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A hybrid full-wave Markov chain approach to calculating radio-frequency wave scattering from scrape-off layer filaments

Part of: Focus on Fusion

Published online by Cambridge University Press:  22 October 2021

Bodhi Biswas Open the ORCID record for Bodhi Biswas [Opens in a new window] ,
Syun'ichi Shiraiwa Open the ORCID record for Syun'ichi Shiraiwa [Opens in a new window] ,
Seung-Gyou Baek Open the ORCID record for Seung-Gyou Baek [Opens in a new window] ,
Paul Bonoli Open the ORCID record for Paul Bonoli [Opens in a new window] ,
Abhay Ram Open the ORCID record for Abhay Ram [Opens in a new window]  and
Anne E. White
Bodhi Biswas*
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge 02193, USA
Syun'ichi Shiraiwa
Affiliation:
Princeton Plasma Physics Laboratory, Princeton 08540, USA
Seung-Gyou Baek
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge 02193, USA
Paul Bonoli
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge 02193, USA
Abhay Ram
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge 02193, USA
Anne E. White
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge 02193, USA
*
†Email address for correspondence: [email protected]
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Abstract

The interaction of radio-frequency (RF) waves with edge turbulence modifies the incident wave spectrum, and can significantly affect RF heating and current drive in tokamaks. Previous lower hybrid (LH) scattering models have either used the weak-turbulence approximation, or treated more realistic, filamentary turbulence in the ray tracing limit. In this work, a new model is introduced which retains full-wave effects of RF scattering in filamentary turbulence. First, a Mie-scattering technique models the interaction of an incident wave with a single Gaussian filament. Next, an effective differential scattering width is derived for a statistical ensemble of filaments. Lastly, a Markov chain solves for the transmitted wave spectrum in slab geometry. This model is applied to LH launching for current drive. The resulting wave spectrum is asymmetrically broadened in angular wavenumber space. This asymmetry is not accounted for in previous LH scattering models. The modified wave spectrum is coupled to a ray tracing/Fokker–Planck solver (GENRAY/CQL3D) to study its impact on current drive. The resulting current profile is greatly altered, and there is significant increase in the on-axis current and decrease in the off-axis peaks. This is attributed to a portion of the modified wave spectrum that is strongly dampened on-axis during the first pass.

Keywords

fusion plasmaplasma simulationplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 5 , October 2021 , 905870510
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Agostini, M., Zweben, S., Cavazzana, R., Scarin, P., Serianni, G., Maqueda, R. & Stotler, D. 2007 Study of statistical properties of edge turbulence in the National Spherical Torus Experiment with the gas puff imaging diagnostic. Phys. Plasmas 14 (10), 102305.CrossRefGoogle Scholar
Andrews, P. & Perkins, F. 1983 Scattering of lower-hybrid waves by drift-wave density fluctuations: solutions of the radiative transfer equation. Phys. Fluids 26 (9), 2537–2545.CrossRefGoogle Scholar
Azzalini, A. & Capitanio, A. 1999 Statistical applications of the multivariate skew normal distribution. J. R. Stat. Soc. 61 (3), 579–602.CrossRefGoogle Scholar
