外加电场作用下的壁面约束衰亡等离子体中带电粒子非平衡输运特性

汪耀庭; 罗岚月; 李和平; 姜东君; 周明胜

doi:10.7498/aps.71.20221431

摘要

以光致电离等离子体中的带电粒子输运为主要研究背景, 从理论上分析了位于两平行极板间的等离子体在外加直流电场作用下的带电粒子非平衡输运特性, 给出了不同等离子体初始参数分布条件下电子对外加直流电场的瞬态响应特性, 包括瞬态响应过程中的电子损失量和振荡频率的理论表达式, 以及对离子引出通量和引出时间产生电子温度效应的临界电子数密度的表达式. 粒子模拟结果与理论分析结果吻合良好. 在此基础上进行了外加直流电场叠加射频电场作用下的离子引出过程一维粒子模拟. 计算结果表明: 在有射频电场存在的情况下, 离子引出过程存在明显的共振现象, 且在共振频率处离子引出通量显著提高; 在本文所研究的特定工况下, 发生射频共振时的离子引出时间缩短到了单纯采用外加直流电场时的5.8%. 进一步的分析表明, 外加射频电场一方面加热了电子, 提高了离子稀疏波的传播速度; 另一方面则加剧了电子振荡, 增大了电子损失, 抬高了等离子体电势, 从而最终提高了离子引出通量、缩短了离子引出时间.

关键词:

衰亡等离子体 /
带电粒子非平衡输运 /
电子振荡 /
理论分析 /
粒子模拟

Abstract

In this work, non-equilibrium transport processes of the charged particles in a plasma confined between two parallel plates with externally applied electric fields are analyzed with the charged-particle transport of laser-induced plasma as the major research background. The theoretical analyses of the transient responses of the electrons to the externally applied electrostatic fields are conducted under different initial distributions of the plasma parameters including the loss and the oscillation frequency of the electrons in the transient oscillation process, and the critical value of the electron number density for the initial electron temperature effect of the ion transport. The particle-in-cell (PIC) modeling results are consistent well with the theoretical predictions. Based on the preceding results, the PIC simulations of the ion extraction process by imposing a radio-frequency (RF) electric field on the electrostatic field are conducted. The modeling results indicate that there exists an obvious resonance phenomenon in the ion extraction process, in which the ion extraction flux is significantly increased. Under a certain operating condition, the ion extraction time at the RF resonance point is reduced to 5.8% of its original value with only an electrostatic field. Further analysis shows that, on the one hand, the electrons will be heated by the externally applied RF electric field, and thus, the propagation velocity of the ion rarefaction wave will be increased; on the other hand, the electron oscillations will be enhanced, resulting in losing more electrons in the electron oscillation process and a higher plasma potential, which ultimately leads to a higher ion extraction flux and a shorter ion extraction time.

Keywords:

decaying plasma /
non-equilibrium transport of charged particles /
electron oscillation /
theoretical analysis /
particle-in-cell simulation

作者及机构信息

汪耀庭,
罗岚月,
李和平,
姜东君,
周明胜

清华大学工程物理系, 北京　100084

通信作者: 李和平, liheping@tsinghua.edu.cn

基金项目: 国家自然科学基金(批准号: 11775128)资助的课题.

Authors and contacts

Wang Yao-Ting,
Luo Lan-Yue,
Li He-Ping,
Jiang Dong-Jun,
Zhou Ming-Sheng

Department of Engineering Physics, Tsinghua University, Beijing 100084, China

Corresponding author: Li He-Ping, liheping@tsinghua.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11775128).

