Abstract
A multi-machine study has been carried out to investigate the impact of a strongly bounded wave propagation domain on the Lower Hybrid current drive, a condition which occurs principally in high aspect ratio tokamaks. In this regime, the condition of kinetic resonance can be far above the upper boundary of the propagation domain, and may not be achieved by the usual toroidal upshift. Therefore no tail of fast electrons can be pulled out from the thermal bulk. Nevertheless, while tokamak plasmas are in principle almost transparent to the wave in this regime so-called “unbridgeable spectral gap”, full current drive is well achieved for the two tokamaks considered in this study, TRIAM-1M (Zushi et al. Nucl Fusion 43:1600, 2003) and WEST (Bourdelle et al. Nucl Fusion 55:063017, 2015), both characterized by a very large aspect ratio \(R/a>5.5\). The case of the high aspect ratio tokamak HL-2A (Liu et al. Nucl Fusion 45:S239, 2005) for which the wave propagation domain has also an upper boundary, but close to the resonance condition, is considered by comparison. First principles modeling of the rf-driven current and the fast electron bremsstrahlung using the ALOHA/C3PO/LUKE/R5-X2 chain of codes shows unambiguously that the spectral gap must be already filled at the separatrix in order to reproduce quantitatively observations and some important parametric dependencies. This result is an important milestone in the physics understanding of the Lower Hybrid current drive, highlighting the existence of a powerful and likely universal alternative mechanism to bridge the spectral gap, that is not related to toroidal magnetic refraction. With an initially broad power spectrum, lobes with low parallel refractive indexes that carry most of the plasma current can be absorbed in almost single pass, restoring the full validity of the ray-tracing approximation for describing the propagation of the Lower Hybrid wave in cold plasmas.
Similar content being viewed by others
References
P.T. Bonoli, Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters. Phys. Plasmas 21, 061508 (2014)
Y. Peysson, P.T. Bonoli, J. Chen, A. Garofalo, J. Hillairet, M. Li, J. Qian, S. Shiraiwa, J. Decker, B.J. Ding, A. Ekedahl, M. Goniche, X. Zhai, Current challenges in the first principle quantitative modelling of the lower hybrid current drive in tokamaks, in EPJ Web of Conferences, vol. 157 (2017), p. 02007
Y. Peysson and the TORE SUPRA Team, Progress towards high-power lower hybrid current drive in TORE SUPRA. Plasma Phys. Control. Fusion 42(12B), 87–114 (2000)
O. Barana, D. Mazon, L. Laborde, F. Turco, Feedback control of the lower hybrid power deposition profile on tore supra. Plasma Phys. Control. Fusion 49, 947–967 (2007)
A. Schmidt, P.T. Bonoli, O. Meneghini, R.R. Parker, M. Porkolab, S. Shiraiwa, G. Wallace, J.C. Wright, R.W. Harvey, J.R. Wilson, Investigation of lower hybrid physics through power modulation experiments on Alcator C-Mod. Phys. Plasmas 18, 056122 (2011)
E. Nilsson, J. Decker, Y. Peysson, J.-F. Artaud, A. Ekedahl, J. Hillairet, T. Aniel, V. Basiuk, M. Goniche, F. Imbeaux, D. Mazon, P. Sharma, Comparative modelling of lower hybrid current drive with two launcher designs in the tore supra tokamak. Nucl. Fusion 53, 083018 (2013)
R.T. Mumgaard, Lower hybrid current drive on Alcator C-Mod: measurements with an upgraded MSE diagnostic and comparisons to simulation. Ph.D. thesis, Massachusetts Institute of Technology (2015)
P.T. Bonoli, Linear theory of lower hybrid heating. IEEE Trans. Plasma Sci. PS–12(2), 95–107 (1984)
N.J. Fisch, Theory of current drive in plasmas. Rev. Mod. Phys. 59(1), 175–234 (1987)
