Optimal design of helicon wave antenna and numerical investigation into power deposition on helicon physics prototype experiment

Ping Lan-Lan; Zhang Xin-Jun; Yang Hua; Xu Guo-Sheng; Chang Lei; Wu Dong-Sheng; Lü Hong; Zheng Chang-Yong; Peng Jin-Hua; Jin Hai-Hong; He Chao; Gan Gui-Hua

doi:10.7498/aps.68.20182107

Abstract

Recently, helicon plasma sources have aroused the great interest particularly in plasma-material interaction under fusion conditions. In this paper, the helicon wave antenna in helicon physics prototype experiment (HPPX) is optimized. To reveal the effect of the radial density configuration on wave field and energy flow, Maxwell's equations for a radially nonuniform plasma with standard cold-plasma dielectric tensor are solved. Helicon wave coupling and power deposition are studied under different types of antennas, different antenna lengths and driving frequencies by using HELIC. Through the numerical simulation, the optimal antenna structure and size are obtained, that is, half helix antenna, which works at 13.56 MHz and has a length of 0.4 m, can generate nonaxisymmetric radio frequency energy coupling to excite higher electron density.The influences of different static magnetic fields and axis plasma densities on power deposition are also analyzed. It is found that the absorbed power of the plasma to the helicon wave has different peak power points in a multiple static magnetic field and axial plasma densities, and the overall coupling trend increases with static magnetic field increasing, but decreases with axis plasma density increasing. According to the simulation results, the ionization mechanism of helicon plasma is discussed. In order to further study the coupling of helicon wave with plasma in HPPX, the induced electromagnetic field and current density distribution are given when the plasma discharges. Under parabolic density distribution, the field intensity of the induced electric field at the edge is large, while neither the induced magnetic field nor current density changes much along the radial direction, the energy is distributed evenly in the whole plasma. Under the Gaussian density distribution, the induced electric field intensity is higher at the edge, while the induced magnetic field and current density in the center are much higher than at the edge. In this paper studied are the structure and size of helicon wave antenna, the influences of static magnetic field and axial plasma density on plasma power deposition and the distribution of induced electromagnetic field and current density during plasma discharge under different density distributions. This work will provide important theoretical basis for helicon wave antena design and relevant physical experiments on HPPX.

Keywords:

Authors and contacts

1.
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China
2.
University of Science and Technology of China, Hefei 230026, China
3.
School of Electronics and Information Engineering, Anhui Jianzhu University, Hefei 230601, China
4.
School of Aeronautics and Astronautics, Sichuan University, Chengdu 610065, China
5.
School of Electronic Engineering, National University of Defense Technology, Hefei 230036, China

Corresponding author: Zhang Xin-Jun, xjzhang@ipp.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61471002, 61372094, 11405271), the Natural Science Foundation of Education Office Anhui Province, China (Grant Nos. KJ2016JD11, KJ2018A0510), and the Natural Science Foundation of Anhui Province, China (Grant No. 1808085MF206)

