Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T20:06:55.685Z Has data issue: false hasContentIssue false
  • English
  • Français

A comparison of turbulent transport in a quasi-helical and a quasi-axisymmetric stellarator

Part of: Focus on Fusion

Published online by Cambridge University Press:  19 September 2019

I. J. McKinney Open the ORCID record for I. J. McKinney [Opens in a new window] ,
M. J. Pueschel ,
B. J. Faber Open the ORCID record for B. J. Faber [Opens in a new window] ,
C. C. Hegna ,
J. N. Talmadge ,
D. T. Anderson ,
H. E. Mynick  and
P. Xanthopoulos
I. J. McKinney*
Affiliation:
Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
M. J. Pueschel
Affiliation:
Institute for Fusion Studies, University of Texas at Austin, Austin, TX 78712, USA
B. J. Faber
Affiliation:
Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
C. C. Hegna
Affiliation:
Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
J. N. Talmadge
Affiliation:
Department of Electrical & Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
D. T. Anderson
Affiliation:
Department of Electrical & Computer Engineering, University of Wisconsin-Madison, Madison, WI 53706, USA
H. E. Mynick
Affiliation:
Princeton Plasma Physics Laboratory, Princeton, NJ 08543, USA
P. Xanthopoulos
Affiliation:
Max-Planck-Institut für Plasmaphysik, Wendelsteinstraße 1, 17491 Greifswald, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Ion-temperature-gradient-driven (ITG) turbulence is compared for two quasi-symmetric (QS) stellarator configurations to determine the relationship between linear growth rates and nonlinear heat fluxes. We focus on the quasi-helically symmetric (QHS) stellarator HSX and the quasi-axisymmetric (QAS) stellarator NCSX. In normalized units, HSX exhibits higher growth rates than NCSX, while heat fluxes in gyro-Bohm units are lower in HSX. These results hold for simulations made with both adiabatic and kinetic electrons. The results show that HSX has a larger number of subdominant modes than NCSX and that eigenmodes are more spatially extended in HSX. We conclude that the consideration of nonlinear physics is necessary to accurately assess the heat flux due to ITG turbulence when comparing QS stellarator equilibria.

Keywords

fusion plasmaplasma instabilitiesplasma nonlinear phenomena
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 5 , October 2019 , 905850503
Copyright
© Cambridge University Press 2019 