文章全文 : translate this paragraph

参考文献

[1]	Dhayal M, Forder D, Parry K L, Short R D, Bradley J W 2003 Surf. Coat. Technol. 173-174 872 Google Scholar
[2]	Aleksandrov N L, Anokhin E M, Kindysheva S V, Kirpichnikov A A, Kosarev I N, Nudnova M M, Starikovskaya S M, Starikovskii A Y 2012 Plasma Phys. Rep. 38 179 Google Scholar
[3]	Khrabrov A V, Kaganovich I D, Chen J, Guo H 2020 Phys. Plasmas 27 123512 Google Scholar
[4]	Lieberman M A 1989 J. Appl. Phys. 66 2926 Google Scholar
[5]	Yamada K, Tetsuka T, Deguchi Y 1991 J. Appl. Phys. 69 8064 Google Scholar
[6]	Yamada K, Tetsuka T, Deguchi Y 1991 J. Appl. Phys. 69 6962 Google Scholar
[7]	Ogura K, Arisawa T, Shibata T 1992 Jpn. J. Appl. Phys. 31 1485 Google Scholar
[8]	Yamada K, Tetsuka T 1994 J. Nucl. Sci. Technol. 31 301 Google Scholar
[9]	Nishio R, Yamada K, Suzuki K, Wakabayashi M 1995 J. Nucl. Sci. Technol. 32 180 Google Scholar
[10]	Matsui T, Tsuchida K, Tsuda S, Suzuki K, Shoji T 1996 Phys. Plasmas 3 4367 Google Scholar
[11]	Shibata T, Ogura K 1996 J. Nucl. Sci. Technol. 33 834 Google Scholar
[12]	Matsui T, Tsuchida K, Tsuda S, Suzuki K, Shoji T 1997 J. Nucl. Sci. Technol. 34 923 Google Scholar
[13]	Matsui Tetsuya, Tsuda S, Tsuchida K, Suzuki K, Shoji T 1997 Phys. Plasmas 4 3527 Google Scholar
[14]	Killian T C, Kulin S, Bergeson S D, Orozco S D, Orzel C, Rolston S L 1999 Phys. Rev. Lett. 83 4776 Google Scholar
[15]	Kulin S, Killian T C, Bergeson S D, Rolston S L 2000 Phys. Rev. Lett. 85 318 Google Scholar
[16]	Mazevet S, Collins L A, Kress J D 2002 Phys. Rev. Lett. 88 055001 Google Scholar
[17]	Robicheaux F, Hanson J D 2002 Phys. Rev. Lett. 88 055002 Google Scholar
[18]	Bergeson S D, Spencer R L 2003 Phys. Rev. E 67 026414 Google Scholar
[19]	Robicheaux F, Hanson J D 2003 Phys. Plasmas 10 2217 Google Scholar
[20]	Pohl T, Pattard T, Rost J M 2004 Phys. Rev. Lett. 92 155003 Google Scholar
[21]	Simien C E, Chen Y C, Gupta P, Laha S, Martinez Y N, Mickelson P G, Nagel S B, Killian T C 2004 Phys. Rev. Lett. 92 143001 Google Scholar
[22]	Cummings E A, Daily J E, Durfee D S, Bergeson S D 2005 Phys. Rev. Lett. 95 235001 Google Scholar
[23]	Fletcher R S, Zhang X L, Rolston S L 2006 Phys. Rev. Lett. 96 105003 Google Scholar
[24]	Zhang X L, Fletcher R S, Rolston S L, Guzdar P N, Swisdak M 2008 Phys. Rev. Lett. 100 235002 Google Scholar
[25]	Gorman G M, Warrens M K, Bradshaw S J, Killian T C 2021 Phys. Rev. Lett. 126 085002 Google Scholar
[26]	Sprenkle R T, Bergeson S D, Silvestri L G, Murillo M S 2022 Phys. Rev. E 105 045201 Google Scholar
[27]	Li H P, Ostrikov K, Sun W T 2018 Phys. Rep. 770–772 1
[28]	李和平, 王鹏, 王鑫, 尤伟, 柴俊杰, 李增耀 2015 高电压技术 41 2825 Google Scholar Li H P, Wang P, Wang X, You W, Chai J J, Li Z Y 2015 High Voltage Eng. 41 2825 Google Scholar
[29]	李和平, 王鑫, 柴俊杰, 李占贤 2016 高电压技术 42 706 Google Scholar Li H P, Wang X, Chai J J, Li Z X 2016 High Voltage Eng. 42 706 Google Scholar
[30]	Wang Y T, Chen J, Li H P, Jiang D J, Zhou M S 2021 Jpn. J. Appl. Phys. 60 SAAB05 Google Scholar
[31]	Chen J, Khrabrov A V, Wang Y T, Li J, Li H P, Jiang D J, Zhou M S 2020 Plasma Sources Sci. Technol. 29 025010 Google Scholar
[32]	Chen J, Fu T Z, Guo H, Li H P, Jiang D J, Zhou M S 2019 Plasma Sci. Technol. 21 045402 Google Scholar
[33]	陈坚, 李静, 李和平, 姜东君, 周明胜 2020 高电压技术 46 729 Google Scholar Chen J, Li J, Li H P, Jiang D J, Zhou M S 2020 High Voltage Eng. 46 729 Google Scholar
[34]	Calder A C, Laframboise J G 1990 Phys. Fluids B 2 655 Google Scholar
[35]	Calder A C, Hulbert G W, Laframboise J G 1993 Phys. Fluids B 5 674 Google Scholar
[36]	Sydorenko D 2006 Ph. D. Dissertation (Saskatchewan: University of Saskatchewan)
[37]	姜巍 2010 博士学位论文 (大连: 大连理工大学) Jiang W 2010 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese)
[38]	Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (Hoboken: Wiley-Interscience) pp389–394
[39]	熊家贵, 王德武 2000 物理学报 49 2420 Google Scholar Xiong J G, Wang D W 2000 Acta Phys. Sin. 49 2420 Google Scholar
[40]	Lu X Y, Yuan C, Zhang X Z, Zhang Z Z 2020 Chin. Phys. B 29 045201 Google Scholar
[41]	卢肖勇, 袁程, 高阳 2021 物理学报 70 145201 Google Scholar Lu X Y, Yuan C, Gao Y 2021 Acta Phys. Sin. 70 145201 Google Scholar