Baek, S., Biswas, B., Bonoli, P., Brunner, D., Faust, I., Hubbard, A., Hughes, J., LaBombard, B., Mumgaard, R., Porkolab, M., et al. 2020 Role of the edge and scrape-off layer plasma in lower hybrid current drive experiment on Alcator C-Mod. In AIP Conference Proceedings, vol. 2254, p. 030006. AIP Publishing LLC.CrossRefGoogle Scholar
Baek, S., Parker, R., Bonoli, P., Shiraiwa, S., Wallace, G., LaBombard, B., Faust, I., Porkolab, M. & Whyte, D. 2015 High density LHRF experiments in alcator C-Mod and implications for reactor scale devices. Nucl. Fusion 55 (4), 043009.CrossRefGoogle Scholar
Baek, S., Wallace, G., Bonoli, P., Brunner, D., Faust, I., Hubbard, A., Hughes, J., LaBombard, B., Parker, R., Porkolab, M., et al. 2018 Observation of efficient lower hybrid current drive at high density in diverted plasmas on the alcator C-Mod tokamak. Phys. Rev. Lett. 121 (5), 055001.CrossRefGoogle ScholarPubMed
Bellan, P. & Wong, K. 1978 Effect of density fluctuations on lower hybrid resonance cone propagation. Phys. Fluids 21 (4), 592–599.CrossRefGoogle Scholar
Bertelli, N., Wallace, G., Bonoli, P., Harvey, R., Smirnov, A., Baek, S., Parker, R., Phillips, C., Valeo, E., Wilson, J., et al. 2013 The effects of the scattering by edge plasma density fluctuations on lower hybrid wave propagation. Plasma Phys. Control. Fusion 55 (7), 074003.CrossRefGoogle Scholar
Biswas, B., Baek, S. G., Bonoli, P., 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
Bonoli, P. T. & Ott, E. 1982 Toroidal and scattering effects on lower-hybrid wave propagation. Phys. Fluids 25 (2), 359–375.CrossRefGoogle Scholar
Carralero, D., Artene, S., Bernert, M., Birkenmeier, G., Faitsch, M., Manz, P., de Marne, P., Stroth, U., Wischmeier, M., Wolfrum, E., et al. 2018 On the role of filaments in perpendicular heat transport at the scrape-off layer. Nucl. Fusion 58 (9), 096015.CrossRefGoogle Scholar
Cesario, R., Amicucci, L., Cardinali, A., Castaldo, C., Marinucci, M., Napoli, F., Paoletti, F., De Arcangelis, D., Ferrari, M., Galli, A., et al. 2014 Spectral broadening of parametric instability in lower hybrid current drive at a high density. Nucl. Fusion 54 (4), 043002.CrossRefGoogle Scholar
Cziegler, I., Terry, J., Hughes, J. & LaBombard, B. 2010 Experimental studies of edge turbulence and confinement in alcator C-Mod. Phys. Plasmas 17 (5), 056120.CrossRefGoogle Scholar
Decristoforo, G., Militello, F., Nicholas, T., Omotani, J., Marsden, C., Walkden, N. & Garcia, O. E. 2020 Blob interactions in 2d scrape-off layer simulations. Phys. Plasmas 27 (12), 122301.CrossRefGoogle Scholar
Ding, B., Bonoli, P., Tuccillo, A., Goniche, M., Kirov, K., Li, M., Li, Y., Cesario, R., Peysson, Y., Ekedahl, A., et al. 2018 Review of recent experimental and modeling advances in the understanding of lower hybrid current drive in iter-relevant regimes. Nucl. Fusion 58 (9), 095003.CrossRefGoogle Scholar
Esposito, L. & House, L. 1978 Radiative transfer calculated from a markov chain formalism. Astrophys. J. 219, 1058–1067.CrossRefGoogle Scholar
Graves, J., Horacek, J., Pitts, R. & Hopcraft, K. 2005 Self-similar density turbulence in the TCV tokamak scrape-off layer. Plasma Phys. Control. Fusion 47 (3), L1.CrossRefGoogle Scholar
Grulke, O., Terry, J., Cziegler, I., LaBombard, B. & Garcia, O. 2014 Experimental investigation of the parallel structure of fluctuations in the scrape-off layer of alcator C-Mod. Nucl. Fusion 54 (4), 043012.CrossRefGoogle Scholar
Harvey, R. & McCoy, M. 1992 The CQL3D Fokker–Planck code. In Proceedings of the IAEA Technical Committee Meeting on Simulation and Modeling of Thermonuclear Plasmas, pp. 489–526. CompX Company.Google Scholar
Hizanidis, K., Ram, A. K., Kominis, Y. & Tsironis, C. 2010 Fokker–Planck description of the scattering of radio frequency waves at the plasma edge. Phys. Plasmas 17 (2), 022505.CrossRefGoogle Scholar
