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Electrostatic gyrokinetic simulations in Wendelstein 7-X geometry: benchmark between the codes stella and GENE

Published online by Cambridge University Press:  10 June 2022

A. González-Jerez*
Affiliation:
Laboratorio Nacional de Fusión, CIEMAT, 28040 Madrid, Spain
P. Xanthopoulos
Affiliation:
Max-Planck Institut für Plasmaphysik, 17491 Greifswald, Germany
J.M. García-Regaña
Affiliation:
Laboratorio Nacional de Fusión, CIEMAT, 28040 Madrid, Spain
I. Calvo
Affiliation:
Laboratorio Nacional de Fusión, CIEMAT, 28040 Madrid, Spain
J. Alcusón
Affiliation:
Max-Planck Institut für Plasmaphysik, 17491 Greifswald, Germany
A. Bañón Navarro
Affiliation:
Max-Planck Institut für Plasmaphysik, 85748 Garching, Germany
M. Barnes
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK
F.I. Parra
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK
J. Geiger
Affiliation:
Max-Planck Institut für Plasmaphysik, 17491 Greifswald, Germany
*
Email address for correspondence: [email protected]

Abstract

The first experimental campaigns have proven that, due to the optimization of the magnetic configuration with respect to neoclassical transport, the contribution of turbulence is essential to understand and predict the total particle and energy transport in Wendelstein 7-X (W7-X). This has spurred much work on gyrokinetic modelling for the interpretation of the available experimental results and for the preparation of the next campaigns. At the same time, new stellarator gyrokinetic codes have just been or are being developed. It is therefore desirable to have a sufficiently complete, documented and verified set of gyrokinetic simulations in W7-X geometry against which new codes or upgrades of existing codes can be tested and benchmarked. This paper attempts to provide such a set of simulations in the form of a comprehensive benchmark between the recently developed code stella and the well-established code GENE. The benchmark consists of electrostatic gyrokinetic simulations in the W7-X magnetic geometry and includes different flux tubes, linear ion-temperature-gradient (ITG) and trapped-electron-mode stability analyses, computation of linear zonal-flow responses and calculation of ITG-driven heat fluxes.

