Multiphysics modeling and simulations of laser-sustained plasmas

Zhang Dong-He-Yu; Liu Jin-Bao; Fu Yang-Yang

doi:10.7498/aps.73.20231056

Abstract

Laser-sustained plasma (LSP), which can be utilized for a novel radiation light source, has advantages such as high irradiance, broad spectral range, and stable emission, demonstrating significant applications in wafer inspection in the field of the semiconductor industry. This paper revisits the historical development of LSP research and introduces fundamental physical processes in LSP. The mathematical description equations for LSP and methods of calculating plasma parameters are provided, thereby a time-dependent two-dimensional fluid model is established by taking into consideration a laser-thermal-hydrodynamic coupling effect. The propagation of the laser in plasma is investigated based on the established model, and the fundamental processes in LSP, including the initial evolution process, laser energy deposition, steady-state characteristics, and instability, are explored. The effectiveness of the simulation model is confirmed through comparing with the experimental results of high-pressure Xe LSP. The findings indicate that the mode, power, F-number of incident lasers, as well as parameters including components, pressure, and flow velocity of gas, can all affect the steady-state properties of LSPs. Under the identical power and F-number conditions, Gaussian mode laser and annular mode laser both produce LSPs with different shapes and positions. Notably, under the conditions of high-power annular laser incidence, large laser F-number, and high flow velocity, the simulation results reveal temporal and spatial instability in LSP. These simulation results contribute significantly to a more in-depth understanding of the underlying physical mechanisms of the LSP. Furthermore, they provide a theoretical basis for designing the light source system and optimizing the multiple parameters. The influence of laser parameters on LSP properties elucidated in this study not only advances the fundamental understanding of LSP but also offers crucial insights for designing and optimizing the light source systems in various applications, particularly in the field of optical detection for semiconductor wafer inspection.

Keywords:

Authors and contacts

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

Corresponding author: Fu Yang-Yang, fuyangyang@tsinghua.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52277154).