Kai, L. & d'Alessio, A. 1995 Finely stratified cylinder model for radially inhomogeneous cylinders normally irradiated by electromagnetic plane waves. Appl. Opt. 34 (24), 5520–5530.CrossRefGoogle ScholarPubMed
Keramidas Charidakos, I., Myra, J., Ku, S., Churchill, R., Hager, R., Chang, C. & Parker, S. 2020 Comparison of edge turbulence characteristics between DIII-D and C-Mod simulations with XGC1. Phys. Plasmas 27 (7), 072302.CrossRefGoogle Scholar
Kirk, A., Ayed, N. B., Counsell, G., Dudson, B., Eich, T., Herrmann, A., Koch, B., Martin, R., Meakins, A., Saarelma, S., et al. 2006 Filament structures at the plasma edge on MAST. Plasma Phys. Control. Fusion 48 (12B), B433.CrossRefGoogle Scholar
Krasheninnikov, S., D'Ippolito, D. & Myra, J. 2008 Recent theoretical progress in understanding coherent structures in edge and SOL turbulence. J. Plasma Phys. 74 (5), 679.CrossRefGoogle Scholar
Kube, R., Theodorsen, A., Garcia, O. E., LaBombard, B. & Terry, J. L. 2016 Fluctuation statistics in the scrape-off layer of alcator C-Mod. Plasma Phys. Control. Fusion 58 (5), 054001.CrossRefGoogle Scholar
Lau, C., Martin, E., Shiraiwa, S. & Wallace, G. 2020 Full-wave model for the lower hybrid wave electric field vector with synthetic turbulence on alcator C-Mod. Nucl. Fusion 60 (3), 036001.CrossRefGoogle Scholar
Madi, M., Peysson, Y., Decker, J. & Kabalan, K. 2015 Propagation of the lower hybrid wave in a density fluctuating scrape-off layer (SOL). Plasma Phys. Control. Fusion 57 (12), 125001.CrossRefGoogle Scholar
Martin, E. H., Lau, C., Wallace, G. M., Shiraiwa, S. & Mumgaard, R. 2019 Experimental evidence of lower hybrid wave scattering in alcator C-Mod due to scrape off layer density fluctuations. Nucl. Fusion 59 (7), 076006.CrossRefGoogle Scholar
Mishchenko, M. I. 2014 Electromagnetic Scattering by Particles and Particle Groups: An Introduction. Cambridge University Press.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
Myra, J. & D'Ippolito, D. 2010 Scattering of radio frequency waves by blob-filaments. Phys. Plasmas 17 (10), 102510.CrossRefGoogle Scholar
Ott, E. 1979 Lower hybrid wave scattering by density fluctuations. Phys. Fluids 22 (9), 1732–1736.CrossRefGoogle Scholar
Peysson, Y., Decker, J., Morini, L. & Coda, S. 2011 RF current drive and plasma fluctuations. Plasma Phys. Control. Fusion 53 (12), 124028.CrossRefGoogle Scholar
Peysson, Y., TORE SUPRA Team, et al. 2000 Progress towards high-power lower hybrid current drive in TORE SUPRA. Plasma Phys. Control. Fusion 42 (12B), B87.CrossRefGoogle Scholar
Porkolab, M. 1977 Parametric instabilities due to lower-hybrid radio frequency heating of tokamak plasmas. Phys. Fluids 20 (12), 2058–2075.CrossRefGoogle Scholar
Ram, A. K. & Hizanidis, K. 2016 Scattering of radio frequency waves by cylindrical density filaments in tokamak plasmas. Phys. Plasmas 23 (2), 022504.CrossRefGoogle Scholar
Shiraiwa, S., Baek, S., Faust, I., Wallace, G., Bonoli, P., Meneghini, O., Mumgaard, R., Parker, R., Scott, S., Harvey, R., et al. 2015 Impact of SOL plasma profiles on lower hybrid current drive: experimental evidence, mitigation and modeling approaches. In AIP Conference Proceedings, vol. 1689, p. 030016. AIP Publishing LLC.CrossRefGoogle Scholar
Shiraiwa, S., Meneghini, O., Parker, R., Bonoli, P., Garrett, M., Kaufman, M., Wright, J. & Wukitch, S. 2010 Plasma wave simulation based on a versatile finite element method solver. Phys. Plasmas 17 (5), 056119.CrossRefGoogle Scholar
Shiraiwa, S., Wright, J., Bonoli, P., Kolev, T. & Stowell, M. 2017 RF wave simulation for cold edge plasmas using the MFEM library. EPJ Web Conf. 157, 03048.CrossRefGoogle Scholar
