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Steady state operation is essential for Tokamak-based fusion reactor, in which the plasma current has to be fully sustained and controlled by non-inductive methods. Lower-hybrid current drive is the most effective radio-frequency current drive method, which, however, has the drawback that the driven current profile is difficult to control. Electron cyclotron current drive has the ability to deposit power and drive current in a highly localized and robustly controllable way, while the efficiency of electron cyclotron current drive is known to be significantly lower than that of lower-hybrid current drive. Due to those complementary features, the combinative usage of lower-hybrid wave and electron cyclotron wave has been proposed. The current driven by simultaneously using the waves might be significantly larger than the sum of the currents driven by the waves individually in the same plasma conditions, which is the so-called synergy effect. While the lower-hybrid current drive and the electron cyclotron current drive are both affected by the trapping effect, which implies that the synergy effect between lower-hybrid current drive and the electron cyclotron current drive may also closely related to the trapping effect. In this paper, the effects of trapping on the synergy of lower-hybrid current drive and the electron cyclotron current drive are investigated by solving the bounce-averaged quasi-linear equation with different trapping angles. The diffusions induced by the lower-hybrid wave and the electron cyclotron wave are considered simultaneously. The resulting steady-state electron distribution function as a balance between the collisions and the wave-induced diffusions is obtained numerically by the CQL3D code, which is then integrated to calculate the driven plasma current. The velocity-space fluxes are analyzed for understanding the mechanism and the physics of the synergy process. It is found that the currents driven by the waves decrease as trapping angle increases. The synergy factors also decrease as trapping angle increases, which means that the current drive processes in the synergy case are more sensitive to the trapping effect than in the single wave case. The current driven by electron cyclotron wave drops rapidly with the increase of trapping angle, while the existence of lower-hybrid wave is helpful in decelerating the dropping. The lower-hybrid wave reduces the dependency of the electron cyclotron current drive on the trapping effect. The decouple effect turns stronger as the resonance region of the lower-hybrid wave becomes wider. Increasing the power of the electron cyclotron wave leads to more accelerated electrons and more electrons with relatively high parallel velocities, which results in stronger synergy effect and less dependence on trapping.
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Keywords:
- trapping electrons /
- synergy effects /
- lower-hybrid waves /