Y.F. Baranov, V.I. Fedorov, Ray-tracing for lower-hybrid waves in a tokamak. Sov. Tech. Phys. Lett. 4(7), 322–323 (1978)
P.T. Bonoli, R.C. Englade, Simulation model for lower hybrid current drive. Phys. Fluids 29(9), 2937–2950 (1986)
J.C. Wright, P.T. Bonoli, M. Brambilla, F. Meo, E. D’Azevedo, D.B. Batchelor, E.F. Jaeger, L.A. Berry, C.K. Phillips, A. Pletzer, Full wave simulations of fast wave mode conversion and lower hybrid wave propagation in tokamaks. Phys. Plasmas 11, 2473–2479 (2004)
J.C. Wright, P.T. Bonoli, A.E. Schmidt, C.K. Phillips, E.J. Valeo, R.W. Harvey, M.A. Brambilla, An assessment of full wave effects on the propagation and absorption of lower hybrid waves. Phys. Plasmas 16(7), 072502 (2009)
A.S. Richardson, P.T. Bonoli, J.C. Wright, The lower hybrid wave cutoff: a case study in eikonal methods. Phys. Plasmas 17, 052107–052118 (2010)
P.T. Bonoli, E. Ott, Toroldal and scattering effects on lower-hybrid wave propagation. Phys. Fluids 25(2), 359–375 (1982)
J.P. Bizarro, D. Moreau, On ray stochasticity during lower hybrid current drive in tokamaks. Phys. Fluids B 5(4), 1227–1238 (1993)
J.P. Bizarro, On the dynamics of the launched power spectrum during lower hybrid current drive in tokamaks. Nucl. Fusion 33, 831–834 (1993)
J. Decker, Y. Peysson, J.-F. Artaud, E. Nilsson, A. Ekedahl, M. Goniche, J. Hillairet, D. Mazon, Damping of lower hybrid waves in large spectral gap configurations. Phys. Plasmas 21, 092504 (2014)
Y. Peysson, J. Decker, E. Nilsson, J.F. Artaud, A. Ekedahl, M. Goniche, J. Hillairet, B. Ding, M. Li, P.T. Bonoli, S. Shiraiwa, M. Madi, Advances in modeling of lower hybrid current drive. Plasma Phys. Control. Fusion 58, 044008 (2016)
Y. Peysson, E. Sébelin, X. Litaudon, D. Moreau, J.C. Miellou, M. Shoucri, I.P. Shkarofsky, Full wave modelling of the lower hybrid current drive in tokamaks. Nucl. Fusion 38(6), 939–944 (1998)
M. Madi, Y. Peysson, J. Decker, K.Y. Kabalan, Propagation of the lower hybrid wave in a density fluctuating sol. Plasma Phys. Control. Fusion 57, 125001 (2015)
Y. Peysson, J. Decker, L. Morini, S. Coda, RF current drive and plasma fluctuations. Plasma Phys. Control. Fusion 53, 124028 (2011)
E.H. Martin, C. Lau, G.M. Wallace, S. Shiraiwa, R.T. Mumgaard, Experimental evidence of lower hybrid wave scattering in alcator c-mod due to scrape off layer density fluctuations. Nucl. Fusion 59, 076006 (2019)
C. Lau, E.H. Martin, S. Shiraiwa, G.M. Wallace, Full-wave model for the lower hybrid wave electric field vector with synthetic turbulence on alcator c-mod. Nucl. Fusion 60, 036001 (2020)
F. Paoletti, D.W. Ignat, J. Kesner, S. Bernabei, R. Kaita, B. Leblanc, F.M. Levinton, S.C. Luckhardt, Lower hybrid current drive accessibility study with reconstructed magnetic equilibria in PBX-M. Nucl. Fusion 34, 771–776 (1994)
E. Barbato, The role of non-resonant collision dissipation of lower hybrid current driven plasmas. Nucl. Fusion 51, 103032 (2011)
S. Moriyama, Y. Nakamura, A. Nagao E. Jotaki, K. Nakamura, N. Hiraki, S. Itoh Ultra-long pulse operation using lower hybrid waves on the superconducting high field tokamak triam-1m. Nucl. Fusion 30, 47–57 (1990)
H. Takahashi, The generalized accessibility and spectral gap of lower hybrid waves in tokamaks. Phys. Plasmas 1(7), 2254–2276 (1994)
H. Zushi, S. Itoh, K. Hanada, K. Nakamura, M. Sakamoto, E. Jotaki, M. Hasegawa, Y.D. Pan, S.V. Kulkarni, A. Iyomasa, S. Kawasaki, H. Nakashima, N. Yoshida, K. Tokunaga, T. Fujiwara, M. Miyamoto, H. Nakano, M. Yuno, A. Murakami, S. Nakamura, N. Sakamoto, K. Shinoda, S. Yamazoe, H. Akanishi, K. Kuramoto, Y. Matsuo, A. Iwamae, T. Fuijimoto, A. Komori, T. Morisaki, H. Suzuki, S. Masuzaki, Y. Hirooka, Y. Nakashima, O. Mitarai, Overview of steady state tokamak plasma experiments in triam-1m. Nucl. Fusion 43, 1600–1609 (2003)