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References

[1]	Carter M D, Baity F W, Barber G C, et al. 2002 Phys. Plasmas 9 5097 Google Scholar
[2]	Batishchev O V 2009 IEEE Trans. Plasma Sci. 37 1563 Google Scholar
[3]	Goulding R H, Caughman J B O, Rapp J, et al. 2017 Fusion Sci. Technol. 72 588 Google Scholar
[4]	Shinohara S, Nishida H, Tanikawa T, et al. 2014 IEEE Trans. Plasma Sci. 42 1245 Google Scholar
[5]	Lee M J, Jung Y D 2018 Phys. Plasmas 25 044501 Google Scholar
[6]	Gallo A, Fedorczak N, Elmore S, et al 2018 Plasma Phys. Control. Fusion 60 014007 Google Scholar
[7]	Aigrain P 1960 Proceedings of the International Conference on Semiconductor Physics Prague, Czech Republic, 1960 p224
[8]	Boswell R W 1970 Phys. Lett. 33A 457
[9]	Chen F F 1991 Plasma Phys. Controlled Fusion 33 339 Google Scholar
[10]	Chen F F, Blackwell D D 1999 Phys. Rev. Lett. 82 2677
[11]	Krmer M, Enk T, Lorenz B 2000 Phys. Scripta T84 132 Google Scholar
[12]	Shamrai K P, Taranov V B 1996 Plasma Sources Sci. Technol. 5 474 Google Scholar
[13]	Afsharmanesh M, Habibi M 2017 Plasma Sci. Technol. 19 105403 Google Scholar
[14]	Arnush D 2000 Phys. Plasmas 7 3042 Google Scholar
[15]	Chen F F, Arnush D 1997 Phys. Plasmas 4 3411 Google Scholar
[16]	Arnush D, Chen F F 1998 Phys. Plasmas 5 1239 Google Scholar
[17]	Mouzouris Y, Scharer J E 1996 IEEE Trans. Plasma Sci. 24 152 Google Scholar
[18]	Melazzi D, Curreli D, Manente M, et al. 2012 Com. Phys. Comm. 183 1182 Google Scholar
[19]	Melazzi D, Lancellotti V 2015 Plasma Sources Sci. Technol. 24 25024 Google Scholar
[20]	成玉国, 程谋森, 王墨戈, 等 2014 物理学报 63 035203 Google Scholar Cheng Y G, Cheng M S, Wang M G, et al. 2014 Acta Phys. Sin. 63 035203 Google Scholar
[21]	杨雄, 程谋森, 王墨戈, 等 2017 物理学报 66 025201 Google Scholar Yang X, Cheng M S, Wang M G, et al. 2017 Acta Phys. Sin. 66 025201 Google Scholar
[22]	Chang L, Li Q C, Zhang H J, et al. 2016 Plasma Sci. Technol. 18 848 Google Scholar
[23]	Chang L, Hu X Y, Gao L, et al. 2018 AIP ADVANCES 8 045016 Google Scholar
[24]	Chang L, Hole M J, Corr C S 2011 Phys. Plasmas 18 042106 Google Scholar
[25]	Boswell R W 1984 Plasma Phys. Control. Fusion 26 1147 Google Scholar
[26]	Chen R T S, Breun R A, Gross S, et al. 1995 Plasma Sources Sci. Technol. 4 337 Google Scholar
[27]	Charles C, Boswell R W, Lieberman M A 2003 Phys. Plasmas 10 891 Google Scholar
[28]	Chi K K, Sheridan T E, Boswell R W 1999 Plasma Sources Sci. Technol. 8 421 Google Scholar
[29]	Jung H D, Park M J, Kim S H, et al 2004 Rev. Sci. Instrum. 75 1878 Google Scholar
[30]	Michael A L, Allan J L 2007 Principles of Plasma Discharges and Materials Processing (Beijing: Science Press) pp291, 292, 350–352, 374–379, 392–399
[31]	Chen F F 2012 Phys. Plasmas 19 093509 Google Scholar

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图 1 HPPX装置结构图

Figure 1. The structure of HPPX.

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图 2 等离子体径向密度分布　(a) 抛物面分布; (b)高斯分布

Figure 2. Radial profiles of plasma density: (a) Parabolic density profile; (b) Gaussian density profile.

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图 3 3种典型的螺旋波天线的径向(z = 0.2 m)和轴向(r = 0.02 m)相对吸收功率　(a)抛物面密度分布下3种天线的径向相对吸收功率; (b)高斯密度分布下3种天线的径向相对吸收功率; (c)抛物面密度分布下3种天线的轴向相对吸收功率; (d)高斯密度分布下3种天线的轴向相对吸收功率

Figure 3. Relative power absorption in radial (z = 0.2 m) and axial (r = 0.02 m) directions for three typical helicon wave antennas: (a) Radial relative absorption power of three antennas under parabolic density distribution; (b) radial relative absorption power of three antennas under Gaussian density distribution; (c) axial relative absorption of power of three antennas under parabolic density distribution; (d) axial relative absorption of power of three antennas under Gaussian density distribution.