- electron cyclotron waves
[1] Gormezano C, Sips A C C, Luce T C, Ide S, Becoulet A, Litaudon X, Isayama A, Hobirk J, Wade M R, Oikawa T, Prater R, Zvonkov A, Lloyd B, Suzuki T, Barbato E, Bonoli P, Phillips C K, Vdovin V, Joffrin E, Casper T, Ferron J, Mazon D, Moreau D, Bundy R, Kessel C, Fukuyama A, Hayashi N, Imbeaux F, Murakami M, Polevoi A R, St John H E 2007 Nucl. Fusion 47 S285
[2] Fisch N J 1978 Phys. Rev. Lett. 41 873
[3] Bonoli P T, Englade R C 1986 Phys. Fluids 29 2937
[4] Peysson Y, Decker J, Nilsson E, Artaud J F, Ekedahl A, Goniche M, Hillairet J, Ding B, Li M, Bonoli P T, Shiraiwa S, Madi M 2016 Plasma Phys. Contr. Fusion 58 044008
[5] Cesario R, Amicucci L, Castaldo C, Kempenaars M, Jachmich S, Mailloux J, Tudisco O, Galli A, Krivska A, Contributors J E 2011 Plasma Phys. Contr. Fusion 53 085011
[6] Ding B J, Li M H, Liu F K, Shan J F, Li Y C, Wang M, Liu L, Zhao L M, Yang Y, Wu Z G, Feng J Q, Hu H C, Jia H, Cheng M, Zang Q, Lyu B, Duan Y M, Lin S Y, Wu J H, Hillairet J, Ekedahl A, Peysson Y, Goniche M, Tuccillo A A, Cesario R, Amicucci L, Shen B, Gong X Z, Xu G S, Zhao H L, Hu L Q, Li J G, Wan B N, EAST Team 2017 Nucl. Fusion 57 022022
[7] Goniche M, Sharma P K, Basiuk V, Baranov Y, Castaldo C, Cesario R, Decker J, Delpech L, Ekedahl A, Hillairet J, Kirov K, Mazon D, Oosako T, Peysson Y, Prou M 2011 AIP Conf. Proc. 1406 407
[8] Li J G, Luo J R, Wan B N, Liu Y X, Gong X Z, Li D C, Jie Y X, Li Z X, Xu X D 2000 Acta Phys. Sin. 49 2414 (in Chinese) [李建刚, 罗家融, 万宝年, 刘岳修, 龚先祖, 李多传, 揭银先, 李智秀, 徐东 2000 物理学报 49 2414]
[9] Decker J, Peysson Y, Hillairet J, Artaud J F, Basiuk V, Becoulet A, Ekedahl A, Goniche M, Hoang G T, Imbeaux F, Ram A K, Schneider M 2011 Nucl. Fusion 51 073025
[10] Song Y T, Wu S T, Li J G, Wan B N, Wan Y X, Fu P, Ye M Y, Zheng J X, Lu K, Gao X G, Liu S M, Liu X F, Lei M Z, Peng X B, Chen Y 2014 IEEE Trans. Plasma Sci. 42 503
[11] Prater R 2004 Phys. Plasmas 11 2349
[12] Gnter S, Gantenbein G, Gude A, Igochine V, Maraschek M, Mck A, Saarelma S, Sauter O, Sips A C C, Zohm H 2003 Nucl. Fusion 43 161
[13] Henderson M A, Alberti S, Angioni C, Arnoux G, Behn R, Blanchard P, Bosshard P, Camenen Y, Coda S, Condrea I, Goodman T P, Hofmann F, Hogge J P, Karpushov A, Manini A, Martynov A, Moret J M, Nikkola P, Nelson-Melby E, Pochelon A, Porte L, Sauter O, Ahmed S M, Andrebe Y, Appert K, Chavan R, Degeling A, Duval B P, Etienne P, Fasel D, Fasoli A, Favez J Y, Furno I, Horacek J, Isoz P, Joye B, Klimanov I, Lavanchy P, Lister J B, Llobet X, Magnin J C, Marletaz B, Marmillod P, Martin Y, Mayor J M, Mylnar J, Paris P J, Perez A, Peysson Y, Pitts R A, Raju D, Reimerdes H, Scarabosio A, Scavino E, Seo S H, Siravo U, Sushkov A, Tonetti G, Tran M Q, Weisen H, Wischmeier M, Zabolotsky A, Yhuang G 2003 Phys. Plasmas 10 1796
[14] Fisch N J, Boozer A H 1980 Phys. Rev. Lett. 45 720
[15] Alikaev V V, Parail V V 1991 Plasma Phys. Contr. Fusion 33 1639