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References

[1]	Raizer Y P 1970 J. Exp. Theor. Phys. 31 1148
[2]	Raizer Y P 1991 Gas Discharge Physics (Heidelberg: Springer) p415
[3]	Raizer Y P 1980 Sov. Phys. Usp. 23 789 Google Scholar
[4]	Kantrowitz A 1972 Astronaut. Aeronaut. 10 74
[5]	Cremers D A, Archuleta F L, Martinez R J 1985 Spectrochim. Acta, Part B 40 665 Google Scholar
[6]	Chen X, Mazumder J 1989 J. Appl. Phys. 66 5756 Google Scholar
[7]	Bezel I, Delgado G, Derstine M, Gross K, Solarz R, Shchemelinin A, Shortt D 2015 Conference on Lasers and Electro-Optics (CLEO) San Jose, USA, May 10–15, 2015 pp1–2
[8]	Islam M, Ciaffoni L, Hancock G, Ritchie G A 2013 Analyst 138 4741 Google Scholar
[9]	Horne S, Smith D, Besen M, Partlow M, Stolyarov D, Zhu H, Holber W 2010 Next-Generation Spectroscopic Technologies III (SPIE) Orlando, USA, April 5–6, 2010 pp105–111
[10]	Bezel I, Zvedenuk L B, Stepanov A E, KRerikh V, Potapkin B V US Patent US11776804 B2[2023-10-03
[11]	Bezel I, Zvedenuk L B, Stepanov A E, Torkaman A 2023 US Patent 2023/0053035 A1 [2023-02-16
[12]	Generalov N A, Zimakov V P, Kozlov G I, Masyukov V A, Raizer Y P 1970 Sov. J. Exp. Theor. Phys. 11 302
[13]	王海兴, 陈熙 2004 工程热物理学报 25 S1 Wang H X, Chen X 2004 J. Eng. Thermophys. 25 S1
[14]	郑志远, 鲁欣, 张杰, 郝作强, 远晓辉, 王兆华 2005 物理学报 54 192 Google Scholar Zheng Z Y, Lu X, Zhang J, Hao Z Q, Yuan X H, Wang Z H 2005 Acta. Phys. Sin. 54 192 Google Scholar
[15]	Krier H, Mazumder J, Rockstroh T, Bender T, Glumb R 1986 AIAA J. 24 1656 Google Scholar
[16]	Shi Z, Yang S, Yu F, Yu X 2023 Opt. Express 31 6132 Google Scholar
[17]	Akarapu R, Nassar A R, Copley S M, Todd J A 2009 J. Laser Appl. 21 169 Google Scholar
[18]	Fowler M C, Smith D C 1975 J. Appl. Phys. 46 138 Google Scholar
[19]	Zimakov V P, Kuznetsov V A, Solovyov N G, Shemyakin A N, Shilov A O, Yakimov M Y 2016 Plasma Phys. Rep. 42 68 Google Scholar
[20]	Hu Y, Wang X, Zuo D 2022 Vacuum 203 111229 Google Scholar
[21]	Gerasimenko M V, Kozlov G I, Kuznetsov V A 1983 Sov. J. Quantum Electron. 13 438 Google Scholar
[22]	Welle R, Keefer D, Peters C 1987 AIAA J. 25 1093 Google Scholar
[23]	Jeng S M, Keefer D 1989 J. Propul. Power 5 577 Google Scholar
[24]	Liu J B, Zhang D H Y, Fu Y Y 2023 New J. Phys. 25 122001 Google Scholar Liu J B, Zhang D H Y, Fu Y Y 2023 New J. Phys. 25 122001 Google Scholar
[25]	Jeng S M, Keefer D R 1987 J. Propul. Power 3 255 Google Scholar
[26]	Batteh J H, Keefer D R 1974 IEEE Trans. Plasma Sci. 2 122 Google Scholar
[27]	Glumb R J, Krier H 1984 J. Spacecr. Rockets 21 70 Google Scholar
[28]	Molvik G A, Choi D, Merkle C L 1985 AIAA J. 23 1053 Google Scholar
[29]	Merkle C L, Molvik G A, Shaw E J H 1986 J. Propul. Power 2 465 Google Scholar
[30]	Jeng S M, Keefer D R, Welle R, Peters C E 1987 AIAA J. 25 1224 Google Scholar
[31]	Conrad R, Raizer Y P, Sarzhikov S T 1996 AIAA J. 34 1584 Google Scholar
[32]	Rafatov I R, Yedierler B, Kulumbaev E B 2009 J. Phys. D: Appl. Phys. 42 055212 Google Scholar
[33]	Keefer D R, Henriksen B B, Braerman W F 1975 J. Appl. Phys. 46 1080 Google Scholar
[34]	Generalov N A, Zakharov A M, Kosynkin V D, Yakimov M Y 1986 Combust., Explos. Shock Waves 22 214 Google Scholar
[35]	Rafatov I 2009 Phys. Lett. A 373 3336 Google Scholar
[36]	Zimakov V P, Kuznetsov V A, Solovyov N G, Shemyakin A N, Shilov A O, Yakimov M Y 2017 J. Phys. Conf. Ser. 815 012003 Google Scholar
[37]	Zimakov V P, Lavrentyev S, Solovyov N, Shemyakin A, Yakimov M A 2019 Physical-Chemical Kinetics in Gas Dynamics 19 1
[38]	Lavrentyev S Y, Solovyov N G, Shemyakin A N, Yu Yakimov M 2019 J. Phys. Conf. Ser. 1394 012012 Google Scholar
[39]	Kotov M A, Lavrentyev S Y, Shemyakin A N, Solovyov N G, Yakimov M Y 2022 Plasma Sources Sci. Technol. 31 124002 Google Scholar
[40]	王海兴, 孙素蓉, 陈士强 2012 物理学报 61 195203 Google Scholar Wang H X, Sun S R, Chen S Q 2012 Acta. Phys. Sin. 61 195203 Google Scholar
[41]	陈艳秋 2014 物理学报 63 205201 Google Scholar Chen Y Q 2014 Acta. Phys. Sin. 63 205201 Google Scholar
[42]	Gordon S, McBride B J 1994 Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications. part 1: Analysis. Tech. Rep. 95 N20180, NASA
[43]	Johnston T W, Dawson J M 1973 Phys. Fluids 16 722 Google Scholar
[44]	Gilleron F, Piron R 2015 High Energy Density Phys. 17 219 Google Scholar
[45]	Chapman S, Cowling T G 1995 The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction, and Diffusion in Gases (3rd Ed.) (Cambridge: Cambridge University Press) p167
[46]	Adibzadeh M, Theodosiou C E 2005 At. Data Nucl. Data Tables 91 8 Google Scholar
[47]	Amdur I, Mason E 1958 Phys. Fluids 1 370 Google Scholar
[48]	Miller J S, Pullins S H, Levandier D J, Chiu Y h, Dressler R A 2002 J. Appl. Phys. 91 984 Google Scholar
[49]	Mason E, Munn R, Smith F J 1967 Phys. Fluids 10 1827 Google Scholar
[50]	Tang K, Toennies J P 1984 J. Chem. Phys. 80 3726 Google Scholar
[51]	Tang K, Toennies J P 1986 Z. Phys. D: At. Mol. Clusters 1 91 Google Scholar
[52]	Monchick L 1959 Phys. Fluids 2 695 Google Scholar
[53]	Hirschfelder J, Curtiss C, Bird R, Mayer M 1954 Molecular Theory of Gases and Liquids (New York: Wiley) pp1126–1127
[54]	Devoto R S 1967 Phys. Fluids 10 354 Google Scholar
[55]	Devoto R S 1967 Phys. Fluids 10 2105 Google Scholar
[56]	Horn K P 1966 Radiative Behavior of Shock Heated Argon Plasma Flows (Stanford: Stanford University) p35
[57]	杜世刚 1998 等离子体物理 (北京: 原子能出版社) 第162页 Du S G 1998 Plasma Physics (Beijing: Atomic Press) p162
[58]	COMSOL Multiphysics® v. 6.0. cn.comsol.com. COMSOL AB, Stockholm, Sweden.
[59]	过增元, 赵文华 1986 电弧和热等离子体(北京: 科学出版社) 第141—157页 Guo Z Y, Zhao W H 1986 Arc and Thermal Plasma (Beijing: Science Press) pp141–157

