Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-19T02:28:27.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Strongly driven surface-global kinetic ballooning modes in general toroidal geometry

Part of: Focus on Fusion PLA 17th European Fusion Theory Conference

Published online by Cambridge University Press:  20 June 2018

A. Zocco Open the ORCID record for A. Zocco [Opens in a new window] ,
K. Aleynikova  and
P. Xanthopoulos
A. Zocco*
Affiliation:
Max-Planck-Institut für Plasmaphysik, D-17491, Greifswald, Germany
K. Aleynikova
Affiliation:
Max-Planck-Institut für Plasmaphysik, D-17491, Greifswald, Germany Moscow Institute of Physics and Technology, Dolgoprudny, Russian Federation
P. Xanthopoulos
Affiliation:
Max-Planck-Institut für Plasmaphysik, D-17491, Greifswald, Germany
*
†Email address for correspondence: Alessandro.zocco@ipp.mpg.de
Get access Rights & Permissions [Opens in a new window]

Abstract

Kinetic ballooning modes in magnetically confined toroidal plasmas are investigated putting emphasis on specific stellarator features. In particular, we propose a Mercier criterion which is purposely designed to allow for direct comparison with local flux-tube gyrokinetics simulations. We investigate the influence on the marginal frequency of the mode of a magnetic curvature which is inhomogeneous on the magnetic flux surface due to the fieldline-label dependence. This is a typical (surface) global effect present in non-axisymmetry. Finally, we propose an artificial equilibrium model that explicitly retains the fieldline-label dependence in the magnetic drift, and analyse the stability of the system by introducing a representation of the perturbations similar to the flux-bundle model of Sugama et al. (Plasma Fusion Res., vol. 7, 2012, 2403094). The coupling of flux bundles is shown to have a stabilising effect on the most unstable local flux-tube mode.

Keywords

fusion plasmaplasma instabilities
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 3 , June 2018 , 745840303
Copyright
© Cambridge University Press 2018 

