[14] Birdsall C K, Langdon A B 1991 Plasma Physics via Computer Simulation (1st Ed.) (New York: IOP Publishing) p7-26, 443-446
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[1] Barker R J, Schamiloglu E 2005 High-Power Microwave Sources and Technologies (Beijing: Tsinghua University Press) p277-312 (in Chinese) [Barker R J, Schamiloglu E 2005 高功率微波源与技术(北京: 清华大学出版社) 第277-312页]
[2] Liao Q L, Zhang Y, Huang Y H, Qi J J, Gao Z J, Xia L S, Zhang H 2008 Acta Phys. Sin. 57 1778 (in Chinese) [廖庆亮, 张跃, 黄运华, 齐俊杰, 高战军, 夏连胜, 张篁 2008 57 1778]
[3] Child C D 1911 Phys. Rev. 32 492
[4] Langmuir I 1913 Phys. Rev. 2 450
[5] Goplen B, Ludeking L, Smithe D, Warren G 1995 Comput. Phys. Commun. 87 54
[6] Feng Y, Verboncoeur J P 2006 Phys. of Plasmas 13 073105
[7] Mesyats G A 1998 Explosive Electrons Emission (Ekaterinburg: URO-Press) p1-49
[8] Cai L B, Wang J G 2011 Acta Phys. Sin. 60 025217 (in Chinese) [蔡利兵, 王建国 2011 60 025217]
[9] Shi Y, Guo C B, Huang J K, Fan D 2011 Acta Phys. Sin. 60 048102 (in Chinese) [石玗, 郭朝博, 黄健康, 樊丁 2011 60 048102]
[10] Wang L D, Chen G D, Zhang J Q, Yang M, Wang Y J, An B 2009 Acta Phys. Sin. 58 7852 (in Chinese) [王六定, 陈国栋, 张教强, 杨敏, 王益军, 安博 2009 58 7852]
[11] Fowler R H, Nordheim L 1928 Proc. R. Soc. London, Ser. A 119 173
[12] Jonge N D, Allioux M, Doytcheva M, Kaiser M 2004 Appl. Phys. Lett. 85 1607
[13] Schwettman H A, Turneaure J P, Waites R F 1974 J. Appl. Phys. 45 914
[14] Birdsall C K, Langdon A B 1991 Plasma Physics via Computer Simulation (1st Ed.) (New York: IOP Publishing) p7-26, 443-446
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