DownLoad: Full-Size Img PowerPoint

图 4 不同天线长度下的径向(z = 0.2 m)吸收功率　(a)抛物面密度分布下天线长度对径向相对吸收功率的影响; (b)高斯密度分布下天线长度对径向相对吸收功率的影响; (c)抛物面密度分布下径向吸收功率随天线长度的变化曲线; (d)高斯密度分布下径向吸收功率随天线长度的变化曲线

Figure 4. Relative power absorption in radial (z = 0.2 m) directions for different antenna lengths: (a) Effect of antenna length on radial relative absorption power under parabolic density distribution; (b) effect of antenna length on radial relative absorption power under Gaussian density distribution; (c) radial relative absorption power of different antennas lengths under parabolic density distribution; (d) radial relative absorption power of different antennas lengths under Gaussian density distribution.

DownLoad: Full-Size Img PowerPoint

图 5 不同运行频率下的径向(z = 0.2 m)吸收功率　(a)抛物面密度分布下天线运行频率对径向相对吸收功率的影响; (b)高斯密度分布下天线运行频率对径向相对吸收功率的影响; (c) 抛物面密度分布下径向吸收功率随运行频率的变化曲线; (d)高斯密度分布下径向吸收功率随运行频率的变化曲线

Figure 5. Relative power absorption in radial (z = 0.2 m) directions for various operating frequencies: (a) Effect of various operating frequencies on radial relative absorption power under parabolic density distribution; (b) effect of various operating frequencies on radial relative absorption power under Gaussian density distribution; (c) radial relative absorption power of various operating frequencies under parabolic density distribution; (d) radial relative absorption power of various operating frequencies under Gaussian density distribution.

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图 6 不同静磁场下的径向(z = 0.2 m)吸收功率　(a)抛物面密度分布下磁场对径向相对吸收功率的影响; (b)高斯密度分布下磁场对径向相对吸收功率的影响; (c)抛物面密度分布下径向吸收功率随磁场强度的变化曲线; (d)高斯密度分布下径向吸收功率随磁场强度的变化曲线

Figure 6. Relative power absorption in radial (z = 0.2 m) directions for various static magnetic intensity: (a) Effect of various magnetic intensity on radial relative absorption power under parabolic density distribution; (b) effect of various magnetic intensity on radial relative absorption power under Gaussian density distribution; (c) radial relative absorption power of various magnetic intensity under parabolic density distribution; (d) radial relative absorption power of various magnetic intensity under Gaussian density distribution.

DownLoad: Full-Size Img PowerPoint

图 7 不同密度下的径向(z = 0.2 m)吸收功率　(a)抛物面密度分布下密度对径向相对吸收功率的影响; (b)高斯密度分布下密度对径向相对吸收功率的影响; (c)抛物面密度分布下径向吸收功率随密度大小的变化曲线; (d)高斯密度分布下径向吸收功率随密度大小的变化曲线

Figure 7. Relative power absorption in radial (z = 0.2 m) directions for various density: (a) Effect of various density on radial relative absorption power under parabolic density distribution; (b) effect of various density on radial relative absorption power under Gaussian density distribution; (c) radial relative absorption power of various density under parabolic density distribution; (d) radialrelative absorption power of various density under Gaussian density distribution.

DownLoad: Full-Size Img PowerPoint

图 8 不同密度分布下的等离子体径向(z = 0.2 m)感应电场、感应磁场及电流密度分布

Figure 8. Radial profiles (z = 0.2 m) of wave electric field, magnetic field and current density in parabolic density profile and Gaussian density profile.

DownLoad: Full-Size Img PowerPoint

表 1 HPPX装置参数及等离子体参数

Table 1. HPPX device parameters and plasma parameters.

