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Magnetic well and Mercier stability of stellarators near the magnetic axis

Part of: Focus on Fusion

Published online by Cambridge University Press:  15 October 2020

Matt Landreman Open the ORCID record for Matt Landreman [Opens in a new window]  and
Rogerio Jorge Open the ORCID record for Rogerio Jorge [Opens in a new window]
Matt Landreman*
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD20742, USA
Rogerio Jorge
Affiliation:
Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD20742, USA
*
†Email address for correspondence: mattland@umd.edu
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Abstract

We have recently demonstrated that by expanding in small distance from the magnetic axis compared with the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate the magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the ‘inverse expansion’ in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

Keywords

fusion plasmaplasma instabilitiesplasma confinement
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 5 , October 2020 , 905860510
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

de Aguilera, A. M., Castejon, F., Ascasibar, E., Blanco, E., de la Cal, E., Hidalgo, C., Liu, B., Lopez-Fraguas, A., Medina, F., Ochando, M. A., et al. 2015 Magnetic well scan and confinement in the TJ-II stellarator. Nucl. Fusion 55, 113014.Google Scholar
Anderson, F. S. B., Almagri, A. F., Anderson, D. T., Matthews, P. G., Talmadge, J. N. & Shohet, J. L. 1995 The helically symmetric experiment (HSX): goals, design, and status. Fusion Technol. 27, 273.Google Scholar
Bauer, F., Betancourt, O., Garabedian, P. & Bauer, F. 1984 Magnetohydrodynamic Equilibrium and Stability of Stellarators. Springer.Google Scholar
Beidler, C., Grieger, G., Herrnegger, F., Harmeyer, E., Kisslinger, J., Lotz, W., Maassberg, H., Merkel, P., Nührenberg, J., Rau, F., et al. 1990 Physics and engineering design for Wendelstein VII-X. Fusion Technol. 17, 148.CrossRefGoogle Scholar
Carreras, B. A., Dominguez, N., Garcia, L., Lynch, V. E., Lyon, J. F., Cary, J. R., Hanson, J.D. & Navarro, A. P. 1988 Low-aspect-ratio torsatron configurations. Nucl. Fusion 28, 1195.Google Scholar
Drevlak, M., Beidler, C. D., Geiger, J., Helander, P. & Turkin, Y. 2019 Optimisation of stellarator equilibria with ROSE. Nucl. Fusion 59, 016010.CrossRefGoogle Scholar
Freidberg, J. P. 2014 Ideal MHD. Cambridge University Press.Google Scholar
Garren, D. A. & Boozer, A. H. 1991 a Existence of quasihelically symmetric stellarators. Phys. Fluids B 3, 2822.Google Scholar
Garren, D. A. & Boozer, A. H. 1991 b Magnetic field strength of toroidal plasma equilibria. Phys. Fluids B 3, 2805.Google Scholar
Geiger, J. E., Weller, A., Zarnstorff, M. C., Nührenberg, C., Werner, A., Kolesnichenko, Y. I. & the W7-AS team 2004 Equilibrium and stability of high-$\beta$ plasmas in Wendelstein 7-AS. Fusion Sci. Technol. 46, 13.Google Scholar
Glasser, A. H., Greene, J. M. & Johnson, J. L. 1975 Resistive instabilities in general toroidal plasma configurations. Phys. Fluids 18 (7), 875–888.Google Scholar
Glasser, A. H., Greene, J. M. & Johnson, J. L. 1976 Resistive instabilities in a tokamak. Phys. Fluids 19, 567.Google Scholar
Greene, J. M. 1998 A brief review of magnetic wells. General Atomics report GA A22135.Google Scholar
Greene, J. M. & Johnson, J. L. 1961 Stability criterion for arbitrary hydromagnetic equilibria. Phys. Rev. Lett. 7, 401.Google Scholar
Greene, J. M. & Johnson, J. L. 1962 a Erratum: stability criterion for arbitrary hydromagnetic equilibria. Phys. Fluids 5, 1488.Google Scholar
Greene, J. M. & Johnson, J. L. 1962 b Stability criterion for arbitrary hydromagnetic equilibria. Phys. Fluids 5, 510.Google Scholar
Hirshman, S. P. & Whitson, J. C. 1983 Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria. Phys. Fluids 26, 3553.Google Scholar
Ichiguchi, K., Nakajima, N., Okamoto, M., Nakamura, Y. & Wakatani, M. 1993 Effects of net toroidal current on the Mercier criterion in the large helical device. Nucl. Fusion 33, 481.Google Scholar
Jorge, R., Sengupta, W. & Landreman, M. 2020 a Construction of quasisymmetric stellarators using a direct coordinate approach. Nucl. Fusion 60, 076021.CrossRefGoogle Scholar
