Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T13:56:12.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Verifying raytracing/Fokker–Planck lower-hybrid current drive predictions with self-consistent full-wave/Fokker–Planck simulations

Published online by Cambridge University Press:  10 November 2022

S.J. Frank Open the ORCID record for S.J. Frank [Opens in a new window] ,
J.P. Lee Open the ORCID record for J.P. Lee [Opens in a new window] ,
J.C. Wright Open the ORCID record for J.C. Wright [Opens in a new window] ,
I.H. Hutchinson Open the ORCID record for I.H. Hutchinson [Opens in a new window]  and
P.T. Bonoli
S.J. Frank*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
J.P. Lee
Affiliation:
Department of Nuclear Engineering, Hanyang University, Seoul, South Korea
J.C. Wright
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
I.H. Hutchinson
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
P.T. Bonoli
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Raytracing/Fokker–Planck (FP) simulations used to model lower-hybrid current drive (LHCD) often fail to reproduce experimental results, particularly when LHCD is weakly damped. A proposed reason for this discrepancy is the lack of ‘full-wave’ effects, such as diffraction and interference, in raytracing simulations and the breakdown of the raytracing approximation. Previous studies of LHCD using non-Maxwellian full-wave/FP simulations have been performed, but these simulations were not self-consistent and enforced power conservation between the FP and full-wave code using a numerical rescaling factor. Here, we have created a fully self-consistent full-wave/FP model for LHCD that is automatically power conserving. This was accomplished by coupling an overhauled version of the non-Maxwellian TORLH full-wave solver and the CQL3D FP code using the Integrated Plasma Simulator. We performed converged full-wave/FP simulations of Alcator C-Mod discharges and compared them with raytracing. We found that excellent agreement in the power deposition profiles from raytracing and TORLH could be obtained, however, TORLH had somewhat lower current drive efficiency and broader power deposition profiles in some cases. This discrepancy appears to be a result of numerical limitations present in the TORLH model and a small amount of diffractional broadening of the TORLH wave spectrum. Our results suggest full-wave simulation of LHCD is likely not necessary as diffraction and interference represented only a small correction that could not account for the differences between simulations and experiment.

Keywords

plasma wavesplasma simulationfusion plasma
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 6 , December 2022 , 905880603
Check for updates
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baek, S.G., Biswas, B., Wallace, G.M., Bonoli, P.T., Ding, B.J., Li, M.H., Li, Y.C., Wang, Y.F., Wang, M., Wu, C.B., et al. 2021 A model investigation of the impact of lower hybrid wave scattering angle on current drive profile in EAST and Alcator C-Mod. Nucl. Fusion 61 (10), 106034.CrossRefGoogle Scholar
Bartiromo, R., Hesse, M., Söldner, F.X., Burhenn, R., Fussmann, G., Leuterer, F., Murmann, H., Eckhartt, D., Eberhagen, A., Giuliana, A., et al. 1986 Experimental study of non-thermal electron generation by lower hybrid waves in the ASDEX tokamak. Nucl. Fusion 26 (8), 1106.CrossRefGoogle Scholar
Bernabei, S., Daughney, C., Efthimion, P., Hooke, W., Hosea, J., Jobes, F., Martin, A., Mazzucato, E., Meservey, E., Motley, R., et al. 1995 Lower-hybrid current drive in the PLT tokamak. Phys. Rev. Lett. 49 (17), 1255.CrossRefGoogle Scholar
Berry, L.A., Jaeger, E.F., Phillips, C.K., Lau, C.H., Bertelli, N. & Green, D.L. 2016 A generalized plasma dispersion function for electron damping in tokamak plasmas. Phys. Plasmas 23 (10), 102504.CrossRefGoogle Scholar
