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Tokamak experiments show that the plasma empirical energy confinement scaling law varies with plasma ion mass (Ai) in a certain range under conditions of different plasma parameters or different devices. In order to understand such a modification of the empirical energy confinement scaling law, the isotope mass dependence of ion temperature gradient (ITG, including impurity modes) turbulence driven transport in the presence of tungsten impurity ions in tokamak plasma is studied by employing the gyrokinetic theory. The effect of heavy (tungsten) impurity ions on ITG and impurity mode is revealed to modify significantly the isotope mass dependence and effective charge effect. As the charge number of impurity ions (Z) or impurity charge concentration (fz) changes, the theoretical scaling law of ITG turbulence transport varies substantially in a relatively large range. The maximum growth rate of ITG mode scales as Mi-0.48 -0.12, whilst that of impurity mode scales as Mi-0.46 -0.3. Here, Mi is the mass number of primary ion in the plasma. In both cases the fitting index with Mi deviates further away from -0.5 when impurity charge concentration fz increases. The isotope mass dependence of ITG turbulence gradually weakens when the effective charge number Zeff increases. The isotope mass dependence of impurity mode turbulence also weakens with Zeff increasing for the same impurity ion charge number (Z). In contrast, the isotope mass dependence gradually strengthens with effective charge number Zeff increasing for the same impurity charge concentration (fz). On average, the maximum growth rates of impurity mode scale roughly as max~Mi-0.35Zeff1.5 and max~Mi-0.4Zeff1, respectively, for Zeff 3 and Zeff 3. The reason for the deviation of isotope scaling law from the normal case is investigated deliberately, and it is demonstrated that the isotope scaling index deviates from -0.5 more or less due to the fact that the impurity species, charge number and impurity concentrations vary in a certain range. These results demonstrate that it is impossible to deduce a unique isotope scaling law due to the variety of micro-instabilities and various plasma parameter regimes in tokamak plasma, which is consistent with the experimental observations. These results may contribute to the transport study involving heavy (tungsten) impurity ions in ITER discharge scenario investigation.
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Keywords:
- ion temperature gradient mode /
- impurity mode /
- anomalous transport /
- isotope effect
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[2] Lorenzini R, Agostini M, Auriemma F, Carraro L, de Masi G, Fassina A, Franz P, Gobbin M, Innocente P, Puiatti M E, Scarin P, Zaniol B, Zuin M 2015 Nucl. Fusion 55 043012
[3] Urano H, Takizuka T, Aiba N, Kikuchi M, Nakano T, Fujita T, Oyama N, Kamada Y, Hayashi N, the JT-6 Team 2013 Nucl. Fusion 53 083003