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

Boozer, A. H. 1981 Plasma equilibrium with rotational magnetic surfaces. Phys. Fluids 24 (11), 1999.Google Scholar
Boozer, A. H. 1983 Transport and isomorphic equilibria. Phys. Fluids 26 (2), 496–499.Google Scholar
Brizard, A. J. & Hahm, T. S. 2007 Foundations of nonlinear gyrokinetic theory. Rev. Mod. Phys. 79 (2), 421–468.Google Scholar
Candy, J., Waltz, R. E. & Dorland, W. 2004 The local limit of global gyrokinetic simulations. Phys. Plasmas 11 (5), L25–L28.Google Scholar
Canik, J. M., Anderson, D. T., Anderson, F. S. B., Clark, C., Likin, K. M., Talmadge, J. N. & Zhai, K. 2007 Reduced particle and heat transport with quasisymmetry in the helically symmetric experiment. Phys. Plasmas 14 (5), 056107.Google Scholar
Citrin, J., Arnichand, H., Bernardo, J., Bourdelle, C., Garbet, X., Jenko, F., Hacquin, S., Pueschel, M. J. & Sabot, R. 2017 Comparison between measured and predicted turbulence frequency spectra in ITG and TEM regimes. Phys. Plasmas 59 (6), 064010.Google Scholar
Coppi, B. 1965 ‘Universal’ instabilities from plasma moment equations. Phys. Lett. 14 (3), 172–174.Google Scholar
Coppi, B., Rosenbluth, M. N. & Sagdeev, R. Z. 1967 Instabilities due to temperature gradients in complex magnetic field configurations. Phys. Fluids 10 (3), 582.Google Scholar
Dewar, R. L. & Glasser, A. H. 1983 Ballooning mode spectrum in general toroidal systems. Phys. Fluids 26 (10), 3038–3052.Google Scholar
Faber, B. J., Pueschel, M. J., Proll, J. H. E., Xanthopoulos, P., Terry, P. W., Hegna, C. C., Weir, G. M., Likin, K. M. & Talmadge, J. N. 2015 Gyrokinetic studies of trapped electron mode turbulence in the Helically Symmetric eXperiment stellarator. Phys. Plasmas 22 (7), 072305.Google Scholar
Faber, B. J., Pueschel, M. J., Terry, P. W., Hegna, C. C. & Roman, J. E. 2018 Stellarator microinstabilities and turbulence at low magnetic shear. J. Plasma Phys. 84 (5), 905840503.Google Scholar
Gates, D. A., Anderson, D. T., Anderson, F. S. B., Zarnstorff, M., Spong, D. A., Weitzner, H., Neilson, G. H., Ruzic, D. N., Andruczyk, D., Harris, J. H. et al. 2018 Stellarator research opportunities: a report of the National Stellarator Coordinating Committee. J. Fusion Energy 37 (1), 51–94.Google Scholar
Greene, J. M. & Johnson, J. L. 1968 Interchange instabilities in ideal hydromagnetic theory. Plasma Phys. 10, 729–745.Google Scholar
Guttenfelder, W., Anderson, D. T., Anderson, F. S. B., Canik, J. M., Likin, K. M. & Talmadge, J. N. 2009 Edge turbulence measurements in electron-heated Helically Symmetric Experiment plasmas. Phys. Plasmas 16 (8), 082508.Google Scholar
Hatch, D. R., Terry, P. W., Nevins, W. M. & Dorland, W. 2009 Role of stable eigenmodes in gyrokinetic models of ion temperature gradient turbulence. Phys. Plasmas 16 (2), 022311.Google Scholar
Hegna, C. C. 2000 Local three-dimensional magnetostatic equilibria. Phys. Plasmas 7 (10), 3921.Google Scholar
Hegna, C. C., Terry, P. W. & Faber, B. J. 2018 Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport. Phys. Plasmas 25 (2), 022511.Google Scholar
Helander, P., Bird, T., Jenko, F., Kleiber, R., Plunk, G. G., Proll, J. H. E., Riemann, J. & Xanthopoulos, P. 2015 Advance in stellarator gyrokinetics. Nucl. Fusion 55 (5), 053030.Google Scholar
Hirshman, S. P., van Rij, W. I. & Merkel, P. 1986 Three-dimensional free boundary calculations using a spectral Green’s function method. Comput. Phys. Commun. 43 (1), 143–155.Google Scholar
Horton, W. Jr, Choi, D.-I. & Tang, W. M. 1981 Toroidal drift modes driven by ion pressure gradients. Phys. Fluids 24 (6), 1077.Google Scholar
Ishizawa, A., Kishimoto, Y., Watanabe, T.-H., Sugama, H., Tanaka, K., Satake, S., Kobayashi, S., Nagasaki, K. & Nakamura, Y. 2017 Multi-machine analysis of turbulent transport in helical systems via gyrokinetic simulation. Nucl. Fusion 57 (6), 066010.Google Scholar
Ishizawa, A., Maeyama, S., Watanabe, T.-H., Sugama, H. & Nakajima, N. 2013 Gyrokinetic turbulence simulations of high-beta taokamak and helical plasmas with full-kinetic and hybrid models. Nucl. Fusion 53 (5), 053007.Google Scholar
Ishizawa, A., Watanabe, T.-H., Sugama, H., Maeyama, S. & Nakajima, N. 2014 Electromagnetic gyrokinetic turbulence in finite-beta helical plasmas. Phys. Plasmas 21 (5), 055905.Google Scholar
Jenko, F. 2000 Massively parallel Vlasov simulation of electromagnetic drift-wave turbulence. Compur. Phys. Commun. 125, 196–209.Google Scholar