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图 1 LSP实验装置结构示意图

Figure 1. Schematic diagram of the LSP experimental setup.

DownLoad: Full-Size Img PowerPoint

图 2 $ {\rm{{CO_2}}} $激光条件下LSP中主要能量传递机制, 包括: 逆韧致辐射(ff)吸收; 自由-自由(ff)/自由-束缚(fb)辐射; 束缚-束缚(bb)辐射; 热扩散

Figure 2. Main energy transfer processes of plasma sustained by $ {\rm{{CO_2}}} $ laser including bremsstrahlung absorption, free-free (ff)/free-bound (fb) emission, bound-bound (bb) emission, and thermal diffusion.

DownLoad: Full-Size Img PowerPoint

图 3 不同压强的平衡状态下Xe气体组分

Figure 3. Composition of Xe plasma at different pressures.

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图 4 $ 10.6{\text{ μm}} $ $ {\rm{{CO_2}}} $激光条件下不同压强Xe等离子体的吸收系数随温度变化

Figure 4. Absorption coefficient of Xe plasmas with temperature at different pressures under the condition of $ 10.6{\text{ μm}} $ $ {\rm{{CO_2}}} $ laser.

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图 5 不同压强下Xe等离子体各参数随温度的变化　(a)恒压比热容; (b)黏滞系数; (c)热导率; (d)各项辐射损失功率密度

Figure 5. Parameters of Xe plasmas scaling with temperature at different pressures: (a) Specific heat capacity; (b) viscosity; (c) thermal conductivity; (d) radiative loss power density.

DownLoad: Full-Size Img PowerPoint

图 6 LSP模拟计算域设置

Figure 6. Setup of the LSP computational domain.

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图 7 仿真得到典型的稳态Xe-LSP参数二维分布　(a)等温线分布; (b)速度流场分布

Figure 7. Two-dimensional (2D) profiles of the steady-state Xe-LSP from the simulation results: (a) Temperature isotherm profile; (b) velocity streamline.