[4] Sokolov V, Sen A K 2003 Phys. Plasmas 10 3174
[5] Bessenrodt-Weberpals M, Wagner F, ASDEX Team 1993 Nucl. Fusion 33 1205
[6] Yushmanov P N, Takizuka T, Riedel K S, Kardaun O J W F, Cordey J G, Kaye S M, Post D E 1990 Nucl. Fusion 30 1999
[7] Goldston R 1984 Plasma Phys. Controll. Fusion 26 87
[8] Hugill J, Sheffiled J 1978 Nucl. Fusion 18 15
[9] Jacquinot J, the JET Team 1999 Plasma Phys. Control. Fusion 41 A13
[10] ITER Physics Expert Groups on Confinement and Transport and Confinement Modelling and Databases, ITER Physics Basic Editors 1999 Nucl. Fusion 39 2175
[11] Schneider P A, Bustos A, Hennequin P, Ryter F, Bernert M, Cavedon M, Dunne M G, Fischer R, Grler T, Happel T, Igochine V, Kurzan B, Lebschy A, McDermott R M, Morel P, Willensdorfer M, the ASDEX Upgrade Team, the EUROfusion MST1 Team 2017 Nucl. Fusion 57 066003
[12] Du H L, Sang C F, Wang L, Sun J Z, Liu S C, Wang H Q, Zhang L, Guo H Y, Wang D Z 2013 Acta Phys. Sin. 62 245206 (in Chinese) [杜海龙, 桑超峰, 王亮, 孙继忠, 刘少承, 汪惠乾, 张凌, 郭后扬, 王德真 2013 物理学报 62 245206]
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[15] Pusztai I, Mollen A, Fulop T, Candy J 2013 Plasma Phys. Control. Fusion 55 074012
[16] Dong J Q, Horton W, Dorland W 1994 Phys. Plasmas 1 3635
[17] Tokar M Z, Kalupin D, Unterberg B 2004 Phys. Rev. Lett. 92 215001
[18] Connor J W, Pogutse O P 2001 Plasma Phys. Control. Fusion 43 155
[19] Shen Y, Dong J Q, Sun A P, Qu H P, Lu G M, He Z X, He H D, Wang L F 2016 Plasma Phys. Control. Fusion 58 045028
[20] Shen Y, Dong J Q, Han M K, Sun A P, Shi Z B 2018 Nucl. Fusion 58 076007
[21] Lu H L, Wang S J 2009 Acta Phys. Sin. 58 354 (in Chinese) [陆赫林, 王顺金 2009 物理学报 58 354]
[22] Zhang K, Cui Z Y, Sun P, Dong C F, Deng W, Dong Y B, Song S D, Jiang M, Li Y G, Lu P, Yang Q W 2016 Chin. Phys. B 25 065202
[23] Zhou Q, Wang B N, Wu Z W, Huang J 2005 Chin. Phys. B 14 2539
[24] Cui X W, Cui Z Y, Feng B B, Pan Y D, Zhou H Y, Sun P, Fu B Z, Lu P, Dong Y B, Gao J M, Song S D, Yang Q W 2013 Chin. Phys. B 22 125201
[25] Pusztai I, Candy J, Gohil P 2011 Phys. Plasmas 18 122501
[26] Guo W X, Wang L, Zhuang G 2016 Phys. Plasmas 23 112301
[27] Xu W, Wan B N, Xie J K 2003 Acta Phys. Sin. 52 1970 (in Chinese) [徐伟, 万宝年, 谢纪康 2003 物理学报 52 1970]
[28] Zhang H, Wen S L, Pan M, Huang Z, Zhao Y, Liu X, Chen J M 2016 Chin. Phys. B 25 056102
[29] Coppi B 1991 Proceedings of the 13th International Conference in Plasma Physics and Controlled Nuclear Fusion Research Washington, USA, July 3-7, 1990 p413
[30] Dominguez R R 1991 Nucl. Fusion 31 2063
[31] Chen L, Tsai S T 1983 Plasma Phys. 25 349
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[1] Sokolov V, Sen A K 2002 Phys. Rev. Lett. 89 095001
[2] Lorenzini R, Agostini M, Auriemma F, Carraro L, de Masi G, Fassina A, Franz P, Gobbin M, Innocente P, Puiatti M E, Scarin P, Zaniol B, Zuin M 2015 Nucl. Fusion 55 043012
