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As a core phenomenon in helicon discharge, the plasma temperature anisotropy may play a crucial role in helicon wave power deposition. Under radially inhomogeneous plasma circumstances, by employing the warm plasma dielectric tensor model and considering the finite Larmor radius (FLR) effect and plasma temperature anisotropy effect, under the typical helicon discharge parameter conditions, the helicon wave and Trivelpiece-Gould (TG) wave mode coupling characteristic and influence of electron temperature anisotropy on the helicon wave power deposition induced by collisional and Landau damping mechanism are theoretically investigated. Detailed analysis shows that for typical helicon plasma electron temperature Te = 3 eV and low magnetic field B0 = 48 G, the electron FLR effect should be considered, while the ion FLR effect can be ignored due to its large inertia effect; compared with the
$| n | < 2 $ cyclotron harmonics, the contribution of the$| n | > 1 $ harmonics in the calculation of plasma dielectric tensor elements can be ignored due to low magnetic field conditions. For the propagation constant, detailed investigation indicates that the phase constant has a maximum value at a certain radial position, near the same position mode coupling between helicon wave and TG wave happens. Full analysis shows that the power deposition of the m = 1 helicon mode peaks at a certain radial position and increases gradually with the increase of the axial electron temperature. Besides, compared with the Landau damping, the collisional damping plays a dominant role in the power deposition under current parameter conditions; importantly, the electron temperature anisotropy exerts a significant influence on the power deposition characteristic, both the increase and decrease of electron temperature anisotropy factor (χ = Te,⊥/Te,z) can lead the power deposition intensity to change drastically. All these conclusions are very important for us to understand the discharge mechanism of helicon plasma.-
Keywords:
- helicon plasma /
- anisotropy /
- propagation characteristics /
- power deposition
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图 1 螺旋波放电产生等离子体柱横向截面示意图
Figure 1. Cross section of helicon wave discharge plasma column.
图 2 碰撞阻尼频率与朗道阻尼频率随电子温度的变化
Figure 2. Dependence of the collisional frequency and Landau frequency on the electron temperature.
图 3 有限拉莫尔半径效应因子随轴向静磁场的变化
Figure 3. Dependence of the FLR effects on the axial static magnetic field.
图 4 |n|≤3次回旋谐波对应的色散函数宗量随电子温度的变化
Figure 4. Dependence of the argument of the plasma dispersion function on electron temperature for the |n| ≤ 3 cyclotron harmonics.
图 5 高斯型等离子体密度及电子-绝缘壁碰撞频率的径向分布
Figure 5. Radial profile of the plasma density distribution and electron-wall collisional frequency.
图 6 相位常数和衰减常数随归一化半径的变化特性
Figure 6. Amplitude of phase and attenuation constants varies with normalized radial position.
图 7 螺旋波和TG波的径向模式耦合特性
Figure 7. Mode coupling characteristic of helicon and TG waves on the normalized radial position.
图 8 归一化功率沉积Pabs/max<Pabs>在(r, Te, z)参量空间的分布 (a) n0 = 1×1013 cm–3; (b) n0 = 1.2×1013 cm–3
Figure 8. Distribution of normalized power deposition Pabs/max<Pabs> in the (r, Te, z) parameter space: (a) n0 = 1×1013 cm–3; (b) n0 = 1.2×1013 cm–3.
图 9 朗道阻尼(a)和碰撞阻尼(b)引起的功率沉积在(r, Te, z)参量空间的分布
Figure 9. Landau damping (a) and collisional damping (b) induced power deposition in the (r, Te, z) parameter space.
图 10 (二维)条件下归一化功率沉积Pabs, CD/max<Pabs, CD>在 (r, χ) 参量空间的分布 (a) ${B_0} = 32{\text{ G}}$; (b) ${B_0} = 40{\text{ G}}$; (c) ${B_0} = 48{\text{ G}}$; (d) ${B_0} = 48{\text{ G}}$
Figure 10. Distribution of normalized power deposition Pabs, CD/max<Pabs, CD> in the (r, χ) parameter space (two dimensional): (a) ${B_0} = 32{\text{ G}}$; (b) ${B_0} = 40{\text{ G}}$; (c) ${B_0} = 48{\text{ G}}$; (d) ${B_0} = 48{\text{ G}}$.
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[1] Tynan G R, Burin M J, Holland C, et al. 2004 Plasma Phys. Controlled Fusion 46 A373
Google Scholar
[2] Windisch T, Grulke O, Klinger T 2006 Phys. Plasmas 13 122303
Google Scholar
[3] Grulke O, Ullrich S, Windisch T, et al. 2007 Plasma Phys. Controlled Fusion 49 B247
Google Scholar
[4] Aliev Y M, Krämer M 2011 Phys. Scr. 83 065504
Google Scholar
[5] Goyal R, Sharma R P, Scime E E 2015 Phys. Plasmas 22 022101
Google Scholar
[6] Marin J F C, Lau C L, Goulding R H, et al. 2021 Plasma Phys. Controlled Fusion 64 025005.
Google Scholar
[7] Breizman B N, Arefiev A V 2000 Phys. Rev. Lett. 84 3863.
Google Scholar
[8] Chen G, Arefiev A V, Bengtson R D, et al. 2006 Phys. Plasmas 13 123507
Google Scholar
[9] Arefiev A V, Breizman B N 2006 Phys. Plasmas 13 062107
Google Scholar
[10] Aliev Y M, Krämer M 2008 Phys. Plasmas 15 104502
Google Scholar
[11] Aliev Y M, Krämer M 2014 Phys. Plasmas 21 013508
Google Scholar
[12] Aliev Y M, Krämer M 2016 Phys. Plasmas 23 103505
Google Scholar
[13] Aliev Y M, Krämer M 2023 Phys. Plasmas 30 032102
Google Scholar
[14] 成玉国, 程谋森, 王墨戈, 李小康 2014 63 035203
Google Scholar
Cheng Y G, Cheng M S, Wang M G, Li X K 2014 Acta Phys. Sin. 63 035203
Google Scholar
[15] 赵高, 熊玉卿, 马超, 刘忠伟, 陈强 2014 63 235202
Google Scholar
Zhao G, Xiong Y Q, Ma C, Liu Z W, Chen Q 2014 Acta Phys. Sin. 63 235202
Google Scholar
[16] Guo X M, Scharer J, Mouzouris Y, et al. 1999 Phys. Plasmas 6 3400
Google Scholar
[17] Correyero Plaza S, Navarro J, Ahedo E 2016 52nd AIAA/ SAE/ASEE Joint Propulsion Conference, Salt Lake City, July 25—27, 2016 p5035
[18] Swanson D G 1989 Plasma Waves (New York: Academic Press) p155
[19] Huba J D 2016 NRL Plasma Formulary (Washington: Naval Research Laboratory) p34
[20] Kamenski I V, Borg G G A 1998 Comput. Phys. Commun. 113 10
Google Scholar
[21] Mouzouris Y, Scharer J E 1998 Phys. Plasmas 5 4253
Google Scholar
[22] Fried B D, Conte S D 2015 The Plasma Dispersion Function: The Hilbert Transform of the Gaussian (New York: Academic Press) p1
[23] Sakawa Y, Kunimatsu H, Kikuchi H, et al. 2003 Phys. Rev. Lett. 90 105001
Google Scholar
[24] Shamrai K P, Shinohara S 2001 Phys. Plasmas 8 4659
Google Scholar
[25] Loewenhardt P K, Blackwell B D, Boswell R W, et al. 1991 Phys. Rev. Lett. 67 2792
Google Scholar
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