Jorge, R., Sengupta, W. & Landreman, M. 2020 b Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis. J. Plasma Phys. 86, 905860106.Google Scholar
Küppers, G. & Tasso, H. 1972 Stability to localized modes for a class of axisymmetric magnetohydrodynamic equilibria. Z. Naturforsch. 27, 23.Google Scholar
Landreman, M. 2019 Optimized quasisymmetric stellarators are consistent with the Garren-Boozer construction. Plasma Phys. Control. Fusion 61, 075001.CrossRefGoogle Scholar
Landreman, M. 2020 a Dataset on Zenodo. Available at: http://doi.org/10.5281/zenodo.4011733.Google Scholar
Landreman, M. 2020 b Dataset on Zenodo. Available at: http://doi.org/10.5281/zenodo.4012185.Google Scholar
Landreman, M. & Sengupta, W. 2018 Direct construction of optimized stellarator shapes. I. Theory in cylindrical coordinates. J. Plasma Phys. 84, 905840616.Google Scholar
Landreman, M. & Sengupta, W. 2019 Constructing stellarators with quasisymmetry to high order. J. Plasma Phys. 85, 905850608.Google Scholar
Landreman, M., Sengupta, W. & Plunk, G. G. 2019 Direct construction of optimized stellarator shapes. II. Numerical quasisymmetric solutions. J. Plasma Phys. 85, 905850103.Google Scholar
Laval, G., Luc, H., Maschke, E. K., Mercier, C. & Pellat, R. 1971 Equilibrium, stability and diffusion of a toroidal plasma of non-circular cross-section. In Plasma Physics and Controlled Nuclear Fusion Research, vol. II, p. 507. International Atomic Energy Agency.Google Scholar
Lortz, D. & Nührenberg, J. 1973 Comparison between necessary and sufficient stability criteria for axially symmetric equilibria. Nucl. Fusion 13, 821.CrossRefGoogle Scholar
Lortz, D. & Nührenberg, J. 1976 Equilibrium and stability of a three-dimensional toroidal MHD configuration near its magnetic axis. Z. Naturforsch. 31a, 1277.Google Scholar
Mercier, C. 1962 Critère de stabilité d'un système toroïdal hydromagnétique en pression scalaire. Nucl. Fusion Supplement, part 2, 801.Google Scholar
Mercier, C. 1964 Equilibrium and stability of a toroidal magnetohydrodynamic system in the neighbourhood of a magnetic axis. Nucl. Fusion 4, 213.Google Scholar
Mercier, C. & Luc, H. 1974 The Magnetohydrodynamic Approach to the Problem of Plasma Confinement in Closed Magnetic Configurations. Commission of the European Communities.Google Scholar
Mikhailovskii, A. B. 1974 Tokamak stability at high plasma pressures. Nucl. Fusion 14, 483.Google Scholar
Mikhailovskii, A. B. & Aburdzhaniya, K. D. 1979 Mercier criterion for a finite-pressure plasma in arbitrary-shaped magnetic axis configurations. Plasma Phys. 21, 109.Google Scholar
Plunk, G. G., Landreman, M. & Helander, P. 2019 Direct construction of optimized stellarator shapes. III. Omnigenity near the magnetic axis. J. Plasma Phys. 85, 905850602.Google Scholar
Pustovitov, V. D. & Shafranov, V. D. 1984 Reviews of Plasma Physics, vol. 15. Consultants Bureau.Google Scholar
Rizk, H. M. 1981 MHD stability of toroidal plasma with modulated curvature planar magnetic axis. Plasma Phys. 23, 385.CrossRefGoogle Scholar
Shafranov, V. D. & Yurchenko, E. I. 1968 Influence of ballooning effects on plasma stability in closed systems. Nucl. Fusion 8, 329.Google Scholar
Solov'ev, L. S. & Shafranov, V. D. 1970 Reviews of Plasma Physics 5. Consultants Bureau.Google Scholar
Watanabe, K. Y., Sakakibara, S., Narushima, Y., Funaba, H., Narihara, K., Tanaka, K., Yamaguchi, T., Toi, K., Ohdachi, S., Kaneko, O., et al. 2005 Effects of global MHD instability on operational high beta-regime in LHD. Nucl. Fusion 45, 1247.CrossRefGoogle Scholar
Weimer, K. E., Frieman, E. A. & Johnson, J. L. 1975 Localized magnetohydrodynamic instabilities in tokamaks with non-circular cross sections. Plasma Phys. 17, 645.Google Scholar
Weller, A., Sakakibara, S., Watanabe, K. Y., Toi, K., Geiger, J., Zarnstorff, M. C., Hudson, S. R., Reiman, A., Werner, A., Nührenberg, C., et al. 2006 Significance of MHD effects in stellarator confinement. Fusion Sci. Technol. 50, 158.Google Scholar
Whiteman, K. J., McNamara, B. & Taylor, J. B. 1965 Negative $V''$ on a general magnetic axis. Phys. Fluids 8, 2293.Google Scholar
Zarnstorff, M. C., Berry, L. A., Brooks, A., Fredrickson, E., Fu, G-Y., Hirshman, S., Hudson, S., Ku, L-P., Lazarus, E., Mikkelsen, D., et al. 2001 Physics of the compact advanced stellarator NCSX. Plasma Phys. Control. Fusion 43, A237.Google Scholar