Type
Research Article
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Alcusón, J.A., Xanthopoulos, P., Plunk, G.G., Helander, P., Wilms, F., Turkin, Y., von Stechow, A. & Grulke, O. 2020 Suppression of electrostatic micro-instabilities in maximum-J stellarators. Plasma Phys. Control. Fusion 62 (3), 035005.CrossRefGoogle Scholar
Alonso, J.A., Sánchez, E., Calvo, I., Velasco, J.L., McCarthy, K.J., Chmyga, A., Eliseev, L.G., Estrada, T., Kleiber, R., Krupnik, L.I., et al. 2017 Observation of oscillatory radial electric field relaxation in a helical plasma. Phys. Rev. Lett. 118 (18).CrossRefGoogle Scholar
Bañón-Navarro, A., Merlo, G., Plunk, G.G., Xanthopoulos, P., von Stechow, A., Di Siena, A., Maurer, M., Hindenlang, F., Wilms, F. & Jenko, F. 2020 Global gyrokinetic simulations of ITG turbulence in the magnetic configuration space of the Wendelstein 7-X stellarator. Plasma Phys. Control. Fusion 62 (10), 105005.CrossRefGoogle Scholar
Barnes, M., Parra, F.I. & Landreman, M. 2019 Stella: an operator-split, implicit–explicit $\delta$f-gyrokinetic code for general magnetic field configurations. J. Comput. Phys. 391, 365380.CrossRefGoogle Scholar
Baumgaertel, J.A., Belli, E.A., Dorland, W., Guttenfelder, W., Hammett, G.W., Mikkelsen, D.R., Rewoldt, G., Tang, W.M. & Xanthopoulos, P. 2011 Simulating gyrokinetic microinstabilities in stellarator geometry with GS2. Phys. Plasmas 18 (12), 122301.CrossRefGoogle Scholar
Beer, M.A., Cowley, S.C. & Hammett, G.W. 1995 Field-aligned coordinates for nonlinear simulations of tokamak turbulence. Phys. Plasmas 2 (7), 26872700.CrossRefGoogle Scholar
Bozhenkov, S.A., Kazakov, Y., Ford, O.P., Beurskens, M.N.A., Alcusón, J., Alonso, J.A., Baldzuhn, J., Brandt, C., Brunner, K.J., Damm, H., et al. 2020 High-performance plasmas after pellet injections in Wendelstein 7-X. Nucl. Fusion 60 (6), 066011.CrossRefGoogle Scholar
Candy, J. & Waltz, R.E. 2003 An Eulerian gyrokinetic-Maxwell solver. J. Comput. Phys. 186 (2), 545581.CrossRefGoogle Scholar
Catto, P.J. 1978 Linearized gyro-kinetics. Plasma Phys. 20 (7), 719722.CrossRefGoogle Scholar
Cole, M.D.J., Hager, R., Moritaka, T., Dominski, J., Kleiber, R., Ku, S., Lazerson, S.A., Riemann, J. & Chang, C.S. 2019 Verification of the global gyrokinetic stellarator code XGC-S for linear ion temperature gradient driven modes. Phys. Plasmas 26 (8), 082501.CrossRefGoogle Scholar
Dimits, A.M., Bateman, G., Beer, M.A., Cohen, B.I., Dorland, W., Hammett, G.W., Kim, C., Kinsey, J.E., Kotschenreuther, M., Kritz, A.H., et al. 2000 Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7 (3), 969983.CrossRefGoogle Scholar
Dorland, W., Jenko, F., Kotschenreuther, M. & Rogers, B.N. 2000 Electron temperature gradient turbulence. Phys. Rev. Lett. 85 (26), 55795582.CrossRefGoogle ScholarPubMed
Garcıa-Regaña, J.M., Barnes, M., Calvo, I., Parra, F.I., Alcusón, J.A., Davies, R., González-Jerez, A., Mollén, A., Sánchez, E., Velasco, J.L., et al. 2021 Turbulent impurity transport simulations in Wendelstein 7-X plasmas. J. Plasma Phys. 87 (1), 85587010.CrossRefGoogle Scholar
Geiger, J., Beidler, C.D., Feng, Y., Maaßberg, H., Marushchenko, N.B. & Turkin, Y. 2015 Physics in the magnetic configuration space of W7-X. Plasma Phys. Control. Fusion 57 (1), 014004.CrossRefGoogle Scholar
Grimm, R.C., Dewar, R.L. & Manickam, J. 1983 Ideal MHD stability calculations in axisymmetric toroidal coordinate systems. J. Comput. Phys. 49 (1), 94117.CrossRefGoogle Scholar
Helander, P., Bird, T., Jenko, F., Kleiber, R., Plunk, G.G., Proll, J.H.E., Riemann, J. & Xanthopoulos, P. 2015 Advances in stellarator gyrokinetics. Nucl. Fusion 55 (5), 053030.CrossRefGoogle Scholar
Helander, P., Mishchenko, A., Kleiber, R. & Xanthopoulos, P. 2011 Oscillations of zonal flows in stellarators. Plasma Phys. Control. Fusion 53 (5), 054006.CrossRefGoogle Scholar
Hirshman, S.P. 1983 Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria. Phys. Fluids 26 (12), 3553.CrossRefGoogle Scholar
Jenko, F. 2000 Massively parallel vlasov simulation of electromagnetic drift-wave turbulence. Comput. Phys. Commun. 125 (1–3), 196209.CrossRefGoogle Scholar
Jolliet, S., Bottino, A., Angelino, P., Hatzky, R., Tran, T.M., Mcmillan, B.F., Sauter, O., Appert, K., Idomura, Y. & Villard, L. 2007 A global collisionless PIC code in magnetic coordinates. Comput. Phys. Commun. 177 (5), 409425.CrossRefGoogle Scholar
Klinger, T., Andreeva, T., Bozhenkov, S., Brandt, C., Burhenn, R., Buttenschön, B., Fuchert, G., Geiger, B., Grulke, O., Laqua, H.P., et al. 2019 Overview of first Wendelstein 7-X high-performance operation. Nucl. Fusion 59 (11), 112004.CrossRefGoogle Scholar
Kornilov, V., Kleiber, R., Hatzky, R., Villard, L. & Jost, G. 2004 Gyrokinetic global three-dimensional simulations of linear ion-temperature-gradient modes in Wendelstein 7-X. Phys. Plasmas 11 (6), 31963202.CrossRefGoogle Scholar