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图 10 高功率、高气体流速下产生的不稳定LSP. 图中结果的气体压强均为$ 10{\rm{\, {atm}}} $, 采用环形激光, 功率为$ 5000{\rm{\, {W}}} $, F数为$ f/3.5 $. 图(a)—(c)展示了入口流速设置为$ 10{\rm{\, {m/s}}} $产生的LSP在$ 3.6 $, $ 4.0$和$ 4.4{\rm{~{ms}}} $的二维温度分布; 图(d)—(f)展示了入口流速设置为$ 20{\rm{\, {m/s}}} $产生的LSP在$ 3.6$, $ 4.0$和$ 4.4{\rm{~{ms}}} $的二维温度分布

Figure 10. Unstable LSP generated under the condition of high laser power and high gas velocity. The gas pressure for all the results is set to $ 10{\rm{\, {atm}}} $. The laser power is $ 5000{\rm{\, {W}}} $ and F-number equals to $ f/3.5 $. Panels (a)–(c) show the two-dimensional temperature distribution of the LSP when inlet velocity is set to $ 10{\rm{\, {m/s}}} $ at $ 3.6 $, $ 4.0 $, and $ 4.4{\rm{~{ms}}} $. Panels (d)–(f) show the two-dimensional temperature distribution of the LSP when inlet velocity is set to $ 20{\rm{\, {m/s}}} $ at $ 3.6 $, $ 4.0 $, and $ 4.4{\rm{~{ms}}} $.

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图 8 (a)相同功率下高斯模式与环形模式激光相对强度径向分布; (b), (c)激光模式对稳态LSP温度分布的影响, 分别为$ f/7 $条件下高斯光束与环形光束结果. 模拟条件为5 atm的Xe环境下, 入射激光功率为500 W, F数为$ f/7 $, 气体流速10 m/s

Figure 8. (a) Radial distribution of relative laser intensity of Gaussian beam and annular beam at a same laser power; (b), (c) effects of laser mode on steady LSP temperature distribution, where (b) and (c) are the results of Gaussian beam and annular beam at $ f/7 $, respectively. Background gas: Xe, pressure: 5 atm, laser power: 500 W, F-number: $ f/7 $, velocity: 10 m/s.

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图 9 不同时刻LSP的温度分布图. 模拟条件为$ 5{\rm{\, {atm}}} $的Xe环境下, 入射激光功率为$ 500{\rm{\, {W}}} $, F数为$ f/7 $, 气体流速为$ 10{\rm{\, {m/s}}} $

Figure 9. Temperature distributions of LSP at different times during laser propagation. Background gas: Xe, pressure: $ 5{\rm{\, {atm}}} $, laser power: $ 500{\rm{\, {W}}} $, F-number: $ f/7 $, velocity: $ 10{\rm{\, {m/s}}} $.

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表 1 输运系数与用于计算的碰撞积分

Table 1. Transport coefficients and the collision integrals used for calculation

输运系数	用于计算的碰撞积分
$ \mu_{\rm{{v}}} $	$ \varOmega^{\left({1, 1}\right)} $; $ \varOmega^{\left({2, 2}\right)} $
$ k_{\rm{{T}}} $	$ \varOmega^{\left({1, s}\right)}, \, s = 1,\cdots, 5 $; $ \varOmega^{\left({2, s}\right)}, \, s = 2, 3, 4 $

DownLoad: CSV

表 2 Xe等离子体中粒子对相互作用对应的碰撞积分计算方法

Table 2. Calculation of collisional integrals corresponding to particle pair interactions in Xe plasmas.

相互作用	计算方法	参考文献
e-Xe	动量转移截面积分	[46]
Xe-Xe	指数势能: $ A = 311,\; \rho = 0.208 $	[47]
Xe-$ {\rm{{Xe}}}^+ $	电荷交换截面: $ A = 9.716, \;B = 0.4204 $	[48]
e-$ {\rm{{Xe}}}^{Z_{i}+} $, $ {\rm{{Xe}}}^{Z_{i}+} $-$ {\rm{{Xe}}}^{Z_{j}+} $	屏蔽库仑势	[49]

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表 3 模型控制方程及对应边界条件

Table 3. Control equations and boundary conditions of the model.

