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The effects of the reflection of electrons and negative ions in magnetized electronegative and collisional plasma sheath on the Bohm criterion and the sheath structure are numerically investigated. The Bohm criterion expression of the sheath with considering the reflection of electrons and negative ions is derived theoretically. The lower limit of ion Mach number versus parameters and the distribution curve of charged particle density in sheath are obtained by numerical simulation when Boltzmannian model and reflection model are applied to electrons and negative ions. The results show that the upper limit of ion Mach number is identical to that of Boltzmannian model, but their lower limit expressions are different. The lower limit of ion Mach number in the reflection model is also related to the wall potential, and with the increase of the wall potential, ion Mach number first increases and then remains unchanged after reaching the same value as that from Boltzmannian model, and the speeds of their reaching the maximum values are different due to the difference in sheath edge negative ion concentration and temperature. In both Boltzmannian and the reflection model, the lower limit of the ion Mach number decreases with the concentration of the negative ion at the sheath edge increasing and the negative ion temperature decreasing, but the maximum value is smaller in the reflection model. The lower limit of ion Mach number for each of the two models increases with sheath edge electric field increasing, but increases faster and the final value is larger in Boltzmannian model. The lower limit of ion Mach number for each of the two models decreases with the increase of collision parameter or magnetic field angle, but decreases faster in Boltzmannian model with the increase of collision parameter or magnetic field angle. The lower limits of ion Mach number in the two models tend to be the same with the increase of magnetic field angle. When the wall potential is small, the reflection of electrons and negative ions has a great influence on the sheath structure. When the wall potential is large, the reflection of electrons and negative ions have little effect on the density distribution of charged particles in the sheath.
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Keywords:
- reflection of electrons and negative ions /
- magnetized electronegative sheath /
- Bohm criterion /
- sheath structure
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图 1 电负性等离子体磁鞘模型示意图
Figure 1. Geometry of the electronegative magnetized plasma sheath model.
图 2 负离子浓度和温度对离子马赫数下限的影响(
$\nu = 0.1$ ,$B = 0.1 \;{\rm T}$ ,$\theta = {30^ \circ }$ ,${E_0} = 0.05$ ,${\eta _{\rm{w}}} = 0.3$ ) (a)玻尔兹曼模型; (b)反射模型Figure 2. The effects of negative ions concentration and temperature on the lower limit of ion Mach number (
$\nu = 0.1$ ,$B = 0.1 \;{\rm T}$ ,$\theta = {30^ \circ }$ ,${E_0} = 0.05$ ,${\eta _{\rm{w}}} = 0.3$ ): (a) Boltzmannian model; (b) reflection model.
图 3 基板电势对离子马赫数下限的影响 (a)整体; (b)局部 (
$\nu = 0.1$ ,$ B = 0.1 \;{\rm T}$ ,$\theta = {30^ \circ }$ ,${E_0} = 0.05$ )Figure 3. The effect of wall potential on the lower limit of ion Mach number: (a) Whole; (b) part (
$\nu = 0.1$ ,$B = 0.1 \;{\rm T}$ ,$\theta = {30^ \circ }$ ,${E_0} = 0.05$ ).
图 4 鞘边电场对离子马赫数下限的影响(
$\nu = 0.1$ ,$B = 0.1 \;{\rm T}$ ,$\theta = {30^ \circ }$ ,$\alpha = 0.2$ ,$\sigma = 50$ ,${\eta _{\rm{w}}} = 0.3$ )Figure 4. The effect of the sheath edge electric field on the lower limit of ion Mach number (
$\nu = 0.1$ ,$B = 0.1 \;{\rm T}$ ,$\theta = {30^ \circ }$ ,$\alpha = 0.2$ ,$\sigma = 50$ ,${\eta _{\rm{w}}} = 0.3$ ).
图 5 碰撞参数对离子马赫数下限的影响(
${E_0} = 0.05$ ,$B = 0.1 \;{\rm T}$ ,$\theta = {30^ \circ }$ ,$\alpha = 0.2$ ,$\sigma = 50$ ,${\eta _{\rm{w}}} = 0.3$ )Figure 5. The effect of collision parameter on the lower limit of ion Mach number (
${E_0} = 0.05$ ,$B = 0.1 \;{\rm T}$ ,$\theta = {30^ \circ }$ ,$\alpha = 0.2$ ,$\sigma = 50$ ,${\eta _{\rm{w}}} = 0.3$ ).
图 6 磁场角度对离子马赫数下限的影响(
${E_0} = 0.05$ ,$B = 0.1\;{\rm{ T}}$ ,$\nu = 0.1$ ,$\alpha = 0.2$ ,$\sigma = 50$ ,${\eta _{\rm{w}}} = 0.3$ )Figure 6. The effect of magnetic field angle on the lower limit of ion Mach number (
${E_0} = 0.05$ ,$B = 0.1\;{\rm{ T}}$ ,$\nu = 0.1$ ,$\alpha = 0.2$ ,$\sigma = 50$ ,${\eta _{\rm{w}}} = 0.3$ ).
图 7 鞘层中带电粒子密度分布(
${\eta _{\rm{w}}} = 0.7$ )Figure 7. The normalized charged particle density (
${\eta _{\rm{w}}} = 0.7$ ).
