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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.
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Keywords:
- decaying plasma /
- non-equilibrium transport of charged particles /
- electron oscillation /
- theoretical analysis /
- particle-in-cell simulation
[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
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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 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 70 145201
Google Scholar
Lu X Y, Yuan C, Gao Y 2021 Acta Phys. Sin. 70 145201
Google Scholar
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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
Figure 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.
图 2 壁面约束条件下的衰亡等离子体模式体系示意图
Figure 2. Schematic of a model system for bounded decaying plasmas.
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
Figure 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.
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
Figure 4. Variations of lmax under different values of d.
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
Figure 5. Variations of text with n0 at different values of Te and d: (a) d = 1 mm; (b) d = 5 mm.
图 6 电子振荡过程中电子数密度空间分布示意图
Figure 6. Schematic of the electron number density distribution during the electron oscillation process.
图 7 电子振荡过程的等效电路模型
Figure 7. Equivalent circuit model for the electron oscillation process.
图 8 d = 1 mm时极板附近的电场振荡曲线(a)及其频谱图(b)
Figure 8. Profiles of the electric fields in the vicinity of the electrodes (a), and their frequency spectra (b) with d = 1 mm.
图 9 d = 5 mm时极板附近的电场振荡曲线(a)及其频谱图(b)
Figure 9. Profiles of the electric fields in the vicinity of the electrodes (a), and their frequency spectra (b) with d = 5 mm.
图 10 电子振荡频率的理论值和模拟值的对比
Figure 10. Comparisons of the theoretical and modeling results of the electron oscillation frequency.
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
Figure 11. Variations of text with the values of frf under different amplitudes of the externally applied radio-frequency electric field.
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
Figure 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.
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
Figure 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.
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 Te, Ti/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 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 70 145201
Google Scholar
Lu X Y, Yuan C, Gao Y 2021 Acta Phys. Sin. 70 145201
Google Scholar
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