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Under intense electric field, the electrons emitted from the cathode by field emission have strong space charge effects, so the space charge limited current of a diode is an important parameter in the design of many intense electron beam apparatus, such as the high power microwave source devices. The field emission current density depends on cathode material and electric field at the cathode surface, while the space charge limited current density is a function of applied voltage and diode gap distance. To investigate the influence of the diode gap distance on space charge effect in field emission, in the paper we build a model of a planar vacuum diode operating with a field emission cathode. The time evolutions of the electric field at the cathode surface with various diode gap distance and applied voltage are studied using the particle-in-cell method, and the steady value of the electric field at the cathode surface is obtained. The electric field at the cathode surface first oscillates and finally reaches a steady state. At a given applied electric field, the longer the diode gap distance, the higher the absolute value of the electric field at the cathode surface is, and it takes more time to reach the steady state for longer diode gap distance; the distribution of the electric field in the diode gap region is steeper for shorter diode gap distance after the electric field at the cathode surface has reached a steady state.
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Keywords:
- diode /
- field emission /
- space charge effects /
- gap distance
[1] Han M, Zou X B, Zhang G X 2010 Fundamentals of Pulsed Power Technology (Beijing: Tsinghua University Press) p124-146 (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124-146页]
[2] 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) pp277-312 (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277—312页]
[3] Mesyats G A 1998 Explosive Electrons Emission (Ekaterinburg: URO-Press) pp1-49
[4] Li F, Xiao L, Liu P K, Yi H X, Wan X S 2011 Acta Phys. Sin. 60 097901 (in Chinese) [李飞, 肖刘, 刘濮鲲, 易红霞, 万晓声 2011 物理学报 60 097901]
[5] Fowler R H, Nordheim L 1928 Proc. R. Soc. London, Ser. A 119 173
[6] Child C D 1911 Phys. Rev. 32 492
[7] Langmuir I 1913 Phys. Rev. 2 450
[8] Barbour J P, Dolan W W, Trolan J K, Martin E E, Dyke W P 1953 Phys. Rev. 92 45
[9] Anderson W A 1993 J. Vac. Sci. Technol. B 11 383
[10] Feng Y 2007 Ph. D. Dissertation (Berkeley: University of California)]
[11] Jensen K L 2009 J. Appl. Phys. 107 014905
[12] Rokhlenko A, Jensen K L, Lebowitz J L 2010 J. Appl. Phys. 107 014904
[13] Wang X X, Liao X H, Luo J R, Zhao Q L 2008 Acta Phys. Sin. 57 1924 (in Chinese) [王小霞, 廖显恒, 罗积润, 赵青兰 2008 物理学报 57 1924]
[14] Liu J, Shu T, Li Z Q 2010 Acta Phys. Sin. 59 2622 (in Chinese) [刘静, 舒挺, 李志强 2010 物理学报 59 2622]
[15] Jonge N D, Allioux M, Doytcheva M, Kaiser M, Teo K B K, Lacerda R G, Milne W I 2004 Appl. Phys. Lett. 85 1607
[16] Birdsall C K 1991 IEEE Trans. Plasma Sci. 19 65
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[1] Han M, Zou X B, Zhang G X 2010 Fundamentals of Pulsed Power Technology (Beijing: Tsinghua University Press) p124-146 (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124-146页]
[2] 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) pp277-312 (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277—312页]
[3] Mesyats G A 1998 Explosive Electrons Emission (Ekaterinburg: URO-Press) pp1-49
[4] Li F, Xiao L, Liu P K, Yi H X, Wan X S 2011 Acta Phys. Sin. 60 097901 (in Chinese) [李飞, 肖刘, 刘濮鲲, 易红霞, 万晓声 2011 物理学报 60 097901]
[5] Fowler R H, Nordheim L 1928 Proc. R. Soc. London, Ser. A 119 173
[6] Child C D 1911 Phys. Rev. 32 492
[7] Langmuir I 1913 Phys. Rev. 2 450
[8] Barbour J P, Dolan W W, Trolan J K, Martin E E, Dyke W P 1953 Phys. Rev. 92 45
[9] Anderson W A 1993 J. Vac. Sci. Technol. B 11 383
[10] Feng Y 2007 Ph. D. Dissertation (Berkeley: University of California)]
[11] Jensen K L 2009 J. Appl. Phys. 107 014905
[12] Rokhlenko A, Jensen K L, Lebowitz J L 2010 J. Appl. Phys. 107 014904
[13] Wang X X, Liao X H, Luo J R, Zhao Q L 2008 Acta Phys. Sin. 57 1924 (in Chinese) [王小霞, 廖显恒, 罗积润, 赵青兰 2008 物理学报 57 1924]
[14] Liu J, Shu T, Li Z Q 2010 Acta Phys. Sin. 59 2622 (in Chinese) [刘静, 舒挺, 李志强 2010 物理学报 59 2622]
[15] Jonge N D, Allioux M, Doytcheva M, Kaiser M, Teo K B K, Lacerda R G, Milne W I 2004 Appl. Phys. Lett. 85 1607
[16] Birdsall C K 1991 IEEE Trans. Plasma Sci. 19 65
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