图 8 鞘层中带电粒子密度分布(
${\eta _{\rm{w}}} = 10$ )Figure 8. The normalized charged particle density (
${\eta _{\rm{w}}} = 10$ ). -
[1] Yamada H, Yoshida Z 1992 J. Plasma Phys. 48 229
Google Scholar
[2] Femandez Palop J I, Ballesteros J, Colomer V, Hemandez M A, Dengra A 1995 J. Appl. Phys. 77 2937
Google Scholar
[3] Femandez Palop J I, Colomer V, Ballesteros J, Hemandez M A, Dengra A 1996 Surf. Coat. Technol. 84 341
Google Scholar
[4] Amemiya H, Annaratone B M, Allen J E 1998 J. Plasma. Phys. 60 81
Google Scholar
[5] Ming L, Michael A V, Steven K D, Brett M J 2000 IEEE Trans. Plasma Sci. 28 248
Google Scholar
[6] WANG Z X, Liu J Y, Zou X, Liu Y, Wang X G 2003 Chin. Phys. Lett. 20 1537
Google Scholar
[7] Yasserian K, Aslaninejad M, Ghoranneviss M 2009 Phys. Plasmas 16 023504
Google Scholar
[8] Hatami M M, Shokri B, Niknam A R 2008 Phys. Plasmas 15 123501
Google Scholar
[9] Gong Y, Duan P, Zhang J H, Zou X, Liu J Y, Liu Y 2010 Chin. J. Comput. Phys. 27 883
[10] Liu J Y, Wang Z X, Wang X G 2003 Phys. Plasmas 10 3032
Google Scholar
[11] Ghomi H, Khoramabadi M, Shukla P K, Ghorannevis M 2010 J. Appl. Phys. 108 063302
Google Scholar
[12] Ghomi H, Khoramabadi M 2010 J. Plasma. Phys. 76 247
Google Scholar
[13] Zou X, Liu H P, Qiu M H, Sun X H 2011 Chin. Phys. Lett. 28 125201
Google Scholar
[14] Ghomi H Khoramabadi M 2011 J Fusion Energ 30 481
Google Scholar
[15] 刘惠平, 邹秀, 邹滨雁, 邱明辉 2012 61 035201
Google Scholar
Liu H P, Zou X, Zou B Y, Qiu M H 2012 Acta Phys. Sin. 61 035201
Google Scholar
[16] 邱明辉, 刘惠平, 邹秀 2012 61 155204
Google Scholar
Qiu M H, Liu H P, Zou X 2012 Acta Phys. Sin. 61 155204
Google Scholar
[17] Hatami M M, Shokri B 2013 Phys. Plasmas 20 033506
Google Scholar
[18] Li J J, Ma J X, Wei Z A 2013 Phys. Plasmas 20 063503
Google Scholar
[19] Yasserian K, Aslaninejad M, Borghei M, Eshghabadi M 2010 J. Theor. Appl. Phys. 4 26
[20] Yasserian K, Aslaninejad M 2012 Phys. Plasmas 19 073507
Google Scholar
[21] Shaw A K, Kar S, Goswami K S 2012 Phys. Plasmas 19 102108
Google Scholar
[22] Moulick R, Mahanta M K, Goswami K S 2013 Phys. Plasmas 20 094501
Google Scholar
[23] 刘惠平, 邹秀, 邹滨雁, 邱明辉 2016 65 245201
Google Scholar
Liu H P, Zou X, Zou B Y, Qiu M H 2016 Acta Phys. Sin. 65 245201
Google Scholar
[24] Sobolewski M A, Wang Y C, Goyette A 2017 J. Appl. Phys. 122 053302
Google Scholar
[25] Regodon G F, Femandez-Palop J I, Tejero-del-Caz A, Diaz-Cabrera J M, Carmona-Cabezas R, Ballesteros J 2018 Plasma Sources Sci. Technol. 2018 27
[26] Oudini N, Sirse N, Taccogna F, Ellingboe A R, Bendib A 2018 Phys. Plasmas 25 053510
Google Scholar
[27] Sternberg N, Poggie J 2004 IEEE Trans. Plasma Sci. 32 2217
Google Scholar
[28] Tskhakaya D D, Shukla P K, Eliasson B, Kuhn S 2005 Phys. Plasmas 12 103503
Google Scholar
[29] Pandey B P, Samarian A, Vladimirov S V 2007 Phys. Plasmas 14 093703
Google Scholar
[30] Zimmermann T M G, Coppins M, Allen J E 2009 Phys. Plasmas 16 043501
Google Scholar
[31] Zimmermann T M G, Coppins M, Allen J E 2010 Phys. Plasmas 17 022301
Google Scholar
[32] Krasheninnikova N S, Tang X, Roytershteyn V S 2010 Phys. Plasmas 17 057103
Google Scholar
[33] Sheehan J P, Hershkowitz N, Kaganovich I D, Wang H, Raitses Y, Barnat E V, Weatherford B R, Sydorenko D 2013 Phys. Rev. Lett. 111 075002
Google Scholar
[34] Sheehan J P, Kaganovich I D, Wang H, Sydorenko D, Raitses Y, Hershkowitz N 2014 Phys. Plasmas 21 063502
Google Scholar
[35] Wang T T, Ma J X, Wei Z A 2015 Phys. Plasmas 22 093505
Google Scholar
[36] Liu J Y, Wang F, Sun J Z 2011 Phys. Plasmas 18 013506
Google Scholar
[37] 邹秀, 邹滨雁, 籍延坤 2010 59 1902
Google Scholar
Zou X, Zou B Y, Ji Y K 2010 Acta Phys. Sin. 59 1902
Google Scholar
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