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电子的非广延分布对等离子体鞘层中二次电子发射的影响

赵晓云 张丙开 王春晓 唐义甲

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电子的非广延分布对等离子体鞘层中二次电子发射的影响

赵晓云, 张丙开, 王春晓, 唐义甲

Effects of q-nonextensive distribution of electrons on secondary electron emission in plasma sheath

Zhao Xiao-Yun, Zhang Bing-Kai, Wang Chun-Xiao, Tang Yi-Jia
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  • 采用一维流体模型研究了非广延分布电子对等离子体鞘层中二次电子发射的影响. 通过数值模拟, 研究了非广延分布电子对考虑二次电子发射的等离子体鞘层玻姆判据、器壁电势、器壁二次电子临界发射系数以及等离子体鞘层中二次电子密度分布的影响. 研究结果发现, 当电子分布偏离麦克斯韦分布(q = 1, 广延分布)时, 非广延参量q的改变对器壁二次电子发射有着重要的影响. 不论电子分布处于超广延(q < 1), 还是处于亚广延状态(q > 1), 随着非广延参量q的增加, 都会出现鞘边临界马赫数跟着减小, 同时对于随着二次电子发射系数的增加, 临界马赫数跟着增加. 器壁电势随着参量q的增加而增加. 器壁二次电子临界发射系数则随着非广延参量的增加而减小, 并且等离子体中所含的离子种类质量数越大, 非广延参量的变化对器壁二次电子临界发射系数的值影响越小. 此外, 随着非广延参量的增加, 鞘层厚度减小, 鞘层中二次电子数密度增加. 通过对数值模拟结果分析, 发现电子分布处于超广延分布状态对等离子体鞘层中二次电子发射特性的影响要比电子处于亚广延分布状态要更明显.
    A one-dimensional fluid model is used to investigate the characteristics of secondary electron emitted by the interaction between electrons and the wall in plasma sheath with nonextensive electrons. The study focuses on the effects of electron nonextensive parameter on Bohm criterion, the wall potential, the critical emission coefficient of secondary electrons and the density of seconday electrons in plasma sheath through numerical simulation. Some conclusions are obtained. It is shown that secondary electron is significantly affected by electron nonextensive parameter. Whether the electron distribution is superextensive or subextensive, the critical Mach number at the sheath edge increases with the secondary electron emission coefficient increasing, but decreases with q-parameter increasing. The increase of q-parameter can cause the wall potential to increase and the critical emission coefficient of secondary electron at the wall to decrease. And for different types of plasmas, the effects of nonextensive parameter on the critical emission coefficient of secondary electron are different. The larger the mass number of ion in plasma, the smaller the influence of nonextensive parameter on the critical secondary electron emission coefficient will be. In addition, the increase of nonextensive parameter can result in the decrease of the sheath thickness and the increase of the number density of secondary electrons. It is found that the superextensive electron distribution has greater influence on the characteristics of secondary electron emission in plasma sheath than the subextensive electron distribution.
      通信作者: 赵晓云, fuyangzxy77@163.com
    • 基金项目: 国家自然科学联合基金(批准号: U1831124)、安徽省自然科学基金(批准号: 1908085MA28)、安徽省高校自然科学研究重点项目(批准号: KJ2018A0341)和阜阳师范学院后续研究项目(批准号: 2018HXXM29)资助的课题.
      Corresponding author: Zhao Xiao-Yun, fuyangzxy77@163.com
    • Funds: Project supported by the Joint Funds of the National Natural Science Foundation of China (Grant No. U1831124), the Natural Science Foundation of Anhui Province, China (Grant No. 1908085MA28), the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. KJ2018A0341), and the Follow-up Research Program of Fuyang Normal University, China (Grant No. 2018HXXM29).
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    Lagoyannis A, Tsavalas P, Mergia K, Provatas G, Triantou K, Tsompopoulou E, Rubel M, Petersson P, Widdowson A, Harissopulos S, Mertzimekis T J, the JET contributors 2017 Nucl. Fusion 57 076027Google Scholar

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    Duan P, Qin H J, Zhou X W, Cao A N, Liu J Y, Qing S W 2014 Acta Phys. Sin. 63 085204Google Scholar

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    吕广宏, 罗广南, 李建刚 2010 中国材料进展 7 42

    Lü G H, Luo G N, Li J G 2010 Mater. China 7 42

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    赵晓云, 刘金远, 段萍, 倪致祥 2011 物理学报 60 045205Google Scholar

    Zhao X Y, Liu J Y, Duan P, Ni Z X 2011 Acta Phys. Sin. 60 045205Google Scholar

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    Yu D R, Qing S W, Yan G J, Duan P 2011 Chin. Phys. B 20 065204Google Scholar