控制方程	左边界(入口)	右边界(出口)	上边界
质量守恒方程: (1)式	$ u_z=u_\text{in}, u_r = 0 $	—	$ {\boldsymbol{{u}}} = 0 $
动量守恒方程: (2)式	$ u_z=u_\text{in}, u_r = 0 $	$ p=p_0 $	$ {\boldsymbol{{u}}} = 0 $
能量守恒方程: (3)式	$ T = 500{\rm{\; {K}}} $	$ T = 500{\rm{\; {K}}} $	$ T = 500{\rm{\; {K}}} $
激光输运方程: (9)式	由激光模式确定	—	—

DownLoad: CSV

[1]	Raizer Y P 1970 J. Exp. Theor. Phys. 31 1148
[2]	Raizer Y P 1991 Gas Discharge Physics (Heidelberg: Springer) p415
[3]	Raizer Y P 1980 Sov. Phys. Usp. 23 789 Google Scholar
[4]	Kantrowitz A 1972 Astronaut. Aeronaut. 10 74
[5]	Cremers D A, Archuleta F L, Martinez R J 1985 Spectrochim. Acta, Part B 40 665 Google Scholar
[6]	Chen X, Mazumder J 1989 J. Appl. Phys. 66 5756 Google Scholar
[7]	Bezel I, Delgado G, Derstine M, Gross K, Solarz R, Shchemelinin A, Shortt D 2015 Conference on Lasers and Electro-Optics (CLEO) San Jose, USA, May 10–15, 2015 pp1–2
[8]	Islam M, Ciaffoni L, Hancock G, Ritchie G A 2013 Analyst 138 4741 Google Scholar
[9]	Horne S, Smith D, Besen M, Partlow M, Stolyarov D, Zhu H, Holber W 2010 Next-Generation Spectroscopic Technologies III (SPIE) Orlando, USA, April 5–6, 2010 pp105–111
[10]	Bezel I, Zvedenuk L B, Stepanov A E, KRerikh V, Potapkin B V US Patent US11776804 B2[2023-10-03
[11]	Bezel I, Zvedenuk L B, Stepanov A E, Torkaman A 2023 US Patent 2023/0053035 A1 [2023-02-16
[12]	Generalov N A, Zimakov V P, Kozlov G I, Masyukov V A, Raizer Y P 1970 Sov. J. Exp. Theor. Phys. 11 302
[13]	王海兴, 陈熙 2004 工程热物理学报 25 S1 Wang H X, Chen X 2004 J. Eng. Thermophys. 25 S1
[14]	郑志远, 鲁欣, 张杰, 郝作强, 远晓辉, 王兆华 2005 物理学报 54 192 Google Scholar Zheng Z Y, Lu X, Zhang J, Hao Z Q, Yuan X H, Wang Z H 2005 Acta. Phys. Sin. 54 192 Google Scholar
[15]	Krier H, Mazumder J, Rockstroh T, Bender T, Glumb R 1986 AIAA J. 24 1656 Google Scholar
[16]	Shi Z, Yang S, Yu F, Yu X 2023 Opt. Express 31 6132 Google Scholar
[17]	Akarapu R, Nassar A R, Copley S M, Todd J A 2009 J. Laser Appl. 21 169 Google Scholar
[18]	Fowler M C, Smith D C 1975 J. Appl. Phys. 46 138 Google Scholar
[19]	Zimakov V P, Kuznetsov V A, Solovyov N G, Shemyakin A N, Shilov A O, Yakimov M Y 2016 Plasma Phys. Rep. 42 68 Google Scholar
[20]	Hu Y, Wang X, Zuo D 2022 Vacuum 203 111229 Google Scholar
[21]	Gerasimenko M V, Kozlov G I, Kuznetsov V A 1983 Sov. J. Quantum Electron. 13 438 Google Scholar
[22]	Welle R, Keefer D, Peters C 1987 AIAA J. 25 1093 Google Scholar
[23]	Jeng S M, Keefer D 1989 J. Propul. Power 5 577 Google Scholar
[24]	Liu J B, Zhang D H Y, Fu Y Y 2023 New J. Phys. 25 122001 Google Scholar Liu J B, Zhang D H Y, Fu Y Y 2023 New J. Phys. 25 122001 Google Scholar
[25]	Jeng S M, Keefer D R 1987 J. Propul. Power 3 255 Google Scholar
[26]	Batteh J H, Keefer D R 1974 IEEE Trans. Plasma Sci. 2 122 Google Scholar
[27]	Glumb R J, Krier H 1984 J. Spacecr. Rockets 21 70 Google Scholar
[28]	Molvik G A, Choi D, Merkle C L 1985 AIAA J. 23 1053 Google Scholar
[29]	Merkle C L, Molvik G A, Shaw E J H 1986 J. Propul. Power 2 465 Google Scholar
[30]	Jeng S M, Keefer D R, Welle R, Peters C E 1987 AIAA J. 25 1224 Google Scholar