Kotschenreuther, M., Rewoldt, G. & Tang, W.M. 1995 Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities. Comput. Phys. Commun. 88 (2–3), 128140.CrossRefGoogle Scholar
Lin, Z. 1998 Turbulent transport reduction by zonal flows: massively parallel simulations. Science 281 (5384), 18351837.CrossRefGoogle ScholarPubMed
Maurer, M., Bañón-Navarro, A., Dannert, T., Restelli, M., Hindenlang, F., Görler, T., Told, D., Jarema, D., Merlo, G. & Jenko, F. 2020 GENE-3D: a global gyrokinetic turbulence code for stellarators. J. Comput. Phys. 420, 109694.CrossRefGoogle Scholar
Merz, F. 2009 Gyrokinetic simulation of multimode plasma turbulence. PhD thesis, Universität Münster.Google Scholar
Mishchenko, A., Helander, P. & Könies, A. 2008 Collisionless dynamics of zonal flows in stellarator geometry. Phys. Plasmas 15 (7), 072309.CrossRefGoogle Scholar
Monreal, P., Calvo, I., Sánchez, E., Parra, F.I., Bustos, A., Könies, A., Kleiber, R. & Görler, T. 2016 Residual zonal flows in tokamaks and stellarators at arbitrary wavelengths. Plasma Phys. Control. Fusion 58 (4), 045018.CrossRefGoogle Scholar
Monreal, P., Sánchez, E., Calvo, I., Bustos, A., Parra, F.I., Mishchenko, A., Könies, A. & Kleiber, R. 2017 Semianalytical calculation of the zonal-flow oscillation frequency in stellarators. Plasma Phys. Control. Fusion 59 (6), 065005.CrossRefGoogle Scholar
Parker, S.E., Lee, W.W. & Santoro, R.A. 1993 Gyrokinetic simulation of ion temperature gradient driven turbulence in 3D toroidal geometry. Phys. Rev. Lett. 71 (13), 20422045.CrossRefGoogle ScholarPubMed
Peeters, A.G., Camenen, Y., Casson, F.J., Hornsby, W.A., Snodin, A.P., Strintzi, D. & Szepesi, G. 2009 The nonlinear gyro-kinetic flux tube code GKW. Comput. Phys. Commun. 180 (12), 26502672.CrossRefGoogle Scholar
Proll, J.H.E. 2014 Trapped-particle instabilities in quasi-isodynamic stellarators. PhD thesis, Max-Planck-Institute für Plasmaphysik.Google Scholar
Proll, J.H.E., Mynick, H.E., Xanthopoulos, P., Lazerson, S.A. & Faber, B.J. 2015 TEM turbulence optimisation in stellarators. Plasma Phys. Control. Fusion 58 (1), 014006.CrossRefGoogle Scholar
Proll, J.H.E., Xanthopoulos, P. & Helander, P. 2013 Collisionless microinstabilities in stellarators. II. numerical simulations. Phys. Plasmas 20 (12), 122506.CrossRefGoogle Scholar
Riemann, J., Kleiber, R. & Borchardt, M. 2016 Effects of radial electric fields on linear ITG instabilities in W7-X and LHD. Plasma Phys. Control. Fusion 58 (7), 074001.CrossRefGoogle Scholar
Rosenbluth, M.N. & Hinton, F.L. 1998 Poloidal flow driven by ion-temperature-gradient turbulence in tokamaks. Phys. Rev. Lett. 80 (4), 724727.CrossRefGoogle Scholar
Sánchez, E., Garcıa-Regaña, J.M., Bañón Navarro, A., Proll, J.H.E., Mora Moreno, C., González-Jerez, A., Calvo, I., Kleiber, R., Riemann, J., Smoniewski, J., et al. 2021 Gyrokinetic simulations in stellarators using different computational domains. Nucl. Fusion 61 (11), 116074.CrossRefGoogle Scholar
Sánchez, E., Mishchenko, A., García, J.M.-Regana, Kleiber, R., Bottino, A. & Villard, L. 2020 Nonlinear gyrokinetic PIC simulations in stellarators with the code Euterpe. J. Plasma Phys. 86 (5), 855860501.CrossRefGoogle Scholar
Smoniewski, J., Sánchez, E., Calvo, I., Pueschel, M.J. & Talmadge, J.N. 2021 Comparison of local and global gyrokinetic calculations of collisionless zonal flow damping in quasi-symmetric stellarators. Phys. Plasmas 28 (4), 042503.CrossRefGoogle Scholar
Sugama, H. & Watanabe, T.-H. 2005 Dynamics of zonal flows in helical systems. Phys. Rev. Lett. 94 (11).CrossRefGoogle ScholarPubMed
Wang, H.Y., Holod, I., Lin, Z., Bao, J., Fu, J.Y., Liu, P.F., Nicolau, J.H., Spong, D. & Xiao, Y. 2020 Global gyrokinetic particle simulations of microturbulence in W7-X and LHD stellarators. Phys. Plasmas 27 (8), 082305.CrossRefGoogle Scholar
Watanabe, T.H. & Sugama, H. 2005 Velocity–space structures of distribution function in toroidal ion temperature gradient turbulence. Nucl. Fusion 46 (1), 2432.CrossRefGoogle Scholar
Wolf, R.C., Ali, A., Alonso, A., Baldzuhn, J., Beidler, C., Beurskens, M., Biedermann, C., Bosch, H.-S., Bozhenkov, S., Brakel, R., et al. 2017 Major results from the first plasma campaign of the Wendelstein 7-X stellarator. Nucl. Fusion 57 (10), 102020.CrossRefGoogle Scholar
Xanthopoulos, P. & Jenko, F. 2007 Gyrokinetic analysis of linear microinstabilities for the stellarator Wendelstein 7-X. Phys. Plasmas 14 (4), 042501.CrossRefGoogle Scholar
Xanthopoulos, P., Merz, F., Görler, T. & Jenko, F. 2007 Nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence for the optimized Wendelstein 7-X stellarator. Phys. Rev. Lett. 99 (3).CrossRefGoogle ScholarPubMed
Xanthopoulos, P., Mischchenko, A., Helander, P., Sugama, H. & Watanabe, T.-H. 2011 Zonal flow dynamics and control of turbulent transport in stellarators. Phys. Rev. Lett. 107 (24).CrossRefGoogle ScholarPubMed
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