施引文献

图 1 不同应用中的衰亡等离子体体系示意图　(a) 余辉等离子体; (b) 等离子体浸没离子注入; (c) 光致电离等离子体离子引出; (d) 超冷等离子体

Fig. 1. Schematics of decaying plasmas in various applications: (a) Afterglow plasma; (b) plasma immersion ion implantation; (c) ion extraction in laser-induced plasmas; (d) ultra-cold plasmas.

下载: 全尺寸图片幻灯片

图 2 壁面约束条件下的衰亡等离子体模式体系示意图

Fig. 2. Schematic of a model system for bounded decaying plasmas.

下载: 全尺寸图片幻灯片

图 3 初始电子振荡不同阶段的电子数密度分区示意图　(a) 阶段I; (b) 阶段II

Fig. 3. Schematics of the spatial distributions of the electron number density at different stages during the initial electron oscillations: (a) Stage I; (b) Stage II.

下载: 全尺寸图片幻灯片

图 4 不同等离子体-极板间隙下的电子初始振荡最大距离变化曲线

Fig. 4. Variations of l_max under different values of d.

下载: 全尺寸图片幻灯片

图 5 不同等离子体-极板间隙、不同初始电子温度下离子引出时间随初始等离子体密度的变化规律　(a) d = 1 mm; (b) d = 5 mm

Fig. 5. Variations of t_ext with n₀ at different values of T_e and d: (a) d = 1 mm; (b) d = 5 mm.

下载: 全尺寸图片幻灯片

图 6 电子振荡过程中电子数密度空间分布示意图

Fig. 6. Schematic of the electron number density distribution during the electron oscillation process.

下载: 全尺寸图片幻灯片

图 7 电子振荡过程的等效电路模型

Fig. 7. Equivalent circuit model for the electron oscillation process.

下载: 全尺寸图片幻灯片

图 8 d = 1 mm时极板附近的电场振荡曲线(a)及其频谱图(b)

Fig. 8. Profiles of the electric fields in the vicinity of the electrodes (a), and their frequency spectra (b) with d = 1 mm.

下载: 全尺寸图片幻灯片

图 9 d = 5 mm时极板附近的电场振荡曲线(a)及其频谱图(b)

Fig. 9. Profiles of the electric fields in the vicinity of the electrodes (a), and their frequency spectra (b) with d = 5 mm.

下载: 全尺寸图片幻灯片

图 10 电子振荡频率的理论值和模拟值的对比

Fig. 10. Comparisons of the theoretical and modeling results of the electron oscillation frequency.

