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Eliminating turbulent self-interaction through the parallel boundary condition in local gyrokinetic simulations

Part of: Focus on Fusion

Published online by Cambridge University Press:  20 March 2020

Justin Ball Open the ORCID record for Justin Ball [Opens in a new window] ,
Stephan Brunner  and
Ajay C.J.
Justin Ball*
Affiliation:
Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015Lausanne, Switzerland
Stephan Brunner
Affiliation:
Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015Lausanne, Switzerland
Ajay C.J.
Affiliation:
Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015Lausanne, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

In this work, we highlight an issue that may reduce the accuracy of many local nonlinear gyrokinetic simulations – turbulent self-interaction through the parallel boundary condition. Given a sufficiently long parallel correlation length, individual turbulent eddies can span the full domain and ‘bite their own tails’, thereby altering their statistical properties. Such self-interaction is only modelled accurately when the simulation domain corresponds to a full flux surface, otherwise it is artificially strong. For Cyclone Base Case parameters and typical domain sizes, we find that this mechanism modifies the heat flux by approximately 40 % and it can be even more important. The effect is largest when using kinetic electrons, low magnetic shear and strong turbulence drive (i.e. steep background gradients). It is found that parallel self-interaction can be eliminated by increasing the parallel length and/or the binormal width of the simulation domain until convergence is achieved.

Keywords

fusion plasmaplasma nonlinear phenomenaplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 2 , April 2020 , 905860207
Copyright
© Cambridge University Press 2020