Jenko, F., Dannert, T. & Angioni, C. 2005 Heat and particle transport in a tokamak: advances in nonlinear gyrokinetics. Plasma Phys. Control. Fusion 47 (12B), B195–B206.Google Scholar
Kadomtsev, B. B. & Pogutse, O. P. 1971 Trapped particles in toroidal magnetic systems. Nucl. Fusion 11, 67–92.Google 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.Google Scholar
Mynick, H. E. 2006 Transport optimization in stellarators. Phys. Plasmas 13 (5), 058102.Google Scholar
Mynick, H. E., Pomphrey, N. & Xanthopoulos, P. 2010 Optimizing stellarators for turbulent transport. Phys. Rev. Lett. 105 (9), 095004.Google Scholar
Mynick, H. E., Pomphrey, N. & Xanthopoulos, P. 2011 Reducing turbulent transport in toroidal configurations via shaping. Phys. Plasmas 18, 056101.Google Scholar
Nakata, M., Nunami, M. & Watanabe, T.-H. 2017 Isotope effects on trapped-electron-mode driven turbulence and zonal flows in helical and tokamak plasmas. Phys. Rev. Lett. 118 (16), 165002.Google Scholar
Neilson, G. H., Zarnstorff, M. C., Lyon, J. F.& The NCSX Team 2002 Quasi-symmetry in stellarator research 5. Status of physics design of quasi-axisymmetry stellarators 5.1 Physics design of the National Compact Stellarator Experiment. J. Plasma Fusion Res. 78 (3), 214–219.Google Scholar
Nunami, M., Watanabe, T.-H. & Sugama, H. 2013 A reduced model for ion temperature gradient turbulent transport in helical plasmas. Phys. Plasmas 20 (9), 092307.Google Scholar
Plunk, G. G., Helander, P., Xanthopoulos, P. & Connor, J. W. 2014 Collisionless microinstabilities in stellarators. III. The ion-temperature-gradient mode. Phys. Plasmas 21 (3), 032112.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.Google Scholar
Pueschel, M. J., 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.Google Scholar
Pueschel, M. J., Faber, B. J., Citrin, J., Hegna, C. C., Terry, P. W. & Hatch, D. R. 2016 Stellarator turbulence: subdominant eigenmodes and quasilinear modeling. Phys. Rev. Lett. 116 (8), 085001.Google Scholar
Pueschel, M. J., Görler, T., Jenko, F., Hatch, D. R. & Cianciara, A. J. 2013 On secondary and tertiary instability in electromagnetic plasma microturbulence. Phys. Plasmas 20 (10), 102308.Google Scholar
Pueschel, M. J., Jenko, F., Told, D. & Büchner, J. 2011 Gyrokinetic simulations of magnetic reconnection. Phys. Plasmas 18 (11), 112102.Google Scholar
Pueschel, M. J., Kammerer, M. & Jenko, F. 2008 Gyrokinetic turbulence simulations at high plasma beta. Phys. Plasmas 15 (10), 102310.Google Scholar
Rewoldt, G., Ku, L.-P. & Tang, W. M. 2005 Comparison of microinstability properties for stellarator magnetic geometries. Phys. Plasmas 12 (10), 102512.Google Scholar
Rudakov, L. I. & Sagdeev, R. Z. 1961 On the instability of a nonuniform rarefied plasma in a strong magnetic field. Dokl. Akad. Nauk SSR 138 (3), 581–583.Google Scholar
Talmadge, J. N., Anderson, F. S. B., Anderson, D. T., Deng, C., Guttenfelder, W., Likin, K. M., Lore, J., Schmitt, J. C. & Zhai, K. 2008 Experimental tests of quasisymmetry in HSX. Plasma Fusion Res. 3, S1002.Google Scholar
Terry, P. W., Baver, D. A. & Gupta, S. 2006 Role of stable eigenmodes in saturated local plasma turbulence. Phys. Plasmas 13 (2), 022307.Google Scholar
Terry, P. W., Faber, B. J., Hegna, C. C., Mirnov, V. V., Pueschel, M. J. & Whelan, G. G. 2018 Saturation scalings of toroidal ion temperature gradient turbulence. Phys. Plasmas 25 (1), 012308.Google Scholar
Toda, S., Nakata, M., Nunami, M., Ishizawa, A., Watanabe, T.-H. & Sugama, H. 2019 Transport simulation for helical plasmas by use of gyrokinetic transport model. Plasma Fusion Res. 14 (1), 3403061.Google Scholar
Weir, G. M.2014 Heat transport experiments on the HSX stellarator. PhD Thesis.Google Scholar
Xanthopoulos, P., Cooper, W. A., Jenko, F., Turkin, Y., Runov, A. & Geiger, J. 2009 A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations. Phys. Plasmas 16 (8), 082303.Google Scholar
Xanthopoulos, P. & Jenko, F. 2007 Gyrokinetic analysis of linear microinstabilities for the stellarator Wendelstein 7-X. Phys. Plasmas 14 (4), 042501.Google Scholar
Xanthopoulos, P., Mynick, H. E., Helander, P., Turkin, Y., Plunk, G. G., Jenko, F., GÖRLER, T., Told, D., Bird, T. & Proll, J. H. E. 2014 Controlling turbulence in present and future stellarators. Phys. Rev. Lett. 113 (15), 155011.Google Scholar