C. Bourdelle, J.F. Artaud, V. Basiuk, M. Becoulet, S. Bremond, J. Bucalossi, H. Bufferand, G. Ciraolo, L. Colas, Y. Corre, X. Courtois, J. Decker, L. Delpech, P. Devynck, G. Dif-Pradalier, R.P. Doerner, D. Douai, R. Dumont, A. Ekedahl, N. Fedorczak, C. Fenzi, M. Firdaouss, J. Garcia, P. Ghendrih, C. Gil, G. Giruzzi, M. Goniche, C. Grisolia, A. Grosman, D. Guilhem, R. Guirlet, J. Gunn, P. Hennequin, J. Hillairet, T. Hoang, F. Imbeaux, I. Ivanova-Stanik, E. Joffrin, A. Kallenbach, J. Linke, T. Loarer, P. Lotte, P. Maget, Y. Marandet, M.L. Mayoral, O. Meyer, M. Missirlian, P. Mollard, P. Monier-Garbet, P. Moreau, E. Nardon, B. Pegourie, Y. Peysson, R. Sabot, F. Saint-Laurent, M. Schneider, J.M. Travere, E. Tsitrone, S. Vartanian, L. Vermare, M. Yoshida, R. Zagorski, J.E.T. Contributors, West physics basis. Nucl. Fusion 55, 063017 (2015)
Y. Liu, X.T. Ding, Q.W. Yang, L.W. Yan, D.Q. Liu, W.M. Xuan, L.Y. Chen, X.M. Song, Z. Cao, J.H. Zhang, W.C. Mao, C.P. Zhou, X.D. Li, S.J. Wang, J.C. Yan, M.N. Bu, Y.H. Chen, C.H. Cui, Z.Y. Cui, Z.C. Deng, W.Y. Hong, H.T. Hu, Y. Huang, Z.H. Kang, B. Li, W. Li, F.Z. Li, G.S. Li, H.J. Li, Q. Li, Y.G. Li, Z.J. Li, Y. Liu, Z.T. Liu, C.W. Luo, X.H. Mao, Y.D. Pan, J. Rao, K. Shao, X.Y. Song, M. Wang, M.X. Wang, Q.M. Wang, Z.G. Xiao, Y.F. Xie, L.H. Yao, L.Y. Yao, Y.J. Zheng, G.W. Zhong, Y. Zhou, C.H. Pan, Recent advances in the HL-2a tokamak experiments. Nucl. Fusion 45, S239–S244 (2005)
J. Hillairet, D. Voyer, A. Ekedahl, M. Goniche, M. Kazda, O. Meneghini, D. Milanesio, M. Preynas, Aloha: an advanced lower hybrid antenna coupling code. Nucl. Fusion 50(12), 125010 (2010)
Y. Peysson, J. Decker, L. Morini, A versatile ray-tracing code for studying RF wave propagation in toroidal magnetized plasmas. Plasma Phys. Control. Fusion 54, 045003 (2012)
Y. Peysson, J. Decker, Numerical simulations of the radio-frequency driven toroidal current in tokamaks. Fusion Sci. Technol. 65, 22–42 (2014)
Y. Peysson, J. Decker, Fast electron bremsstrahlung in axisymmetric magnetic configuration. Phys. Plasmas 15(9), 092509 (2008)
M. Brambilla, Kinetic Theory of Plasma Waves (Oxford Science Publications, Oxford, 1998)
X. Bai, B. Lu, H. Zeng, J. Liang, C. Wang, G.Xiao, H. Wang, Y. Chen, J. Wang, K. Feng, S. Song, M. Huang, J. Rao, X. Song, R. Mao, J. Cheng, Y. Zhang, D. Yu, Y. Zhou, Z. Shi, A. Ekedahl, J. Hillairet, E. Bertrand, L. Delpech, G. Giruzzi, T. Hoang, R. Magne, D. Mazon, Y. Peysson, X. Zou, and the HL-2A Team. Development and application of 3.7 ghz LHCD system on HL-2a and development of RF heating system on HL-2m, in EPJ Web of Conferences, vol. 157 (2017), p. 02001
L.L. Lao, H.E.St. John, Q. Peng, J.R. Ferron, E.J. Strait, T.S. Taylor, W.H. Meyer, C. Zhang, K.I. You, MHD equilibrium reconstruction in the DIII-D tokamak. Fusion Sci. Technol. 48, 968–977 (2005). (EFIT reference)
S. Ide, O. Naito, T. Kondoh, Y. Ikeda, K. Ushigusa, Enhancement of absorption of lower hybrid wave by filling the spectral gap. Phys. Rev. Lett. 73(17), 2312–2315 (1994)
D. van Houtte, G. Martin, A. Bécoulet, J. Bucalossi, F. Saint-Laurent, B. Saoutic, X. Tore supra team, Real time control of fully non-inductive operation in tore supra leading to 6 min, 1 gj plasma discharges. Fusion Eng. Des. 74, 651–658 (2005)
J. Decker, Y. Peysson, J. Hillairet, J.-F. Artaud, V. Basiuk, A. Becoulet, A. Ekedahl, M. Goniche, G.T. Hoang, F. Imbeaux, A.K. Ram, M. Schneider, Calculations of lower hybrid current drive in iter. Nucl. Fusion 51, 073025 (2011)