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References

Abel, I., Plunk, G., Wang, E., Barnes, M., Cowley, S., Dorland, W. & Schekochihin, A. 2013 Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport, and energy flows. Rep. Prog. Phys. 76, 116201.Google ScholarPubMed
Barnes, M., Parra, F. & Landreman, M. 2019 stella: An operator-split, implicit–explicit $\unicode[STIX]{x1D6FF}$f-gyrokinetic code for general magnetic field configurations. J. Comput. Phys. 391, 365.10.1016/j.jcp.2019.01.025CrossRefGoogle Scholar
Beer, M., Cowley, S. & Hammett, G. 1995 Field-aligned coordinates for nonlinear simulations of tokamak turbulence. Phys. Plasmas 2 (7), 2687.CrossRefGoogle Scholar
Brizard, A. & Hahm, T. 2007 Foundations of nonlinear gyrokinetic theory. Rev. Mod. Phys. 79 (2), 421.10.1103/RevModPhys.79.421CrossRefGoogle Scholar
C.J., Ajay, Brunner, S., McMillan, B., Ball, J., Dominski, J. & Merlo, G.2020 How the self-interaction mechanism affects zonal flow drive and the convergence of turbulent transport in flux-tube simulations. J. Plasma Phys. (in preparation).Google Scholar
Candy, J. 2005 Beta scaling of transport in microturbulence simulations. Phys. Plasmas 12 (7), 072307.CrossRefGoogle Scholar
Candy, J. & Waltz, R. 2003 An Eulerian gyrokinetic-Maxwell solver. J. Comput. Phys. 186 (2), 545.10.1016/S0021-9991(03)00079-2CrossRefGoogle Scholar
Catto, P. 1978 Linearized gyro-kinetics. Plasma Phys. 20 (7), 719.10.1088/0032-1028/20/7/011CrossRefGoogle Scholar
Courant, R., Friedrichs, K. & Lewy, H. 1967 On the partial difference equations of mathematical physics. IBM J. Res. Dev. 11 (2), 215–234.10.1147/rd.112.0215CrossRefGoogle Scholar
Dimits, A., Bateman, G., Beer, M., Cohen, B., Dorland, W., Hammett, G., Kim, C., Kinsey, J., Kotschenreuther, M., Kritz, A. et al. 2000 Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7, 969.CrossRefGoogle Scholar
Dominski, J., Brunner, S., Goerler, T., Jenko, F., Told, D. & Villard, L. 2015 How non-adiabatic passing electron layers of linear microinstabilities affect turbulent transport. Phys. Plasmas 22 (6), 062303.CrossRefGoogle Scholar
Dominski, J., McMillan, B., Brunner, S., Merlo, G., Tran, T.-M. & Villard, L. 2017 An arbitrary wavelength solver for global gyrokinetic simulations. Application to the study of fine radial structures on microturbulence due to non-adiabatic passing electron dynamics. Phys. Plasmas 24 (2), 022308.CrossRefGoogle Scholar
Faber, B., Pueschel, M., Terry, P., Hegna, C. & Roman, J. 2018 Stellarator microinstabilities and turbulence at low magnetic shear. J. Plasma Phys. 84 (5), 905840503.CrossRefGoogle Scholar
Frieman, E. & Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25, 502.10.1063/1.863762CrossRefGoogle Scholar
Görler, T., Lapillonne, X., Brunner, S., Dannert, T., Jenko, F., Merz, F. & Told, D. 2011 The global version of the gyrokinetic turbulence code GENE. J. Comput. Phys. 230 (18), 7053.10.1016/j.jcp.2011.05.034CrossRefGoogle Scholar
Guttenfelder, W., Candy, J., Kaye, S., Nevins, W., Wang, E., Bell, R., Hammett, G., LeBlanc, B., Mikkelsen, D. & Yuh, H. 2011 Electromagnetic transport from microtearing mode turbulence. Phys. Rev. Lett. 106 (15), 155004.10.1103/PhysRevLett.106.155004CrossRefGoogle ScholarPubMed
Hallatschek, K. & Dorland, W. 2005 Giant electron tails and passing electron pinch effects in tokamak-core turbulence. Phys. Rev. Lett. 95, 055002.10.1103/PhysRevLett.95.055002CrossRefGoogle ScholarPubMed
Hazeltine, R., Dobrott, D. & Wang, T. 1975 Kinetic theory of tearing instability. Phys. Fluids 18 (12), 1778–1786.10.1063/1.861097CrossRefGoogle Scholar
Jenko, F., Dorland, W., Kotschenreuther, M. & Rogers, B. 2000 Electron temperature gradient driven turbulence. Phys. Plasmas 7 (5), 1904.CrossRefGoogle Scholar
Lin, Z., Ethier, S., Hahm, T. & Tang, W. 2012 Verification of gyrokinetic particle simulation of device size scaling of turbulent transport. Plasma Sci. Technol. 14 (12), 1125.Google Scholar
Luxon, J. 2002 A design retrospective of the DIII-D tokamak. Nucl. Fusion 42 (5), 614.10.1088/0029-5515/42/5/313CrossRefGoogle Scholar
Martin, M., Landreman, M., Xanthopoulos, P., Mandell, N. & Dorland, W. 2018 The parallel boundary condition for turbulence simulations in low magnetic shear devices. Plasma Phys. Control. Fusion 60 (9), 095008.CrossRefGoogle Scholar
McMillan, B., Lapillonne, X., Brunner, S., Villard, L., Jolliet, S., Bottino, A., Görler, T. & Jenko, F. 2010 System size effects on gyrokinetic turbulence. Phys. Rev. Lett. 105 (15), 155001.CrossRefGoogle ScholarPubMed
Parra, F. & Barnes, M. 2015 Intrinsic rotation in tokamaks: theory. Plasma Phys. Control. Fusion 57 (4), 045002.CrossRefGoogle Scholar
Parra, F., Barnes, M. & Peeters, A. 2011 Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks. Phys. Plasmas 18 (6), 062501.CrossRefGoogle Scholar
Parra, F. & Calvo, I. 2011 Phase-space Lagrangian derivation of electrostatic gyrokinetics in general geometry. Plasma Phys. Control. Fusion 53 (4), 045001.CrossRefGoogle Scholar
Peeters, A., Angioni, C. et al. 2005 Linear gyrokinetic calculations of toroidal momentum transport in a tokamak due to the ion temperature gradient mode. Phys. Plasmas 12 (7), 072515.CrossRefGoogle Scholar
Pueschel, M., Dannert, T. & Jenko, F. 2010 On the role of numerical dissipation in gyrokinetic Vlasov simulations of plasma microturbulence. Comput. Phys. Commun. 181 (8), 1428–1437.CrossRefGoogle Scholar
Scott, B. 1998 Global consistency for thin flux tube treatments of toroidal geometry. Phys. Plasmas 5 (6), 2334–2339.10.1063/1.872907CrossRefGoogle Scholar
Scott, B. 2001 Shifted metric procedure for flux tube treatments of toroidal geometry: avoiding grid deformation. Phys. Plasmas 8 (2), 447–458.CrossRefGoogle Scholar
Sugama, H., Watanabe, T., Nunami, M. & Nishimura, S. 2011 Momentum balance and radial electric fields in axisymmetric and nonaxisymmetric toroidal plasmas. Plasma Phys. Control. Fusion 53 (2), 024004.CrossRefGoogle Scholar
Told, D. & Jenko, F. 2010 Applicability of different geometry approaches to simulations of turbulence in highly sheared magnetic fields. Phys. Plasmas 17 (4), 042302.CrossRefGoogle Scholar
Waltz, R., Austin, M., Burrell, K. & Candy, J. 2006 Gyrokinetic simulations of off-axis minimum-$q$ profile corrugations. Phys. Plasmas 13 (5), 052301.CrossRefGoogle Scholar
Watanabe, T.-H. & Sugama, H. 2006 Velocity–space structures of distribution function in toroidal ion temperature gradient turbulence. Nucl. Fusion 46 (1), 24.CrossRefGoogle Scholar
Watanabe, T.-H., Sugama, H., Ishizawa, A. & Nunami, M. 2015 Flux tube train model for local turbulence simulation of toroidal plasmas. Phys. Plasmas 22 (2), 022507.CrossRefGoogle Scholar
Weikl, A., Peeters, A., Rath, F., Seiferling, F., Buchholz, R., Grosshauser, S. & Strintzi, D. 2018 The occurrence of staircases in ITG turbulence with kinetic electrons and the zonal flow drive through self-interaction. Phys. Plasmas 25 (7), 072305.10.1063/1.5035184CrossRefGoogle Scholar