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

Aleynikova, K. & Zocco, A. 2017 Quantitative study of kinetic ballooning mode theory in simple geometry. Phys. Plasmas 24 (9), 092106.Google Scholar
Aleynikova, K., Zocco, A., Xanthopoulos, P., Helander, P. & Nührenberg, C. 2018 Kinetic ballooning modes in tokamaks and stellarators. J. Plasma Phys. (to appear on this issue).CrossRefGoogle Scholar
Bauer, F., Betancourt, O. & Garabedian, P. 1984 Magnetohydrodynamic Equilibrium and Stability of Stellarators. Springer.Google Scholar
Baumgaertel, J. A., Hammett, G. W., Mikkelsen, D. R., Nunami, M. & Xanthopoulos, P. 2012 Gyrokinetic studies of the effect of $\unicode[STIX]{x1D6FD}$ on drift-wave stability in the national compact stellarator experiment. Phys. Plasmas 19 (12), 122306.Google Scholar
Boozer, A. H. 1981 Plasma equilibrium with rational magnetic surfaces. Phys. Fluids 24 (11), 1999–2003.CrossRefGoogle Scholar
Boozer, A. H. 1982 Establishment of magnetic coordinates for a given magnetic field. Phys. Fluids 25 (3), 520–521.CrossRefGoogle Scholar
Chen, L. & Zonca, F. 2016 Physics of Alfvén waves and energetic particles in burning plasmas. Rev. Mod. Phys. 88, 015008.CrossRefGoogle Scholar
Connor, J. W., Tang, W. M. & Allen, L. 1984 Finite-Larmor-radius modification of the Mercier criterion. Nucl. Fusion 24 (8), 1023.Google Scholar
Connor, J. W., Hastie, R. J. & Taylor, J. B. 1978 Phys. Rev. Lett. 40 (6), 396.Google Scholar
Connor, J. W., Hastie, R. J. & Taylor, J. B. 1979 High mode number stability of an axisymmetric toroidal plasma. Proc. R. Soc. Lond. A 365 (1720), 1–17.Google Scholar
Cooper, A. 1992 Variational formulation of the linear MHD stability of 3D plasmas with noninteracting hot electrons. Plasma Phys. Control. Fusion 34 (6), 1011.Google Scholar
Cooper, W. A., Singleton, D. B. & Dewar, R. L. 1996 Spectrum of ballooning instabilities in a stellarator. Phys. Plasmas 3 (1), 275–280.Google Scholar
Correa-Restrepo, D. 1978 Ballooning modes in three-dimensional MHD equilibria. Z. Naturforsch. 33a, 789–791.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
Fu, G. Y., Cooper, W. A., Gruber, R., Schwenn, U. & Anderson, D. V. 1992 Fully three-dimensional ideal magnetohydrodynamic stability analysis of low- $n$ modes and Mercier modes in stellarators. Phys. Fluids B 4 (6), 1401–1411.Google Scholar
Gardner, H. J. & Blackwell, D. B. 1992 Calculation of Mercier stability limits of toroidal heliacs. Nucl. Fusion 32 (11), 2009.Google Scholar
Glasser, A. H., Green, J. M. & Johnson, J. L. 1976 Resistive instabilities in a tokamak. Phys. Fluids 19, 567–574.Google Scholar
Hamada, S. 1962 Hydromagnetic equilibria and their proper coordinates. Nucl. Fusion 2, 23.Google Scholar
Hastie, R. J. & Taylor, J. B. 1981 Validity of ballooning representation and mode number dependence of stability. Nucl. Fusion 21 (2), 187.CrossRefGoogle Scholar
Hegna, C. C. & Nakajima, N. 1998 On the stability of Mercier and ballooning modes in stellarator configurations. Phys. Plasmas 5 (5), 1336–1344.Google 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.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
Ishizawa, A., Watanabe, T.-H., Sugama, H., Nunami, M., Tanaka, K., Maeyama, S. & Nakajima, N. 2015 Turbulent transport of heat and particles in a high ion temperature discharge of the large helical device. Nucl. Fusion 55 (4), 043024.CrossRefGoogle Scholar
Jenko, F. & Kendl, A. 2002 Radial and zonal modes in hyperfine-scale stellarator turbulence. Phys. Plasmas 9 (10), 4103.Google Scholar
Johnson, J. L. & Greene, J. M. 1967 Resistive interchanges and the negative $V^{\prime \prime }$ criterion. Plasma Phys. 9 (5), 611.CrossRefGoogle Scholar
Mercier, C. 1960 Un critere necessaire de stabilité hydromagnetic pour un plasma en symetry de revolution. Nucl. Fusion 1, 47–53.Google Scholar
Mercier, C. & Luc, H. 1974 Lectures in Plasma Physics. Commision of the European Communities.Google Scholar
Mishchenko, A., Borchardt, M., Cole, M., Hatzky, R., Fehér, T., Kleiber, R., Könies, A. & Zocco, A. 2015 Global linear gyrokinetic particle-in-cell simulations including electromagnetic effects in shaped plasmas. Nucl. Fusion 55 (5), 053006.CrossRefGoogle Scholar
Nührenberg, J. & Zille, R. 1987 Equilibrium and stability of low-shear stellarators. Theory of Fusion Plasmas 3–23.Google Scholar
Nunami, M., Watanabe, T.-H. & Sugama, H. 2010 Gyrokinetic Vlasov code including full three-dimensional geometry of experiments. Plasma Fusion Res. 5, 016–016.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, 032112-1–032112-14.Google Scholar
Porcelli, F. & Rosenbluth, M. N. 1998 Modified Mercier criterion. Plasma Phys. Control. Fusion 40 (4), 481.Google Scholar
Proll, J. H. E., Xanthopoulos, P. & Helander, P. 2013 Collisionless microinstabilities in stellarators. II. Numerical simulations. Phys. Plasmas 20 (12), 122506.Google Scholar
Roberts, K. V. & Taylor, J. B. 1965 Magnetohydrodynamic equations for finite Larmor radius. Phys. Rev. Lett. 8 (5), 197–198.CrossRefGoogle Scholar
Sugama, H. & Watanabe, T.-H. 2004 Study of electromagnetic microinstabilities in helical systems with the stellarator expansion method. Phys. Plasmas 11 (6), 3068–3077.Google Scholar
Sugama, H., Watanabe, T.-H., Nunami, M., Satake, S., Matsuoka, S. & Tanaka, K. 2012 Kinetic simulations of neoclassical and anomalous transport processes in helical systems. Plasma Fusion Res. 7, 2403094.Google Scholar
Tang, W. M., Connor, J. W. & Hastie, R. J. 1980 Nucl. Fusion 20 (11), 1439.Google Scholar
Xanthopoulos, P., Cooper, W. A., Jenko, F., Turkin, Yu., Runov, A. & Geiger, J. 2009 A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations. Phys. Plasmas 16 (8).CrossRefGoogle Scholar
Xanthopoulos, P., Plunk, G. G., Zocco, A. & Helander, P. 2016 Intrinsic turbulence stabilization in a stellarator. Phys. Rev. X 6, 021033; 021033-1–021033-5.Google Scholar
Zocco, A., Plunk, G. G., Xanthopoulos, P. & Helander, P. 2016 Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. I. Nearly axisymmetric systems. Phys. Plasmas 23 (8).Google Scholar
Zocco, A., Xanthopoulos, P. & Helander, P.2018. Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. II. Non-axisymmetric systems. (in preparation).Google Scholar