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    Li W, Ma J X, Li J J, Zheng Y B, Tan M S 2012 Phys. Plasmas 19 030704Google Scholar

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    Langendorf S, Walker M 2015 Phys. Plasmas 22 033515Google Scholar

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    Ou J, Zhao X Y 2017 Contrib. Plasma Phys. 57 50Google Scholar

    [25]

    Zhao L L, Liu Y, Samir T 2018 Chin. Phys. B 27 025201Google Scholar

    [26]

    Moslem W M 2006 Chaos, Soliton. Fract. 28 994Google Scholar

    [27]

    Asaduzzaman M, Mamun A A 2012 Phys. Rev. E 86 016409Google Scholar

    [28]

    Saslaw W C, Arp H 1986 Phys. Today 39 61

    [29]

    Huang X P, Anderegg F, Hollmann E M, Driscoll C F, O'neil T M 1997 Phys. Rev. Lett. 78 875Google Scholar

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    Cáceres M O 1999 Braz. J. Phys. 29 125Google Scholar

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    Tsallis C 1988 J. Stat. Phys. 52 479Google Scholar

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    Tribeche M, Djebarni L, Amour R 2010 Phys. Plasmas 17 042114Google Scholar

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    Gougam L A, Tribeche M 2011 Astrophysics Space Sci. 331 181Google Scholar

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    Liu Y, Liu S Q, Zhou L 2013 Phys. Plasmas 20 043702Google Scholar

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    Hatami M M 2015 Phys. Plasmas 22 013508Google Scholar

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    Hatami M M 2015 Phys. Plasmas 22 023506Google Scholar

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    Driouch I, Chatei H 2017 Eur. Phys. J. D 71 9Google Scholar

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    Arghand-Hesar A, Esfandyari-Kalejahi A, Akbari-Moghanjoughi M 2017 Phys. Plasmas 24 063504Google Scholar

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    Borgohain D R, Saharia K 2018 Phys. Plasmas 25 032122Google Scholar

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  • 图 1  等离子体鞘层示意图

    Fig. 1.  Schematic diagram of plasma sheath

    图 2  二次电子发射系数不同时临界马赫数随q的变化($\gamma = 0$, $\gamma = 0.4$$\gamma = 0.8$)

    Fig. 2.  Critical Mach number versus nonextensive parameter q for different values of secondary electron emission coefficients ($\gamma = 0$, $\gamma = 0.4$ and $\gamma = 0.8$).

    图 3  二次电子发射系数不同时器壁电势随参量q的变化 (a) q = 0.5—1.0; (b) q = 1.0—2.0

    Fig. 3.  Wall potential versus nonextensive parameter q for different values of secondary electron emission coefficients ($\gamma = 0$, $\gamma = 0.4$ and $\gamma = 0.8$): (a) q = 0.5−1.0; (b) q = 1.0−2.0.

    图 4  器壁二次电子临界发射系数${\gamma _{\rm{c}}}$q的变化

    Fig. 4.  Critical emission coefficient of secondary electrons versus nonextensive parameter q for different kinds of plasma.

    图 5  参量q对鞘层中二次电子数密度的影响($\gamma = 0.4$)

    Fig. 5.  Normalized density of secondary electrons in plasma sheath versus x for different values of nonextensive parameter q ($\gamma = 0.4$).

    图 6  参量q对不同发射系数下到达鞘边二次电子数密度的影响

    Fig. 6.  Normalized density of secondary electrons at the sheath edge versus nonextensive parameter q for different values of secondary electron emission coefficients ($\gamma = 0$, $\gamma = 0.4$ and $\gamma = 0.8$).

  • [1]

    Hecimovic A, Böke M, Winter J 2014 J. Phys. D: Appl. Phys. 47 102003Google Scholar

    [2]

    Gupta D 2011 Int. J. Adv. Technol. 2 471

    [3]

    Gunn J P 2012 Plasma Phys. Controlled Fusion 54 085007Google Scholar

    [4]

    Sheehan J P, Raitses Y, Hershkowitz N, Kaganovich I, Fisch N J 2011 Phys. Plasmas 18 073501Google Scholar

    [5]

    Sheehan J P, Hershkowitz N, Kaganovich I D, Wang H, Raitses Y, Barnat E V, Weatherford B R 2013 Phys. Rev. Lett. 111 075002Google Scholar

    [6]

    Lagoyannis A, Tsavalas P, Mergia K, Provatas G, Triantou K, Tsompopoulou E, Rubel M, Petersson P, Widdowson A, Harissopulos S, Mertzimekis T J, the JET contributors 2017 Nucl. Fusion 57 076027Google Scholar

