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旋转和旋转剪切能抑制磁流体不稳定性和增强等离子体约束. 低杂波电流驱动作为未来聚变堆上可能的旋转驱动手段, 探索低杂波在现有托卡马克装置上驱动等离子体旋转的驱动机制, 可以为未来的聚变堆上旋转预测提供重要参考. 在东方超环托卡马克装置上, 早期发现了2.45 GHz的低杂波能有效驱动等离子体旋转的现象, 认为是边界旋转的改变导致芯部旋转的同电流方向的增加造成的. 更高频率下4.6 GHz低杂波电流驱动可以更有效地驱动同电流方向的等离子体旋转. 本论文分析在欧姆背景等离子体下, 不同功率的低杂波对等离子体环向旋转的影响, 研究安全因子剖面变化对环向旋转的关系, 利用功率调制获得了低杂波驱动旋转实验中的环向动量输运系数变化情况, 发现环向动量扩散系数(χφ)、环向动量箍缩系数(Vpinch)的数值大小趋势是从芯部向靠外的区域逐渐变大. 这与低杂波驱动环向旋转时, 环向旋转速度由靠外的区域向芯部传递的特性吻合.Rotation and its shear can reduce the magnetohydrodynamic instabilities and enhance the confinement. The LHCD has been proposed as a possible means of rotation driving on a future fusion reactor. Exploring the mechanisms of LHCD rotation driving on the current tokamaks can provide important reference for future reactors. On EAST, it was previously shown that 2.45 GHz LHCD can drive plasma toroidal rotation and the change of edge plasma rotation leads the co-current core rotation to increase. At higher frequency, 4.6 GHz lower hybrid wave can more effectively drive co-current plasma toroidal rotation. On EAST, at the lower current, the effects of different LHCD power on plasma toroidal rotation are analyzed. Higher power LHCD has a better driving efficiency. The effect of safety factor (q) profile on toroidal rotation is also presented. The LHCD can change the profile of safety factor due to current drive. It is found that when the power exceeds 1.4MW, the q profile remains unchanged and the rotation changes only very slightly with LHCD power, suggesting that the current profile is closely related to rotation. In order to further analyze the dynamic process of plasma toroidal rotation driven by lower hybrid current drive on EAST, the toroidal momentum transport due to LHCD is deduced by using the modulated LHCD power injection. Based on the momentum balance equation, the toroidal momentum diffusion coefficient (χφ) and the toroidal momentum pinch coefficient (Vpinch) are obtained by the method of separation of variables and Fourier analysis for the region where the external momentum source can be ignored. It is found that the momentum diffusion coefficient (χφ) and momentum pinch coefficient (Vpinch) tend to increase from the core to the outer region. This is consistent with the characteristic that the toroidal rotation velocity first changes in the outer region and then propagates to the core when the toroidal rotation is driven by LHCD.
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Keywords:
- lower hybrid current drive /
- toroidal rotation velocity /
- safety factor /
- toroidal momentum transport
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图 1 典型参数随时间变化的波形图 (#70938) (a) 等离子体电流 (黑色), 低杂波功率 (蓝色); (b) 环电压 (黑色)和内感 (蓝色); (c) 芯部弦平均电子密度; (d) 储能; (e) 芯部电子温度 (黑色)和芯部离子温度 (红色); (f) 芯部环向速度变化
Fig. 1. Waveforms of typical parameters of an LHCD shot (#70938) on EAST: (a) Plasma current (black) and LHCD power)(blue); (b) loop voltage (black) and internal inductance (blue); (c) central line averaged electron density; (d) stored energy; (e) central ion (red) and electron (black) temperature; (f) the change of core toroidal rotation velocity.
图 2 不同低杂波功率下典型参数随时间变化的波形图 (a) 等离子体电流; (b) 芯部弦平均电子密度; (c) 低杂波功率; (d) 芯部环向旋转速度变化
Fig. 2. Waveforms of typical parameters at different LHCD power levels: (a) plasma current; (b) central line averaged electron density; (c) LHCD power; (d) the change of core toroidal rotation velocity.
图 3 低杂波功率与芯部环向旋转速度变化关系
Fig. 3. The relationship between the change of core toroidal rotation velocity and LHCD power.
图 5 典型参数随时间变化的波形图 (a) 电子温度; (b) 离子温度; (c) 环向旋转速度对调制束的响应; (d) LHCD功率(黑色)和芯部弦平均电子密度(蓝色)
Fig. 5. Waveforms of typical parameters: (a) Electron temperature; (b) ion temperature; (c) toroidal rotation velocity; (d) LHCD power (black) and central line averaged electron density (blue).
图 6 (a) 环向速度调制幅度(Vt0)的剖面图; (b) 环向速度相位变换(φ)的剖面图
Fig. 6. (a) Profile of toroidal velocity modulation amplitude; (b) profile of toroidal velocity phase transformation.