Bertelli, N., Maj, O., Poli, E., Harvey, R., Wright, J.C., Bonoli, P.T., Phillips, C.K., Smirnov, A.P., Valeo, E. & Wilson, J.R. 2012 Paraxial Wentzel–Kramers–Brillouin method applied to the lower hybrid wave propagation. Phys. Plasmas 19 (8), 082510.CrossRefGoogle Scholar
Bertelli, N., Valeo, E.J., Green, D.L., Gorelenkova, M., Phillips, C.K., Podestà, M., Lee, J.P., Wright, J.C. & Jaeger, E.F. 2017 Full-wave simulations of ICRF heating regimes in toroidal plasma with non-Maxwellian distribution functions. Nucl. Fusion 57 (5), 056035.CrossRefGoogle Scholar
Biswas, B., Baek, S.G., Bonoli, P.T., Shiraiwa, S., Wallace, G. & White, A. 2020 Study of turbulence-induced refraction of lower hybrid waves using synthetic scrape-off layer filaments. Plasma Phys. Control. Fusion 62 (11), 115006.CrossRefGoogle Scholar
Biswas, B., Shiraiwa, S., Baek, S.-G., Bonoli, P., Ram, A. & White, A.E. 2021 A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments. J. Plasma Phys. 87 (5), 905870510.CrossRefGoogle Scholar
Bonoli, P.T. 1985 Linear theory of lower hybrid waves in tokamak plasmas. In Wave Heating and Current Drive in Plasmas (ed. V.L. Granatstein & P.L. Colestock). Gordon and Breach Science Publishers.Google Scholar
Bonoli, P.T. 2014 Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters. Phys. Plasmas 21 (6), 061508.CrossRefGoogle Scholar
Bonoli, P.T. & Englade, R.C. 1986 Simulation model for lower hybrid current drive. Phys. Fluids 29, 2937.CrossRefGoogle Scholar
Bonoli, P.T. & Ott, E. 1981 Accessibility and energy deposition of lower-hybrid waves in a tokamak with density fluctuations. Phys. Rev. Lett. 46 (6), 424.CrossRefGoogle Scholar
Bonoli, P.T. & Ott, E. 1982 Toroidal and scattering effects on lower-hybrid wave propagation. Phys. Fluids 25 (2), 359.CrossRefGoogle Scholar
Brambilla, M 1996 A full wave code for ion cyclotron wave in toroidal plasmas. Tech. Rep. IPP 5/66. Max-Planck-Institute for Plasma Physics.Google Scholar
Cesario, R., Amicucci, L., Castaldo, M., Marinucci, M., Panaccione, L., Santini, F., Tudisco, O., Apicella, M.L., Calabro, G., Cianfarani, C., et al. 2010 Current drive at plasma densities required for thermonuclear reactors. Nat. Commun. 1 (1), 55.CrossRefGoogle ScholarPubMed
Cesario, R., Cardinali, A., Castaldo, C., Paoletti, F. & Mazon, D. 2004 Modeling of a lower-hybrid current drive by including spectral broadening induced by parametric instability in tokamak plasmas. Phys. Rev. Lett. 92 (17), 175002.CrossRefGoogle ScholarPubMed
Chui, C.K. & Mhaskar, H.N. 2010 MRA contextual-recovery extension of smooth functions on manifolds. Appl. Comput. Harmon. Anal. 28 (1), 104–113.CrossRefGoogle Scholar
Decker, J., Peysson, Y., Artaud, J.-F., Nilsson, E., Ekedahl, A., Goniche, M., Hillairet, J. & Mazon, D. 2014 Damping of lower hybrid waves in large spectral gap configurations. Phys. Plasmas 21 (9), 092504.CrossRefGoogle Scholar
Elwasif, W.R., Bernholdt, D.E., Shet, A.G., Foley, S.S., Bramley, R., Batchelor, D.B. & Berry, L.A. 2010 The design and implementation of the SWIM integrated plasma simulator. In 2010 18th Euromicro Conference on Parallel, Distributed and Network-Based Processing, pp. 419–427. IEEE.CrossRefGoogle Scholar
Fisch, N.J. 1978 Confining a tokamak plasma with rf-driven currents. Phys. Rev. Lett. 42 (6), 410.CrossRefGoogle Scholar
Fisch, N.J. 1987 Theory of current drive in plasmas. Rev. Mod. Phys. 59, 175–234.CrossRefGoogle Scholar
Fisch, N.J. & Boozer, A.H. 1980 Creating an asymmetric plasma resistivity with waves. Phys. Rev. Lett. 45 (9), 720.CrossRefGoogle Scholar
Frank, S., Bonoli, P.T., Batchelor, D.B., Wright, J.C. & Hutchinson, I.H. 2019 Coupling of lower-hybrid full wave and 3D Fokker–Planck codes in weak damping scenarios. In APS Division of Plasma Physics Meeting Abstracts, p. UP10.069. APS.Google Scholar
Frank, S.J., Wright, J.C., Hutchinson, I.H. & Bonoli, P.T. 2022 An assessment of full-wave effects on Maxwellian lower-hybrid wave damping. Plasma Phys. Control. Fusion 64 (10), 105023.CrossRefGoogle Scholar