[31]	Conrad R, Raizer Y P, Sarzhikov S T 1996 AIAA J. 34 1584 Google Scholar
[32]	Rafatov I R, Yedierler B, Kulumbaev E B 2009 J. Phys. D: Appl. Phys. 42 055212 Google Scholar
[33]	Keefer D R, Henriksen B B, Braerman W F 1975 J. Appl. Phys. 46 1080 Google Scholar
[34]	Generalov N A, Zakharov A M, Kosynkin V D, Yakimov M Y 1986 Combust., Explos. Shock Waves 22 214 Google Scholar
[35]	Rafatov I 2009 Phys. Lett. A 373 3336 Google Scholar
[36]	Zimakov V P, Kuznetsov V A, Solovyov N G, Shemyakin A N, Shilov A O, Yakimov M Y 2017 J. Phys. Conf. Ser. 815 012003 Google Scholar
[37]	Zimakov V P, Lavrentyev S, Solovyov N, Shemyakin A, Yakimov M A 2019 Physical-Chemical Kinetics in Gas Dynamics 19 1
[38]	Lavrentyev S Y, Solovyov N G, Shemyakin A N, Yu Yakimov M 2019 J. Phys. Conf. Ser. 1394 012012 Google Scholar
[39]	Kotov M A, Lavrentyev S Y, Shemyakin A N, Solovyov N G, Yakimov M Y 2022 Plasma Sources Sci. Technol. 31 124002 Google Scholar
[40]	王海兴, 孙素蓉, 陈士强 2012 物理学报 61 195203 Google Scholar Wang H X, Sun S R, Chen S Q 2012 Acta. Phys. Sin. 61 195203 Google Scholar
[41]	陈艳秋 2014 物理学报 63 205201 Google Scholar Chen Y Q 2014 Acta. Phys. Sin. 63 205201 Google Scholar
[42]	Gordon S, McBride B J 1994 Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications. part 1: Analysis. Tech. Rep. 95 N20180, NASA
[43]	Johnston T W, Dawson J M 1973 Phys. Fluids 16 722 Google Scholar
[44]	Gilleron F, Piron R 2015 High Energy Density Phys. 17 219 Google Scholar
[45]	Chapman S, Cowling T G 1995 The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction, and Diffusion in Gases (3rd Ed.) (Cambridge: Cambridge University Press) p167
[46]	Adibzadeh M, Theodosiou C E 2005 At. Data Nucl. Data Tables 91 8 Google Scholar
[47]	Amdur I, Mason E 1958 Phys. Fluids 1 370 Google Scholar
[48]	Miller J S, Pullins S H, Levandier D J, Chiu Y h, Dressler R A 2002 J. Appl. Phys. 91 984 Google Scholar
[49]	Mason E, Munn R, Smith F J 1967 Phys. Fluids 10 1827 Google Scholar
[50]	Tang K, Toennies J P 1984 J. Chem. Phys. 80 3726 Google Scholar
[51]	Tang K, Toennies J P 1986 Z. Phys. D: At. Mol. Clusters 1 91 Google Scholar
[52]	Monchick L 1959 Phys. Fluids 2 695 Google Scholar
[53]	Hirschfelder J, Curtiss C, Bird R, Mayer M 1954 Molecular Theory of Gases and Liquids (New York: Wiley) pp1126–1127
[54]	Devoto R S 1967 Phys. Fluids 10 354 Google Scholar
[55]	Devoto R S 1967 Phys. Fluids 10 2105 Google Scholar
[56]	Horn K P 1966 Radiative Behavior of Shock Heated Argon Plasma Flows (Stanford: Stanford University) p35
[57]	杜世刚 1998 等离子体物理 (北京: 原子能出版社) 第162页 Du S G 1998 Plasma Physics (Beijing: Atomic Press) p162
[58]	COMSOL Multiphysics® v. 6.0. cn.comsol.com. COMSOL AB, Stockholm, Sweden.
[59]	过增元, 赵文华 1986 电弧和热等离子体(北京: 科学出版社) 第141—157页 Guo Z Y, Zhao W H 1986 Arc and Thermal Plasma (Beijing: Science Press) pp141–157

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Vol. 73, Issue 2 - 2024-01-20

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