图 7 (a) 环向动量扩散系数(χφ) 的剖面图; (b) 箍缩系数(Vpinch)的剖面图
Fig. 7. (a) Profile of toroidal momentum diffusion coefficient; (b) profile of toroidal momentum pinch coefficient.
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[1] Betti R, Freidberg J P 1995 Phys. Rev. Lett. 74 2949
Google Scholar
[2] Rice J E, Podpaly Y A, Reinke M L, Gao C, Shiraiwa S, Terry J L, Theiler C, Wallace G M, Bonoli P T, Brunner D 2013 Nucl. Fusion. 53 093015
Google Scholar
[3] Rice J E, Gao C, Mumgaard R, et al. 2016 Nucl. Fusion. 56 036015
Google Scholar
[4] Chouli B, Fenzi C, Garbet X, et al. 2014 Plasma Phys. Controlled Fusion. 56 095018
Google Scholar
[5] Chouli B, Fenzi C, Garbet X, Bourdelle C, Sarazin Y, Rice J, Aniel T, Artaud J F, Baiocchi B, Basiuk V, Cottier P, Decker J, Imbeaux F, Irishkin M, Mazon D, Schneider M, the Tore Supra Team 2015 Plasma Phys. Controlled Fusion. 57 125007
Google Scholar
[6] Shi Y, Xu G, Wang F, Wang M, Fu J, Li Y, Zhang W, Chang J, Lv B, Qian J, Shan J, Liu F, Ding S, Wan B, Lee S G, Bitter M, Hill K 2011 Phys. Rev. Lett. 106 235001
Google Scholar
[7] Yin X H, Chen J, Hu R J, Yi Y Y, Wang F D, Fu J, Ding B J, Wang M, Liu F K, Zang Q, Shi Y J, Lyu B, Wan B N, the EAST team 2017 Chin. Phys. B 26 115203
Google Scholar
[8] Koide Y, Tuda T, Ushigusa K, Asakura N, Sakasai A, Ide S, Ishida S, Kikuchi M, Azumi M, Funahashi A 1992 Plasma Phys. Control. Nucl. Fusion. Res. 1 777
[9] Eriksson L G, Hellsten T, Nave F, Brzozowski J, Holmström K, Johnson T, Ongena J, Zastrow K D 2009 Plasma Phys. Controlled Fusion. 51 044008
Google Scholar
[10] Nave M F F, Kirov K, Bernardo J, Brix M, Ferreira J, Giroud C, Hawkes N, Hellsten T, Jonsson T, Mailloux J, Ongena J, Parra F, JET Contributors 2017 Nucl. Fusion. 57 034002
Google Scholar
[11] Wan B N, Liang Y F, Gong X Z, Li J G, Xiang N, Xu G S, Sun Y W, Wang L, Qian J P, Liu H Q, Zhang X D, Hu L Q, Hu J S, Liu F K, Hu C D, Zhao Y P, Zeng L, Wang M, Xu H D, Luo G N 2017 Nucl. Fusion. 57 102019
Google Scholar
[12] Ding B J, Li Y C, Zhang L, et al. 2015 Nucl. Fusion. 55 093030
Google Scholar
[13] Lyu B, Wang F D, Pan X Y, et al. 2014 Rev. Sci. Instruments. 85 11E406
Google Scholar
[14] Lyu B, Chen J, Hu R J, et al. 2016 Rev. Sci. Instruments. 87 11E326
Google Scholar
[15] Lyu B, Chen J, Hu R J, et al. 2018 Rev. Sci. Instruments. 89 10F112
Google Scholar
[16] Li Y Y, Fu J, Lyu B, Du X W, Li C Y, Zhang Y, Yin X H, Yu Y, Wang Q P, von Hellermann M 2014 Rev. Sci. Instruments. 85 11E428
Google Scholar
[17] Rice J E, Ince-Cushman A, deGrassie J S, Eriksson L G, Sakamoto Y, Scarabosio A, Bortolon A, Burrell K H, Duval B P, Fenzi-Bonizec C, Greenwald M J, Groebner R J, Hoang G T, Koide Y, Marmar E S, Pochelon A, Podpaly Y 2007 Nucl. Fusion. 47 1618
Google Scholar
[18] Liu H Q, Qian J P, Jie Y X, et al. 2016 Rev. Sci. Instruments. 87 11D903
Google Scholar
[19] Yoshida M, Koide Y, Takenaga H, Urano H, Oyama N, Kamiya K, Sakamoto Y, Kamada Y and the JT-60 Team 2006 Plasma Phys. Control. Fusion. 48 1673
Google Scholar
[20] Yoshida M, Koide Y, Takenaga H, Urano H, Oyama N, Kamiya K, Sakamoto Y, Matsunaga G, Kamada Y and the JT-60U Team 2007 Nucl. Fusion. 47 856
Google Scholar
[21] Ida K, Miura Y, Itoh K, Itoh S I, Matsuda T 1998 J. Phys. Soc. Japan. 67 4089
Google Scholar
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