Fried, B.D. & Conte, S.C. 1961 The Plasma Dispersion Function. Academic.Google Scholar
Harvey, R.W. & McCoy, M.G. 1992 The CQL3D code. In Proceedings of the IAEA TCM on Advances in Sim. and Modeling of Thermonuclear Plasmas Montreal, pp. 489–526. IOP Publishing.Google Scholar
Hugon, H., Bizarro, J.P.S. & Rodrigues, P. 2020 An improved asymptotic matching technique to trace the wave amplitude of rays across singularities: application to lower-hybrid wave propagation in tokamaks. Phys. Plasmas 27 (8), 082508.CrossRefGoogle Scholar
Ide, S., Imai, T., Ushigusa, K., Naito, O., Ikeda, Y., Nemoto, M. & Sato, M. 1992 Investigation of the wave spectrum gap in the JT-60 LHCD plasma. Nucl. Fusion 32 (2), 282.CrossRefGoogle Scholar
Jacquinot, J. 1991 Heating, current drive and confinement regimes with the JET ICRH and LHCD systems. Plasma Phys. Control. Fusion 33 (13), 1657.CrossRefGoogle Scholar
Jaeger, E.F., Berry, L.A., Ahern, S.D., Barrett, R.F., Batchelor, D.B., Carter, M.D., D'Azevedo, E.F., Moore, R.D., Harvey, R.W., Myra, J.R., et al. 2006 Self-consistent full-wave and Fokker–Planck calculations for ion cyclotron heating in non-Maxwellian plasmas. Phys. Plasmas 13 (5), 056101.CrossRefGoogle Scholar
Karney, C.F.F. & Fisch, N.J. 1979 Numerical studies of current generation by radio-frequency traveling waves. Phys. Fluids 22 (9), 1817–1824.CrossRefGoogle Scholar
Kaufman, A.N. 1972 Quasilinear diffusion of an axisymmetric toroidal plasma. Phys. Fluids 15 (6), 1063–1069.CrossRefGoogle Scholar
Kennel, C.F. & Engelmann, F. 1966 Velocity space diffusion from weak plasma turbulence in a magnetic field. Phys. Fluids 9 (12), 2377–2388.CrossRefGoogle Scholar
Lasiecka, I., Damelin, S.B. & Hoang, N.S. 2018 On surface completion and image inpainting by biharmonic functions: numerical aspects. Intl J. Math. Sci. 2018, 3950312.Google Scholar
Lee, J., Smithe, D., Wright, J. & Bonoli, P. 2017 a A positive-definite form of bounce-averaged quasilinear velocity diffusion for the parallel inhomogeneity in a tokamak. Plasma Phys. Control. Fusion 60 (2), 025007.CrossRefGoogle Scholar
Lee, J.P. & Wright, J.C. 2014 A block-tridiagonal solver with two level parallelization for finite element-spectral codes. Comput. Phys. Commun. 185, 2598.CrossRefGoogle Scholar
Lee, J., Wright, J., Bertelli, N., Jaeger, E.F., Valeo, E., Harvey, R. & Bonoli, P. 2017 b Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas. Phys. Plasmas 24 (5), 052502.CrossRefGoogle Scholar
Lerche, I. 1968 Quasilinear theory of resonant diffusion in a magneto-active, relativistic plasma. Phys. Fluids 11 (8), 1720–1727.CrossRefGoogle Scholar
Liu, F.K., Ding, B.J., Li, J.G., Wan, B.N., Shan, J.F., Wang, M., Liu, L., Zhao, L.M., Li, M.H., Li, Y.C., et al. 2015 First results of LHCD experiments with 4.6 GHz system toward steady-state plasma in EAST. Nucl. Fusion 55 (12), 123022.CrossRefGoogle Scholar
Meneghini, O. 2012 Full-wave modeling of lower hybrid waves on Alcator C-Mod. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Moriyama, S., Nakamura, Y., Nagao, A., Nakamura, K., Hiraki, N. & Itoh, S. 1990 Ultra-long pulse operation using lower hybrid waves on the superconducting high field tokamak TRIAM-1M. Nucl. Fusion 30 (1), 47.CrossRefGoogle Scholar
Mumgaard, R.T. 2015 Lower hybrid current drive on Alcator C-Mod: measurements with an upgraded MSE diagnostic and comparisons to simulation. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Pereverzev, G.V. 1992 Use of the multidimensional WKB method to describe propagation of lower hybrid waves in tokamak plasma. Nucl. Fusion 32 (7), 1091–1106.CrossRefGoogle Scholar
Petrov, Yu.V. & Harvey, R.W. 2016 A fully-neoclassical finite-orbit-width version of the CQL3D Fokker–Planck code. Plasma Phys. Control. Fusion 58 (11), 115001.CrossRefGoogle Scholar