    [7]

    Ou J, Lin B B, Zhao X Y 2017 Phys. Plasmas 24 012510Google Scholar

    [8]

    Ou J, Zhao X Y, Lin B B 2018 Chin. Phys. B 27 025204Google Scholar

    [9]

    Raitses Y, Smirnov A, Staack D, Fisch N J 2006 Phys. Plasmas 13 014502Google Scholar

    [10]

    Zhang F K, Ding Y J, Qing S W, Wu X D 2011 Chin. Phys. B 20 125201Google Scholar

    [11]

    段萍, 覃海娟, 周新维, 曹安宁, 刘金远, 卿少伟 2014 物理学报 63 085204Google Scholar

    Duan P, Qin H J, Zhou X W, Cao A N, Liu J Y, Qing S W 2014 Acta Phys. Sin. 63 085204Google Scholar

    [12]

    Croes V, Tavant A, Lucken R, Bourdon A, Charbert P 2018 Phys. Plasmas 25 063522Google Scholar

    [13]

    Hobbs G D, Wesson J A 1967 Plasma Phys. 9 85Google Scholar

    [14]

    Taccogna F, Longo S, Capitelli M 2004 Phys. Plasmas 11 1220Google Scholar

    [15]

    吕广宏, 罗广南, 李建刚 2010 中国材料进展 7 42

    Lü G H, Luo G N, Li J G 2010 Mater. China 7 42

    [16]

    Schwager L A 1993 Phys. Fluids B 5 631

    [17]

    Ahedo E 2002 Phys. Plasmas 9 4340Google Scholar

    [18]

    Sydorenko D, Kaganovich I, Raitses Y, Smolyakov A 2009 Phys. Rev. Lett. 103 145004Google Scholar

    [19]

    Gyergyek T, Kovačič J, Čerček M 2010 Contrib. Plasma Phys. 50 121

    [20]

    赵晓云, 刘金远, 段萍, 倪致祥 2011 物理学报 60 045205Google Scholar

    Zhao X Y, Liu J Y, Duan P, Ni Z X 2011 Acta Phys. Sin. 60 045205Google Scholar

    [21]

    Yu D R, Qing S W, Yan G J, Duan P 2011 Chin. Phys. B 20 065204Google Scholar

    [22]

    Li W, Ma J X, Li J J, Zheng Y B, Tan M S 2012 Phys. Plasmas 19 030704Google Scholar

    [23]

    Langendorf S, Walker M 2015 Phys. Plasmas 22 033515Google Scholar

    [24]

    Ou J, Zhao X Y 2017 Contrib. Plasma Phys. 57 50Google Scholar

    [25]

    Zhao L L, Liu Y, Samir T 2018 Chin. Phys. B 27 025201Google Scholar

    [26]

    Moslem W M 2006 Chaos, Soliton. Fract. 28 994Google Scholar

    [27]

    Asaduzzaman M, Mamun A A 2012 Phys. Rev. E 86 016409Google Scholar

    [28]

    Saslaw W C, Arp H 1986 Phys. Today 39 61

    [29]

    Huang X P, Anderegg F, Hollmann E M, Driscoll C F, O'neil T M 1997 Phys. Rev. Lett. 78 875Google Scholar

    [30]

    Cáceres M O 1999 Braz. J. Phys. 29 125Google Scholar

    [31]

    Tsallis C 1988 J. Stat. Phys. 52 479Google Scholar

    [32]

    Tribeche M, Djebarni L, Amour R 2010 Phys. Plasmas 17 042114Google Scholar

    [33]

    Gougam L A, Tribeche M 2011 Astrophysics Space Sci. 331 181Google Scholar

    [34]

    Liu Y, Liu S Q, Zhou L 2013 Phys. Plasmas 20 043702Google Scholar

    [35]

    Hatami M M 2015 Phys. Plasmas 22 013508Google Scholar

    [36]

    Hatami M M 2015 Phys. Plasmas 22 023506Google Scholar

    [37]

    Driouch I, Chatei H 2017 Eur. Phys. J. D 71 9Google Scholar

    [38]

    Arghand-Hesar A, Esfandyari-Kalejahi A, Akbari-Moghanjoughi M 2017 Phys. Plasmas 24 063504Google Scholar

    [39]

    Borgohain D R, Saharia K 2018 Phys. Plasmas 25 032122Google Scholar

    [40]

    Riemann K U 1991 J. Phys. D: Appl. Phys. 24 493Google Scholar

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  • PDF下载量:  68
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-02-20
  • 修回日期:  2019-06-13
  • 上网日期:  2019-09-01
  • 刊出日期:  2019-09-20

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