X.M. Zhai, N. Xiang, J.L. Chen, P.T. Bonoli, S. Shiraiwa, A.M. Garofalo, C. Yang, M.H. Li, J.P. Qian, G.Q. Li, K. Li, H.Q. Liu, B. Lyu, Q. Zang, Theoretical analysis of key factors achieving reversed magnetic shear q-profiles sustained with lower hybrid waves on east. Plasma Phys. Control. Fusion 61, 045002 (2019)
X.M. Zhai, J.L. Chen, N. Xiang, P.T. Bonoli, S. Shiraiwa, Synergy of two lower hybrid waves with different frequencies on east. Phys. Plasmas 26, 052509 (2019)
S. Itoh, Y. Nakamura, N. Hiraki, K. Nakamura, A. Nagao, S. Moriyama, E. Jotaki, S. Kawasaki, Initial operation of the high field superconducting tokamak triam-1m. Plasma Phys. Control. Nucl. Fusion Res. 3, 321 (1986)
Y. Nakamura, Y. Takabatake, E. Jotaki, S. Moriyama, A. Nagao, K. Nakamura, N. Hiraki, S. Itoh, Radial profiles of hard x-ray emission during steady state current drive in the triam-1m tokamak. Nucl. Fusion 30, 689 (1990)
G. Tonon, Heating and current drive by lh-waves on toroidal plasmas: problems and perspectives. Plasma Phys. Control. Fusion 26, 145–155 (1984)
Y. Peysson, Transport of fast electrons during lhcd in ts, jet and asdex. Plasma Phys. Control. Fusion 35(12B), B253–B262 (1993)
Y. Peysson, P. Froissard, C. Pocheau, Study of radiation scattering in the hard X-ray energy range by a tokamak inner wall. Nucl. Fusion 33(8), 1133–1145 (1993)
J.F. Artaud, F. Imbeaux, J. Garcia, G. Giruzzi, T. Aniel, V. Basiuk, A. Bécoulet, C. Bourdelle, Y. Buravand, J. Decker, R. Dumont, L.G. Eriksson, X. Garbet, R. Guirlet, G.T. Hoang, P. Huynh, E. Joffrin, X. Litaudon, P. Maget, D. Moreau, R. Nouailletas, B. Pégourié, Y. Peysson, M. Schneider, J. Urban, Metis: a fast integrated tokamak modelling tool for scenario design. Nuc. Fusion 58, 105001 (2018)
B. Lu, X.Y. Bai, Y. Peysson, Y.P. Zhang, D. Mazon, G.L. Xiao, X.L. Zou, H. Zeng, J. Liang, C. Wang, Y.L. Chen, A. Ekedahl, L. Delpech, J.Q. Wang, K. Feng, H. Wang, J. Rao, B. Li, S. Wang, X.M. Song, J. Cheng, Y. Zhou, Z.B. Shi, J. Hillairet, E. Bertrand, G. Giruzzi, T. Hoang. Recent LHCD experiments on HL-2a and LHCD system development on HL-2m, in Proceedings of the 23rd Topical Conference on Radiofrequency Power in Plasmas (Hefei, China) (2019)
P.T. Bonoli, J. Ko, R. Parker, A.E. Schmidt, G. Wallace, J.C. Wright, C.L. Fiore, A.E. Hubbard, J. Irby, E. Marmar, M. Porkolab, D. Terry, S.M. Wolfe, S.J. Wukitch, the Alcator C-Mod Team, J.R. Wilson, Lower hybrid current drive experiments on alcator c-mod: comparison with theory and simulation. Phys. Plasmas 15, 056117 (1–13) (2008)
Y. Peysson and the Tore Supra Team, High power lower hybrid current drive experiments in the tore supra tokamak. Nucl. Fusion 41(11), 1703–1713 (2001)
C.F. Kennel, F. Engelmann, Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9(12), 2377–2387 (1966)
I. Lerche, Quasilinear theory of resonant diffusion in a magneto-active relativistic plasma. Phys. Fluids 11(8), 1720–1726 (1968)
P. Pavlo, L. Krlin, Limits of applicability of the quasilinear approximation to the lower hybrid wave–plasma interaction. Plasma Phys. Control. Fusion 41, 541–550 (1999)
L. Krlin, P. Pavlo, R. Panek, R. Klima, V. Petrzilka, Nonlinear effects in LH wave–plasma interaction. Plasma Phys. Control. Fusion 44, 159–170 (2002)
Acknowledgements
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the European research and training programme under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. The LHCD experiments on HL-2A was supported by the Natural Science Foundation of China (NSFC) project (No. 11575054). This work was supported by the HARMONIA Grant nr 2018/30/M/ST2/00799 and PL-Grid Infrastructure.
Author information
Authors and Affiliations
Consortia
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.