Peysson, Y., Decker, J., Nilsson, E., Artaud, J.-F., Ekedahl, A., Goniche, M., Hillairet, J., Ding, B., Li, M., Bonoli, P.T., et al. 2016 Advances in modeling of lower hybrid current drive. Plasma Phys. Control. Fusion 58 (4), 044008.CrossRefGoogle Scholar
Peysson, Y., Sébelin, E., Litaudon, X., Moreau, D., Miellou, J.-C., Shoucri, M.M. & Shkarofsky, I.P. 1998 Full wave modelling of lower hybrid current drive in tokamaks. Nucl. Fusion 38 (6), 939–944.CrossRefGoogle Scholar
Peysson, Y. & Tore Supra Team 2001 High power lower hybrid current drive experiments in the Tore Supra tokamak. Nucl. Fusion 41 (11), 1703.CrossRefGoogle Scholar
Poli, E., Bock, A., Lochbrunner, M., Maj, O., Reich, M., Snicker, A., Stegmeir, A., Volpe, F., Bertelli, N., Bilato, R., et al. 2018 Torbeam 2.0, a paraxial beam tracing code for electron-cyclotron beams in fusion plasmas for extended physics applications. Comput. Phys. Commun. 225, 36–46.CrossRefGoogle Scholar
Porkolab, M., Schuss, J.J., Lloyd, B., Takase, Y., Texter, S., Bonoli, P., Fiore, C., Gandy, R., Gwinn, D., Lipschultz, B., et al. 1984 Observation of lower-hybrid current drive at high densities in the Alcator C tokamak. Phys. Rev. Lett. 53 (5), 450–453.CrossRefGoogle Scholar
Schmidt, A. 2011 Measurements and modeling of lower hybrid driven fast electrons on Alcator C-Mod. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Schmidt, A., Bonoli, P.T., Meneghini, O., Parker, R.R., Porkolab, M., Shiraiwa, S., Wallace, G., Wright, J.C., Harvey, R.W. & Wilson, J.R. 2011 Investigation of lower hybrid physics through power modulation experiments on Alcator C-Mod. Phys. Plasmas 18 (5), 056122.CrossRefGoogle Scholar
Shiraiwa, S., Ko, J., Parker, R., Schmidt, A.E., Scott, S., Greenwald, M., Hubbard, A.E., Hughes, J., Ma, Y., Podpaly, Y., et al. 2011 a Full wave effects on lower hybrid wave spectrum and driven current profile in tokamak plasmas. Phys. Plasmas 18, 080705.CrossRefGoogle Scholar
Shiraiwa, S., Meneghini, O., Parker, R.R., Wallace, G., Wilson, J., Faust, I., Lau, C., Mumgaard, R., Scott, S., Wukitch, S., et al. 2011 b Design, and initial experiment results of a novel LH launcher on Alcator C-Mod. Nucl. Fusion 51 (10), 103024.CrossRefGoogle Scholar
Stix, T.H. 1992 Waves in Plasmas, 2nd edn. Springer.Google Scholar
Trubnikov, B.A. 1965 Particle interactions in a fully ionized plasma. Rev. Plasma Phys. 1, 105.Google Scholar
Wallace, G.M., Hubbard, A.E., Bonoli, P.T., Faust, I.C., Harvey, R.W., Hughes, J.W., LaBombard, B.L., Meneghini, O., Parker, R.R., Schmidt, A.E., et al. 2011 Lower hybrid current drive at high density in Alcator C-Mod. Nucl. Fusion 51 (8), 083032.CrossRefGoogle Scholar
Wilson, J.R., Parker, R., Bitter, M., Bonoli, P.T., Fiore, C., Harvey, R.W., Hill, K., Hubbard, A.E., Hughes, J.W., Ince-Cushman, A., et al. 2009 Lower hybrid heating and current drive on the Alcator C-Mod tokamak. Nucl. Fusion 49 (11), 115015.CrossRefGoogle Scholar
Wright, J.C., Bader, A., Berry, L.A., Bonoli, P.T., Harvey, R.W., Jaeger, E.F., Lee, J.P., Schmidt, A., D'Azevedo, E., Faust, I., et al. 2014 Time dependent evolution of RF-generated non-thermal particle distributions in fusion plasmas. Plasma Phys. Control. Fusion 56 (4), 045007.CrossRefGoogle Scholar
Wright, J.C., Bonoli, P.T., Schmidt, A.E., Philips, C.K., Valeo, E.J., Harvey, R.W. & Brambilla, M.A. 2009 An assessment of full wave effects on the propagation and absorption of lower hybrid waves. Phys. Plasmas 16 (7), 072502.CrossRefGoogle Scholar
Wright, J.C., Lee, J.P., Valeo, E., Bonoli, P., Philips, C.K., Jaeger, E.F. & Harvey, R.W. 2010 Challenges in self-consistent full-wave simulations of lower hybrid waves. IEEE Trans. Plasma Sci. 38 (9), 2136.CrossRefGoogle Scholar
Yang, C., Bonoli, P.T., Wright, J.C., Ding, B.J., Parker, R., Shiraiwa, S. & Li, M.H. 2014 Modelling of the EAST lower-hybrid current drive experiment using GENRAY/CQL3D and TORLH/CQL3D. Plasma Phys. Control. Fusion 56 (12), 125003.CrossRefGoogle Scholar