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Non-axisymmetric local magnetostatic equilibrium

Part of: Focus on Fusion

Published online by Cambridge University Press:  24 March 2015

J. Candy  and
E. A. Belli
J. Candy*
Affiliation:
General Atomics, P.O. Box 85608, San Diego, CA 92186-5608, USA
E. A. Belli
Affiliation:
General Atomics, P.O. Box 85608, San Diego, CA 92186-5608, USA
*
†Email address for correspondence: candy@fusion.gat.com
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Abstract

In this work we outline an approach to the problem of local equilibrium in non-axisymmetric configurations that adheres closely to Miller's original method for axisymmetric plasmas (Miller et al. 1998 Phys. Plasmas5, 973). Importantly, this method is novel in that it allows not only specification of 3D shape, but also explicit specification of the shear in the 3D shape. A spectrally-accurate method for solution of the resulting nonlinear partial differential equations is also developed. We verify the correctness of the spectral method, in the axisymmetric limit, through comparisons with an independent numerical solution. Some analytic results for the two-dimensional case are given, and the connection to Boozer coordinates is clarified.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 3 , June 2015 , 905810323
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Copyright
Copyright © Cambridge University Press 2015 

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References

REFERENCES

Baumgaertel, J. A., Belli, E. A., Dorland, W., Guttenfelder, W., Hammett, G. W., Mikkelsen, D. R., Rewoldt, G., Tang, W. M. and Xanthopoulos, P. 2011 Simulating gyrokinetic microinstabilities in stellarator geometry with GS2. Phys. Plasmas 18, 122301.CrossRefGoogle Scholar
Bird, T. M. and Hegna, C. C. 2013 A model for microinstability destabilization and enhanced transport in the presence of shielded 3D magnetic perturbations. Nucl. Fusion 53, 013004.CrossRefGoogle Scholar
Bishop, C. M., Kirby, P., Connor, J. W., Hastie, R. J. and Taylor, J. B. 1984 Ideal MHD ballooning stability in the vicinity of a separatrix. Nucl. Fusion 24, 1579.CrossRefGoogle Scholar
Boozer, A. H. 2002 Local equilibrium of nonrotating plasmas. Phys. Plasmas 9, 3762.CrossRefGoogle Scholar
Candy, J. 2009 A unified method for operator evaluation in local Grad-Shafranov plasma equilibria. Plasma Phys. Control. Fusion 51, 105009.CrossRefGoogle Scholar
Candy, J., Holland, C., Waltz, R. E., Fahey, M. R. and Belli, E. 2009 Tokamak profile prediction using direct gyrokinetic and neoclassical simulation. Phys. Plasmas 16, 060704.CrossRefGoogle Scholar
Greene, J. M. and Chance, M. S. 1981 Nucl. Fusion 21, 453.CrossRefGoogle Scholar
Hegna, C. C. 2000 Local three-dimensional magnetostatic equilibria. Phys. Plasmas 7, 3921.CrossRefGoogle Scholar
Hirshman, S. P., Shaing, K. C., van Rij, W. I., Beasley, C. O. Jr., and Crume, E. C. Jr., 1986 Plasma transport coefficients for nonsymmetric toroidal confinement systems. Phys. Fluids 29, 2951.CrossRefGoogle Scholar
Hirshman, S. P. and Whitson, J. C. 1983 Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria. Phys. Fluids 26, 3553.CrossRefGoogle Scholar
Landreman, M., Smith, H. M., Mollen, A. and Helander, P. 2014 Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas. Phys. Plasmas 21, 042503.CrossRefGoogle Scholar
Mercier, C. and Luc, N. 1974 Tech. Rep. Commission of the European Communities, Report No. EUR-5127e 140, Brussels.Google Scholar
Miller, R. L., Chu, M. S., Greene, J. M., Lin-liu, Y. R. and Waltz, R. E. 1998 Noncircular, finite aspect ratio, local equilibrium model. Phys. Plasmas 5, 973.CrossRefGoogle Scholar
Moré, J. J., Garbow, B. S. and Hillstrom, K. E. 1980 User guide for MINPACK-1. Tech. Rep. ANL-80-74. Argonne National Laboratory, Argonne, IL, USA.CrossRefGoogle Scholar
van Rij, W. I. and Hirshman, S. P. 1989 Variational bounds for transport coefficients in three-dimensional toroidal plasmas. Phys. Fluids B 1, 563.CrossRefGoogle Scholar
Waltz, R. E. and Miller, R. L. 1999 Ion temperature gradient turbulence simulations and plasma flux surface shape. Phys. Plasmas 6, 4265.CrossRefGoogle Scholar
Xanthopoulos, P., Merz, F., Görler, T. and Jenko, F. 2007 Nonlinear gyrokinetic simulations of Ion-temperature-gradient turbulence for the optimized Wendelstein 7-X stellarator. Phys. Rev. Lett. 99, 035002.CrossRefGoogle ScholarPubMed