下载: 全尺寸图片幻灯片

图 11 不同射频电压幅值下离子引出时间随外加射频电场频率的变化曲线

Fig. 11. Variations of t_ext with the values of f_rf under different amplitudes of the externally applied radio-frequency electric field.

下载: 全尺寸图片幻灯片

图 12 不同射频频率(1—4列分别对应0, 200, 477和800 MHz)下等离子体衰亡过程中电势(a)、离子数密度(b)、电子数密度(c)和电子速度分布函数(d)的时空演化

Fig. 12. Spatiotemporal evolutions of the electric potential (a), ion number density (b), electron number density (c) and electron velocity distribution function (d) under different frequencies (columns 1–4 correspond to the frequencies of 0, 200, 477 and 800 MHz, respectively) of the externally applied radio-frequency electric field.

下载: 全尺寸图片幻灯片

图 13 不同射频电场频率下等离子体衰亡过程中负极板附近(x = 0.01 cm)、正极板附近(x = 1.99 cm)和腔室中心(x = 1.00 cm)处电场随时间的演化曲线

Fig. 13. Temporal evolutions of the electric field in the vicinity of the negative electrode (x = 0.01 cm) and the positive electrode (x = 1.99 cm), and the center between electrodes (x = 1.00 cm) under different frequencies of the externally applied radio-frequency electric field.

下载: 全尺寸图片幻灯片

表 1 典型工况参数

Table 1. List of physical parameters for typical cases studied in this paper.

工况 1 2 3 4

d, L/mm 1, 20 2.5, 20 5, 20 2.5, 20
n₀/(10¹⁶ m^–3) 1.0 1.0 1.0 1.0
T_e, T_i/eV 0.5, 0.02 0.5, 0.02 0.5, 0.02 5.0, 0.02
U₀/V 300 300 300 300