参数	数值
等离子体半径R_a/m	0.075
天线半径R_b/m	0.2
真空腔半径R_c/m	0.25
工质粒子种类	Ar⁺
射频天线运行频率f/MHz	13.56
射频天线长度L_A/m	0.4
中心轴处等离子体密度n_e0/cm^–3	4 × 10¹²
轴向静磁场强度B₀/T	0.04
电子温度T_e0/eV	5
中性轴压强P_g0/mTorr	10
步长N	49
碰撞因子	1

DownLoad: CSV

[1]	Carter M D, Baity F W, Barber G C, et al. 2002 Phys. Plasmas 9 5097 Google Scholar
[2]	Batishchev O V 2009 IEEE Trans. Plasma Sci. 37 1563 Google Scholar
[3]	Goulding R H, Caughman J B O, Rapp J, et al. 2017 Fusion Sci. Technol. 72 588 Google Scholar
[4]	Shinohara S, Nishida H, Tanikawa T, et al. 2014 IEEE Trans. Plasma Sci. 42 1245 Google Scholar
[5]	Lee M J, Jung Y D 2018 Phys. Plasmas 25 044501 Google Scholar
[6]	Gallo A, Fedorczak N, Elmore S, et al 2018 Plasma Phys. Control. Fusion 60 014007 Google Scholar
[7]	Aigrain P 1960 Proceedings of the International Conference on Semiconductor Physics Prague, Czech Republic, 1960 p224
[8]	Boswell R W 1970 Phys. Lett. 33A 457
[9]	Chen F F 1991 Plasma Phys. Controlled Fusion 33 339 Google Scholar
[10]	Chen F F, Blackwell D D 1999 Phys. Rev. Lett. 82 2677
[11]	Krmer M, Enk T, Lorenz B 2000 Phys. Scripta T84 132 Google Scholar
[12]	Shamrai K P, Taranov V B 1996 Plasma Sources Sci. Technol. 5 474 Google Scholar
[13]	Afsharmanesh M, Habibi M 2017 Plasma Sci. Technol. 19 105403 Google Scholar
[14]	Arnush D 2000 Phys. Plasmas 7 3042 Google Scholar
[15]	Chen F F, Arnush D 1997 Phys. Plasmas 4 3411 Google Scholar
[16]	Arnush D, Chen F F 1998 Phys. Plasmas 5 1239 Google Scholar
[17]	Mouzouris Y, Scharer J E 1996 IEEE Trans. Plasma Sci. 24 152 Google Scholar
[18]	Melazzi D, Curreli D, Manente M, et al. 2012 Com. Phys. Comm. 183 1182 Google Scholar
[19]	Melazzi D, Lancellotti V 2015 Plasma Sources Sci. Technol. 24 25024 Google Scholar
[20]	成玉国, 程谋森, 王墨戈, 等 2014 物理学报 63 035203 Google Scholar Cheng Y G, Cheng M S, Wang M G, et al. 2014 Acta Phys. Sin. 63 035203 Google Scholar
[21]	杨雄, 程谋森, 王墨戈, 等 2017 物理学报 66 025201 Google Scholar Yang X, Cheng M S, Wang M G, et al. 2017 Acta Phys. Sin. 66 025201 Google Scholar
[22]	Chang L, Li Q C, Zhang H J, et al. 2016 Plasma Sci. Technol. 18 848 Google Scholar
[23]	Chang L, Hu X Y, Gao L, et al. 2018 AIP ADVANCES 8 045016 Google Scholar
[24]	Chang L, Hole M J, Corr C S 2011 Phys. Plasmas 18 042106 Google Scholar
[25]	Boswell R W 1984 Plasma Phys. Control. Fusion 26 1147 Google Scholar
[26]	Chen R T S, Breun R A, Gross S, et al. 1995 Plasma Sources Sci. Technol. 4 337 Google Scholar
[27]	Charles C, Boswell R W, Lieberman M A 2003 Phys. Plasmas 10 891 Google Scholar
[28]	Chi K K, Sheridan T E, Boswell R W 1999 Plasma Sources Sci. Technol. 8 421 Google Scholar
[29]	Jung H D, Park M J, Kim S H, et al 2004 Rev. Sci. Instrum. 75 1878 Google Scholar
[30]	Michael A L, Allan J L 2007 Principles of Plasma Discharges and Materials Processing (Beijing: Science Press) pp291, 292, 350–352, 374–379, 392–399
[31]	Chen F F 2012 Phys. Plasmas 19 093509 Google Scholar

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