[16] Ridolfini V P, Barbato E, Bruschi A, Dumont R, Gandini F, Giruzzi G, Gormezano C, Granucci G, Panaccione L, Peysson Y, Podda S, Saveliev A N 2001 AIP Conf. Proc. 595 225
[17] Chen S Y, Tang C J, Zhang X J 2013 Chin. Phys. Lett. 30 065202
[18] Giruzzi G, Artaud J F, Dumont R J, Imbeaux F, Bibet P, Berger-By G, Bouquey F, Clary J, Darbos C, Ekedahl A, Hoang G T, Lennholm M, Maget P, Magne R, Segui J L, Bruschi A, Granucci G 2004 Phys. Rev. Lett. 93 255002
[19] Fidone I, Giruzzi G, Granata G, Meyer R L 1984 Phys. Fluids 27 2468
[20] Maehara T, Yoshimura S, Minami T, Hanada K, Nakamura M, Maekawa T, Terumichi Y 1998 Nucl. Fusion 38 39
[21] Chen S Y, Hong B B, Liu Y, Lu W, Huang J, Tang C J, Ding X T, Zhang X J, Hu Y J 2012 Plasma Phys. Contr. Fusion 54 115002
[22] Huang J, Bai X Y, Zeng H, Tang C J 2013 Acta Phys. Sin. 62 025202 (in Chinese) [黄捷, 白兴宇, 曾浩, 唐昌建 2013 物理学报 62 025202]
[23] Hong B B, Chen S Y, Tang C J, Zhang X J, Hu Y J 2012 Acta Phys. Sin. 61 115207 (in Chinese) [洪斌斌, 陈少永, 唐昌建, 张新军, 胡有俊 2012 物理学报 61 115207]
[24] Dumont R J, Giruzzi G 2005 Radio Frequency Power in Plasmas 787 257
[25] Dumont R J, Giruzzi G 2004 Phys. Plasmas 11 3449
[26] Jiao Y M, Long Y X, Dong J Q, Shi B R, Gao Q D 2005 Acta Phys. Sin. 54 180 (in Chinese) [焦一鸣, 龙永兴, 董家齐, 石秉仁, 高庆弟 2005 物理学报 54 180]
[27] Harvey R W, Mccoy M G 1992 IAEA Technical Committee Meeting on Advances in Simulation and Modeling of Thermonuclear Plasmas (Montreal: IAEA Institute of Physics Publishing) pp489-526
[28] Kennel C F, Engelmann F 1966 Phys. Fluids 9 2377
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[1] Gormezano C, Sips A C C, Luce T C, Ide S, Becoulet A, Litaudon X, Isayama A, Hobirk J, Wade M R, Oikawa T, Prater R, Zvonkov A, Lloyd B, Suzuki T, Barbato E, Bonoli P, Phillips C K, Vdovin V, Joffrin E, Casper T, Ferron J, Mazon D, Moreau D, Bundy R, Kessel C, Fukuyama A, Hayashi N, Imbeaux F, Murakami M, Polevoi A R, St John H E 2007 Nucl. Fusion 47 S285
[2] Fisch N J 1978 Phys. Rev. Lett. 41 873
[3] Bonoli P T, Englade R C 1986 Phys. Fluids 29 2937
[4] Peysson Y, Decker J, Nilsson E, Artaud J F, Ekedahl A, Goniche M, Hillairet J, Ding B, Li M, Bonoli P T, Shiraiwa S, Madi M 2016 Plasma Phys. Contr. Fusion 58 044008
[5] Cesario R, Amicucci L, Castaldo C, Kempenaars M, Jachmich S, Mailloux J, Tudisco O, Galli A, Krivska A, Contributors J E 2011 Plasma Phys. Contr. Fusion 53 085011
[6] Ding B J, Li M H, Liu F K, Shan J F, Li Y C, Wang M, Liu L, Zhao L M, Yang Y, Wu Z G, Feng J Q, Hu H C, Jia H, Cheng M, Zang Q, Lyu B, Duan Y M, Lin S Y, Wu J H, Hillairet J, Ekedahl A, Peysson Y, Goniche M, Tuccillo A A, Cesario R, Amicucci L, Shen B, Gong X Z, Xu G S, Zhao H L, Hu L Q, Li J G, Wan B N, EAST Team 2017 Nucl. Fusion 57 022022
[7] Goniche M, Sharma P K, Basiuk V, Baranov Y, Castaldo C, Cesario R, Decker J, Delpech L, Ekedahl A, Hillairet J, Kirov K, Mazon D, Oosako T, Peysson Y, Prou M 2011 AIP Conf. Proc. 1406 407
[8] Li J G, Luo J R, Wan B N, Liu Y X, Gong X Z, Li D C, Jie Y X, Li Z X, Xu X D 2000 Acta Phys. Sin. 49 2414 (in Chinese) [李建刚, 罗家融, 万宝年, 刘岳修, 龚先祖, 李多传, 揭银先, 李智秀, 徐东 2000 物理学报 49 2414]