Sierchio, J., Cziegler, I., Terry, J., White, A. & Zweben, S. 2016 Comparison of velocimetry techniques for turbulent structures in gas-puff imaging data. Rev. Sci. Instrum. 87 (2), 023502.CrossRefGoogle ScholarPubMed
Smirnov, A. & Harvey, R. 2001 The GENRAY ray tracing code. CompX Report No. CompX-2000-01.Google Scholar
Stix, T. H. 1992 Waves in Plasmas. Springer Science & Business Media.Google Scholar
Terry, J., Zweben, S., Hallatschek, K., LaBombard, B., Maqueda, R., Bai, B., Boswell, C., Greenwald, M., Kopon, D., Nevins, W., et al. 2003 Observations of the turbulence in the scrape-off-layer of alcator C-Mod and comparisons with simulation. Phys. Plasmas 10 (5), 1739–1747.CrossRefGoogle Scholar
Tierens, W., Zhang, W., Manz, P., EUROfusion MST1 Team & ASDEX Upgrade Team 2020 a The importance of realistic plasma filament waveforms for the study of resonant wave-filament interactions in tokamak edge plasmas. Phys. Plasmas 27 (5), 052102.CrossRefGoogle Scholar
Tierens, W., Zhang, W., Myra, J. & EUROfusion MST1 Team 2020 b Filament-assisted mode conversion in magnetized plasmas. Phys. Plasmas 27 (1), 010702.CrossRefGoogle Scholar
Tsironis, C., Peeters, A. G., Isliker, H., Strintzi, D., Chatziantonaki, I. & Vlahos, L. 2009 Electron-cyclotron wave scattering by edge density fluctuations in ITER. Phys. Plasmas 16 (11), 112510.CrossRefGoogle Scholar
Wallace, G., Parker, R., Bonoli, P., Hubbard, A., Hughes, J., LaBombard, B., Meneghini, O., Schmidt, A., Shiraiwa, S., Whyte, D., et al. 2010 Absorption of lower hybrid waves in the scrape off layer of a diverted tokamak. Phys. Plasmas 17 (8), 082508.CrossRefGoogle Scholar
Wright, J. C., Bonoli, P., Schmidt, A., Phillips, C., Valeo, E., Harvey, R. & Brambilla, M. 2009 An assessment of full wave effects on the propagation and absorption of lower hybrid waves. Phys. Plasmas 16 (7), 072502.CrossRefGoogle Scholar
Wu, X. B. 1994 Scattering from an anisotropic cylindrical dielectric shell. Intl J. Infrared Millimeter Waves 15 (10), 1733–1744.CrossRefGoogle Scholar
Xu, F., Davis, A. B., West, R. A. & Esposito, L. W. 2011 Markov chain formalism for polarized light transfer in plane-parallel atmospheres, with numerical comparison to the Monte Carlo method. Opt. Express 19 (2), 946–967.CrossRefGoogle ScholarPubMed
Yang, S., Xiao, D., Li, X. & Ma, Z. 2018 Markov chain investigation of discretization schemes and computational cost reduction in modeling photon multiple scattering. Appl. Sci. 8 (11), 2288.CrossRefGoogle Scholar
Zhang, W., Tierens, W., Bobkov, V., Cathey, A., Cziegler, I., Griener, M., Hoelzl, M., Kardaun, O., et al. 2021 Interaction between filaments and icrf in the plasma edge. Nucl. Mater. Energy 26, 100941.CrossRefGoogle Scholar
Zweben, S., Myra, J., Davis, W., D'Ippolito, D., Gray, T., Kaye, S., LeBlanc, B., Maqueda, R., Russell, D., Stotler, D., et al. 2016 Blob structure and motion in the edge and sol of NSTX. Plasma Phys. Control. Fusion 58 (4), 044007.CrossRefGoogle Scholar
Zweben, S., Stotler, D., Terry, J., LaBombard, B., Greenwald, M., Muterspaugh, M., Pitcher, C., Group, A. C.-M., Hallatschek, K., Maqueda, R., et al. 2002 Edge turbulence imaging in the Alcator C-Mod tokamak. Phys. Plasmas 9 (5), 1981–1989.CrossRefGoogle Scholar
Zweben, S., Terry, J., LaBombard, B., Agostini, M., Greenwald, M., Grulke, O., Hughes, J., D'Ippolito, D., Krasheninnikov, S., Myra, J., et al. 2011 Estimate of convective radial transport due to SOL turbulence as measured by GPI in alcator C-Mod. J. Nucl. Mater. 415 (1), S463–S466.CrossRefGoogle Scholar