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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.
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Keywords:
- secondary electron emission /
- nonextensive /
- plasma /
- sheath
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图 2 二次电子发射系数不同时临界马赫数随q的变化(
$\gamma = 0$ ,$\gamma = 0.4$ 和$\gamma = 0.8$ )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
${\gamma _{\rm{c}}}$ 随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 102003
Google Scholar
[2] Gupta D 2011 Int. J. Adv. Technol. 2 471
[3] Gunn J P 2012 Plasma Phys. Controlled Fusion 54 085007
Google Scholar
[4] Sheehan J P, Raitses Y, Hershkowitz N, Kaganovich I, Fisch N J 2011 Phys. Plasmas 18 073501
Google 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 075002
Google 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 076027
Google Scholar
[7] Ou J, Lin B B, Zhao X Y 2017 Phys. Plasmas 24 012510
Google Scholar
[8] Ou J, Zhao X Y, Lin B B 2018 Chin. Phys. B 27 025204
Google Scholar
[9] Raitses Y, Smirnov A, Staack D, Fisch N J 2006 Phys. Plasmas 13 014502
Google Scholar
[10] Zhang F K, Ding Y J, Qing S W, Wu X D 2011 Chin. Phys. B 20 125201
Google Scholar
[11] 段萍, 覃海娟, 周新维, 曹安宁, 刘金远, 卿少伟 2014 63 085204
Google Scholar
Duan P, Qin H J, Zhou X W, Cao A N, Liu J Y, Qing S W 2014 Acta Phys. Sin. 63 085204
Google Scholar
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Google Scholar
[13] Hobbs G D, Wesson J A 1967 Plasma Phys. 9 85
Google Scholar
[14] Taccogna F, Longo S, Capitelli M 2004 Phys. Plasmas 11 1220
Google 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 4340
Google Scholar
[18] Sydorenko D, Kaganovich I, Raitses Y, Smolyakov A 2009 Phys. Rev. Lett. 103 145004
Google 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 60 045205
Google Scholar
Zhao X Y, Liu J Y, Duan P, Ni Z X 2011 Acta Phys. Sin. 60 045205
Google Scholar
[21] Yu D R, Qing S W, Yan G J, Duan P 2011 Chin. Phys. B 20 065204
Google Scholar
[22] Li W, Ma J X, Li J J, Zheng Y B, Tan M S 2012 Phys. Plasmas 19 030704
Google Scholar
[23] Langendorf S, Walker M 2015 Phys. Plasmas 22 033515
Google Scholar
[24] Ou J, Zhao X Y 2017 Contrib. Plasma Phys. 57 50
Google Scholar
[25] Zhao L L, Liu Y, Samir T 2018 Chin. Phys. B 27 025201
Google Scholar
[26] Moslem W M 2006 Chaos, Soliton. Fract. 28 994
Google Scholar
[27] Asaduzzaman M, Mamun A A 2012 Phys. Rev. E 86 016409
Google 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. 78 875
Google Scholar
[30] Cáceres M O 1999 Braz. J. Phys. 29 125
Google Scholar
[31] Tsallis C 1988 J. Stat. Phys. 52 479
Google Scholar
[32] Tribeche M, Djebarni L, Amour R 2010 Phys. Plasmas 17 042114
Google Scholar
[33] Gougam L A, Tribeche M 2011 Astrophysics Space Sci. 331 181
Google Scholar
[34] Liu Y, Liu S Q, Zhou L 2013 Phys. Plasmas 20 043702
Google Scholar
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Google Scholar
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Google Scholar
[37] Driouch I, Chatei H 2017 Eur. Phys. J. D 71 9
Google Scholar
[38] Arghand-Hesar A, Esfandyari-Kalejahi A, Akbari-Moghanjoughi M 2017 Phys. Plasmas 24 063504
Google Scholar
[39] Borgohain D R, Saharia K 2018 Phys. Plasmas 25 032122
Google Scholar
[40] Riemann K U 1991 J. Phys. D: Appl. Phys. 24 493
Google Scholar
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