[9] Decker J, Peysson Y, Hillairet J, Artaud J F, Basiuk V, Becoulet A, Ekedahl A, Goniche M, Hoang G T, Imbeaux F, Ram A K, Schneider M 2011 Nucl. Fusion 51 073025
[10] Song Y T, Wu S T, Li J G, Wan B N, Wan Y X, Fu P, Ye M Y, Zheng J X, Lu K, Gao X G, Liu S M, Liu X F, Lei M Z, Peng X B, Chen Y 2014 IEEE Trans. Plasma Sci. 42 503
[11] Prater R 2004 Phys. Plasmas 11 2349
[12] Gnter S, Gantenbein G, Gude A, Igochine V, Maraschek M, Mck A, Saarelma S, Sauter O, Sips A C C, Zohm H 2003 Nucl. Fusion 43 161
[13] Henderson M A, Alberti S, Angioni C, Arnoux G, Behn R, Blanchard P, Bosshard P, Camenen Y, Coda S, Condrea I, Goodman T P, Hofmann F, Hogge J P, Karpushov A, Manini A, Martynov A, Moret J M, Nikkola P, Nelson-Melby E, Pochelon A, Porte L, Sauter O, Ahmed S M, Andrebe Y, Appert K, Chavan R, Degeling A, Duval B P, Etienne P, Fasel D, Fasoli A, Favez J Y, Furno I, Horacek J, Isoz P, Joye B, Klimanov I, Lavanchy P, Lister J B, Llobet X, Magnin J C, Marletaz B, Marmillod P, Martin Y, Mayor J M, Mylnar J, Paris P J, Perez A, Peysson Y, Pitts R A, Raju D, Reimerdes H, Scarabosio A, Scavino E, Seo S H, Siravo U, Sushkov A, Tonetti G, Tran M Q, Weisen H, Wischmeier M, Zabolotsky A, Yhuang G 2003 Phys. Plasmas 10 1796
[14] Fisch N J, Boozer A H 1980 Phys. Rev. Lett. 45 720
[15] Alikaev V V, Parail V V 1991 Plasma Phys. Contr. Fusion 33 1639
[16] Ridolfini V P, Barbato E, Bruschi A, Dumont R, Gandini F, Giruzzi G, Gormezano C, Granucci G, Panaccione L, Peysson Y, Podda S, Saveliev A N 2001 AIP Conf. Proc. 595 225
[17] Chen S Y, Tang C J, Zhang X J 2013 Chin. Phys. Lett. 30 065202
[18] Giruzzi G, Artaud J F, Dumont R J, Imbeaux F, Bibet P, Berger-By G, Bouquey F, Clary J, Darbos C, Ekedahl A, Hoang G T, Lennholm M, Maget P, Magne R, Segui J L, Bruschi A, Granucci G 2004 Phys. Rev. Lett. 93 255002
[19] Fidone I, Giruzzi G, Granata G, Meyer R L 1984 Phys. Fluids 27 2468
[20] Maehara T, Yoshimura S, Minami T, Hanada K, Nakamura M, Maekawa T, Terumichi Y 1998 Nucl. Fusion 38 39
[21] Chen S Y, Hong B B, Liu Y, Lu W, Huang J, Tang C J, Ding X T, Zhang X J, Hu Y J 2012 Plasma Phys. Contr. Fusion 54 115002
[22] Huang J, Bai X Y, Zeng H, Tang C J 2013 Acta Phys. Sin. 62 025202 (in Chinese) [黄捷, 白兴宇, 曾浩, 唐昌建 2013 物理学报 62 025202]
[23] Hong B B, Chen S Y, Tang C J, Zhang X J, Hu Y J 2012 Acta Phys. Sin. 61 115207 (in Chinese) [洪斌斌, 陈少永, 唐昌建, 张新军, 胡有俊 2012 物理学报 61 115207]
[24] Dumont R J, Giruzzi G 2005 Radio Frequency Power in Plasmas 787 257
[25] Dumont R J, Giruzzi G 2004 Phys. Plasmas 11 3449
[26] Jiao Y M, Long Y X, Dong J Q, Shi B R, Gao Q D 2005 Acta Phys. Sin. 54 180 (in Chinese) [焦一鸣, 龙永兴, 董家齐, 石秉仁, 高庆弟 2005 物理学报 54 180]
[27] Harvey R W, Mccoy M G 1992 IAEA Technical Committee Meeting on Advances in Simulation and Modeling of Thermonuclear Plasmas (Montreal: IAEA Institute of Physics Publishing) pp489-526
[28] Kennel C F, Engelmann F 1966 Phys. Fluids 9 2377
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