[3] Urano H, Takizuka T, Aiba N, Kikuchi M, Nakano T, Fujita T, Oyama N, Kamada Y, Hayashi N, the JT-6 Team 2013 Nucl. Fusion 53 083003
[4] Sokolov V, Sen A K 2003 Phys. Plasmas 10 3174
[5] Bessenrodt-Weberpals M, Wagner F, ASDEX Team 1993 Nucl. Fusion 33 1205
[6] Yushmanov P N, Takizuka T, Riedel K S, Kardaun O J W F, Cordey J G, Kaye S M, Post D E 1990 Nucl. Fusion 30 1999
[7] Goldston R 1984 Plasma Phys. Controll. Fusion 26 87
[8] Hugill J, Sheffiled J 1978 Nucl. Fusion 18 15
[9] Jacquinot J, the JET Team 1999 Plasma Phys. Control. Fusion 41 A13
[10] ITER Physics Expert Groups on Confinement and Transport and Confinement Modelling and Databases, ITER Physics Basic Editors 1999 Nucl. Fusion 39 2175
[11] Schneider P A, Bustos A, Hennequin P, Ryter F, Bernert M, Cavedon M, Dunne M G, Fischer R, Grler T, Happel T, Igochine V, Kurzan B, Lebschy A, McDermott R M, Morel P, Willensdorfer M, the ASDEX Upgrade Team, the EUROfusion MST1 Team 2017 Nucl. Fusion 57 066003
[12] Du H L, Sang C F, Wang L, Sun J Z, Liu S C, Wang H Q, Zhang L, Guo H Y, Wang D Z 2013 Acta Phys. Sin. 62 245206 (in Chinese) [杜海龙, 桑超峰, 王亮, 孙继忠, 刘少承, 汪惠乾, 张凌, 郭后扬, 王德真 2013 物理学报 62 245206]
[13] Itoh S I, Itoh K 2012 Chin. Phys. B 21 095201
[14] Li Q L, Zheng Y Z, Cheng F Y, Deng X B, Deng D S, You P L, Liu G A, Chen X D 2001 Acta Phys. Sin. 50 507 (in Chinese) [李齐良, 郑永真, 程发银, 邓小波, 邓冬生, 游佩林, 刘贵昂, 陈向东 2001 物理学报 50 507]
[15] Pusztai I, Mollen A, Fulop T, Candy J 2013 Plasma Phys. Control. Fusion 55 074012
[16] Dong J Q, Horton W, Dorland W 1994 Phys. Plasmas 1 3635
[17] Tokar M Z, Kalupin D, Unterberg B 2004 Phys. Rev. Lett. 92 215001
[18] Connor J W, Pogutse O P 2001 Plasma Phys. Control. Fusion 43 155
[19] Shen Y, Dong J Q, Sun A P, Qu H P, Lu G M, He Z X, He H D, Wang L F 2016 Plasma Phys. Control. Fusion 58 045028
[20] Shen Y, Dong J Q, Han M K, Sun A P, Shi Z B 2018 Nucl. Fusion 58 076007
[21] Lu H L, Wang S J 2009 Acta Phys. Sin. 58 354 (in Chinese) [陆赫林, 王顺金 2009 物理学报 58 354]
[22] Zhang K, Cui Z Y, Sun P, Dong C F, Deng W, Dong Y B, Song S D, Jiang M, Li Y G, Lu P, Yang Q W 2016 Chin. Phys. B 25 065202
[23] Zhou Q, Wang B N, Wu Z W, Huang J 2005 Chin. Phys. B 14 2539
[24] Cui X W, Cui Z Y, Feng B B, Pan Y D, Zhou H Y, Sun P, Fu B Z, Lu P, Dong Y B, Gao J M, Song S D, Yang Q W 2013 Chin. Phys. B 22 125201
[25] Pusztai I, Candy J, Gohil P 2011 Phys. Plasmas 18 122501
[26] Guo W X, Wang L, Zhuang G 2016 Phys. Plasmas 23 112301
[27] Xu W, Wan B N, Xie J K 2003 Acta Phys. Sin. 52 1970 (in Chinese) [徐伟, 万宝年, 谢纪康 2003 物理学报 52 1970]
[28] Zhang H, Wen S L, Pan M, Huang Z, Zhao Y, Liu X, Chen J M 2016 Chin. Phys. B 25 056102
[29] Coppi B 1991 Proceedings of the 13th International Conference in Plasma Physics and Controlled Nuclear Fusion Research Washington, USA, July 3-7, 1990 p413
[30] Dominguez R R 1991 Nucl. Fusion 31 2063
[31] Chen L, Tsai S T 1983 Plasma Phys. 25 349
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