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[1]	Dhayal M, Forder D, Parry K L, Short R D, Bradley J W 2003 Surf. Coat. Technol. 173-174 872 Google Scholar
[2]	Aleksandrov N L, Anokhin E M, Kindysheva S V, Kirpichnikov A A, Kosarev I N, Nudnova M M, Starikovskaya S M, Starikovskii A Y 2012 Plasma Phys. Rep. 38 179 Google Scholar
[3]	Khrabrov A V, Kaganovich I D, Chen J, Guo H 2020 Phys. Plasmas 27 123512 Google Scholar
[4]	Lieberman M A 1989 J. Appl. Phys. 66 2926 Google Scholar
[5]	Yamada K, Tetsuka T, Deguchi Y 1991 J. Appl. Phys. 69 8064 Google Scholar
[6]	Yamada K, Tetsuka T, Deguchi Y 1991 J. Appl. Phys. 69 6962 Google Scholar
[7]	Ogura K, Arisawa T, Shibata T 1992 Jpn. J. Appl. Phys. 31 1485 Google Scholar
[8]	Yamada K, Tetsuka T 1994 J. Nucl. Sci. Technol. 31 301 Google Scholar
[9]	Nishio R, Yamada K, Suzuki K, Wakabayashi M 1995 J. Nucl. Sci. Technol. 32 180 Google Scholar
[10]	Matsui T, Tsuchida K, Tsuda S, Suzuki K, Shoji T 1996 Phys. Plasmas 3 4367 Google Scholar
[11]	Shibata T, Ogura K 1996 J. Nucl. Sci. Technol. 33 834 Google Scholar
[12]	Matsui T, Tsuchida K, Tsuda S, Suzuki K, Shoji T 1997 J. Nucl. Sci. Technol. 34 923 Google Scholar
[13]	Matsui Tetsuya, Tsuda S, Tsuchida K, Suzuki K, Shoji T 1997 Phys. Plasmas 4 3527 Google Scholar
[14]	Killian T C, Kulin S, Bergeson S D, Orozco S D, Orzel C, Rolston S L 1999 Phys. Rev. Lett. 83 4776 Google Scholar
[15]	Kulin S, Killian T C, Bergeson S D, Rolston S L 2000 Phys. Rev. Lett. 85 318 Google Scholar
[16]	Mazevet S, Collins L A, Kress J D 2002 Phys. Rev. Lett. 88 055001 Google Scholar
[17]	Robicheaux F, Hanson J D 2002 Phys. Rev. Lett. 88 055002 Google Scholar
[18]	Bergeson S D, Spencer R L 2003 Phys. Rev. E 67 026414 Google Scholar
[19]	Robicheaux F, Hanson J D 2003 Phys. Plasmas 10 2217 Google Scholar
[20]	Pohl T, Pattard T, Rost J M 2004 Phys. Rev. Lett. 92 155003 Google Scholar
[21]	Simien C E, Chen Y C, Gupta P, Laha S, Martinez Y N, Mickelson P G, Nagel S B, Killian T C 2004 Phys. Rev. Lett. 92 143001 Google Scholar
[22]	Cummings E A, Daily J E, Durfee D S, Bergeson S D 2005 Phys. Rev. Lett. 95 235001 Google Scholar
[23]	Fletcher R S, Zhang X L, Rolston S L 2006 Phys. Rev. Lett. 96 105003 Google Scholar
[24]	Zhang X L, Fletcher R S, Rolston S L, Guzdar P N, Swisdak M 2008 Phys. Rev. Lett. 100 235002 Google Scholar
[25]	Gorman G M, Warrens M K, Bradshaw S J, Killian T C 2021 Phys. Rev. Lett. 126 085002 Google Scholar
[26]	Sprenkle R T, Bergeson S D, Silvestri L G, Murillo M S 2022 Phys. Rev. E 105 045201 Google Scholar
[27]	Li H P, Ostrikov K, Sun W T 2018 Phys. Rep. 770–772 1
[28]	李和平, 王鹏, 王鑫, 尤伟, 柴俊杰, 李增耀 2015 高电压技术 41 2825 Google Scholar Li H P, Wang P, Wang X, You W, Chai J J, Li Z Y 2015 High Voltage Eng. 41 2825 Google Scholar
[29]	李和平, 王鑫, 柴俊杰, 李占贤 2016 高电压技术 42 706 Google Scholar Li H P, Wang X, Chai J J, Li Z X 2016 High Voltage Eng. 42 706 Google Scholar
[30]	Wang Y T, Chen J, Li H P, Jiang D J, Zhou M S 2021 Jpn. J. Appl. Phys. 60 SAAB05 Google Scholar
[31]	Chen J, Khrabrov A V, Wang Y T, Li J, Li H P, Jiang D J, Zhou M S 2020 Plasma Sources Sci. Technol. 29 025010 Google Scholar
[32]	Chen J, Fu T Z, Guo H, Li H P, Jiang D J, Zhou M S 2019 Plasma Sci. Technol. 21 045402 Google Scholar
[33]	陈坚, 李静, 李和平, 姜东君, 周明胜 2020 高电压技术 46 729 Google Scholar Chen J, Li J, Li H P, Jiang D J, Zhou M S 2020 High Voltage Eng. 46 729 Google Scholar
[34]	Calder A C, Laframboise J G 1990 Phys. Fluids B 2 655 Google Scholar
[35]	Calder A C, Hulbert G W, Laframboise J G 1993 Phys. Fluids B 5 674 Google Scholar
[36]	Sydorenko D 2006 Ph. D. Dissertation (Saskatchewan: University of Saskatchewan)
[37]	姜巍 2010 博士学位论文 (大连: 大连理工大学) Jiang W 2010 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese)
[38]	Lieberman M A, Lichtenberg A J 2005 Principles of Plasma Discharges and Materials Processing (Hoboken: Wiley-Interscience) pp389–394
[39]	熊家贵, 王德武 2000 物理学报 49 2420 Google Scholar Xiong J G, Wang D W 2000 Acta Phys. Sin. 49 2420 Google Scholar
[40]	Lu X Y, Yuan C, Zhang X Z, Zhang Z Z 2020 Chin. Phys. B 29 045201 Google Scholar
[41]	卢肖勇, 袁程, 高阳 2021 物理学报 70 145201 Google Scholar Lu X Y, Yuan C, Gao Y 2021 Acta Phys. Sin. 70 145201 Google Scholar

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外加电场作用下的壁面约束衰亡等离子体中带电粒子非平衡输运特性