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High current electron beam emitting from a thermal field emission cathode has an intense space charge effect. In order to investigate the mechanism for the influence of space charge effect on Nottingham effect in thermal field emission, the results of Nottingham effect with and without space charge effect at different work functions and various applied electric fields are obtained numerically on the basis of the theoretical analyses of space charge effect and Nottingham effect. The results demonstrate that the space charge effect has a significant influence on the steady electric field at the cathode surface, and thus the effect of space charge on Nottingham effect is not ignorable. When the work function is in a range of 3.0–4.52 eV and the applied electric field is in a scope of 3×109–9×109 V/m, the average energy delivered per electron in thermal field emission is in a span of 0–2.5 eV larger than that in the case without space charge effect, and the higher the cathode temperature or applied electric field, the larger the difference between them is. The average energy delivered by per electron emitting from cathode is observed to nonlinearly decrease with the increasing of applied electric field when the space charge effect is included. When the cathode temperature is high, the cooling effect in Nottingham effect can be intensified as the gap distance of diode increases.
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Keywords:
- thermal field emission /
- Nottingham effect /
- space charge effect /
- electric field at the cathode surface
[1] Jensen K L, Cahay M 2006 Appl. Phys. Lett. 88 154105
[2] Liu X S 2007 Intense Particle Beams and Its Applications (Beijing: National Defense Industry Press) p139 (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139页]
[3] Peng K, Liu D G 2012 Acta Phys. Sin. 61 121301 (in Chinese) [彭凯, 刘大刚 2012 61 121301]
[4] Miller R B (translated by Liu X S, Zhang L Z, Wu Y B, Lu J P, Zhou P Z) 1982 An Introduction to the Physics of Entense Charged Particle Beams (New York: Plenum Press) p39 [Miller R B 著 (刘锡三, 张兰芝, 吴衍斌, 鲁敬平, 周丕璋 译) 1990 强流带电粒子束物理学导论 (北京: 原子能出版社) 第39页]
[5] Charbonnier F M, Strayer R W, Swanson L W, Martin E E 1964 Phys. Rev. Lett. 13 397
[6] Bergeret H 1985 Phys. Rev. B 31 149
[7] Paulini J, Kiein T, Simon G 1993 J. Phys. D: Appl. Phys. 26 1310
[8] Rossetti P, Paganucci F, Andrenucci M 2002 IEEE Trans. Plasma Sci. 30 1561
[9] Zuo Y H, Wang J G, Fan R Y 2012 Acta Phys. Sin. 61 215202 (in Chinese) [左应红, 王建国, 范如玉 2012 61 215202]
[10] L J Q 2010 Chin. Phys. B 19 032901
[11] Zuo Y H, Wang J G, Zhu J H, Niu S L, Fan R Y 2012 Acta Phys. Sin. 61 177901 (in Chinese) [左应红, 王建国, 朱金辉, 牛胜利, 范如玉 2012 61 177901]
[12] Jensen K L, Lebowitz J, Lau Y Y, Luginsland J 2012 J. Appl. Phys. 111 054917
[13] Murphy E L, Good R H 1956 Phys. Rev. 102 1464
[14] Coulombe S, Meunier J L 1997 J. Phys. D: Appl. Phys. 30 776
[15] He X, Scharer J, Booske J, Sengele S 2008 J. Vac. Sci. Technol. B 26 770
[16] Petrin A B 2009 J. Exp. Theor. Phys. 109 314
[17] Miller S C, Good R H 1953 Phys. Rev. 91 174
[18] Liu G Z, Yang Z F 2010 Chin. Phys. B 19 075207
[19] Sun S, Ang L K 2012 Phys. Plasmas 19 033107
[20] Brattain W H, Becker J A 1933 Phys. Rev. 43 428
[21] Anders A 2008 Cathodic Arcs: from Fractal Spots to Energetic Condensation (New York: Springer Science) p80
[22] Ru G P, Yu R, Jiang Y L, Ruan G 2010 Chin. Phys. B 19 097304
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[1] Jensen K L, Cahay M 2006 Appl. Phys. Lett. 88 154105
[2] Liu X S 2007 Intense Particle Beams and Its Applications (Beijing: National Defense Industry Press) p139 (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139页]
[3] Peng K, Liu D G 2012 Acta Phys. Sin. 61 121301 (in Chinese) [彭凯, 刘大刚 2012 61 121301]
[4] Miller R B (translated by Liu X S, Zhang L Z, Wu Y B, Lu J P, Zhou P Z) 1982 An Introduction to the Physics of Entense Charged Particle Beams (New York: Plenum Press) p39 [Miller R B 著 (刘锡三, 张兰芝, 吴衍斌, 鲁敬平, 周丕璋 译) 1990 强流带电粒子束物理学导论 (北京: 原子能出版社) 第39页]
[5] Charbonnier F M, Strayer R W, Swanson L W, Martin E E 1964 Phys. Rev. Lett. 13 397
[6] Bergeret H 1985 Phys. Rev. B 31 149
[7] Paulini J, Kiein T, Simon G 1993 J. Phys. D: Appl. Phys. 26 1310
[8] Rossetti P, Paganucci F, Andrenucci M 2002 IEEE Trans. Plasma Sci. 30 1561
[9] Zuo Y H, Wang J G, Fan R Y 2012 Acta Phys. Sin. 61 215202 (in Chinese) [左应红, 王建国, 范如玉 2012 61 215202]
[10] L J Q 2010 Chin. Phys. B 19 032901
[11] Zuo Y H, Wang J G, Zhu J H, Niu S L, Fan R Y 2012 Acta Phys. Sin. 61 177901 (in Chinese) [左应红, 王建国, 朱金辉, 牛胜利, 范如玉 2012 61 177901]
[12] Jensen K L, Lebowitz J, Lau Y Y, Luginsland J 2012 J. Appl. Phys. 111 054917
[13] Murphy E L, Good R H 1956 Phys. Rev. 102 1464
[14] Coulombe S, Meunier J L 1997 J. Phys. D: Appl. Phys. 30 776
[15] He X, Scharer J, Booske J, Sengele S 2008 J. Vac. Sci. Technol. B 26 770
[16] Petrin A B 2009 J. Exp. Theor. Phys. 109 314
[17] Miller S C, Good R H 1953 Phys. Rev. 91 174
[18] Liu G Z, Yang Z F 2010 Chin. Phys. B 19 075207
[19] Sun S, Ang L K 2012 Phys. Plasmas 19 033107
[20] Brattain W H, Becker J A 1933 Phys. Rev. 43 428
[21] Anders A 2008 Cathodic Arcs: from Fractal Spots to Energetic Condensation (New York: Springer Science) p80
[22] Ru G P, Yu R, Jiang Y L, Ruan G 2010 Chin. Phys. B 19 097304
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