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Stellarator design

Part of: Frontiers in Plasma Physics Conference Focus on Fusion PLA Tribute to V D Shafranov: 1929-2014

Published online by Cambridge University Press:  09 December 2015

Allen H. Boozer
Allen H. Boozer*
Affiliation:
Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA
*
†Email address for correspondence: [email protected]
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Abstract

This paper is dedicated to Vitaly Shafranov, who became increasingly interested in stellarators. Stellarators have a steady-state magnetic configuration, robust positional stability, and consistency with a plasma current below the level at which runaway electrons become a major issue. The development path for stellarators may be faster and cheaper than for tokamaks: stellarators are amenable to computer design validated by moderate scale experiments to circumvent issues that impede fusion development. This is distinct from the empirical explorations required to find an acceptable nonlinear, self-organized state of a tokamak. Fusion plasmas can be designed and controlled in stellarators in ways that are not possible in tokamaks. This paper outlines computational studies that could be carried at low cost during the next few years that would clarify the reactor potential of the stellarator and are needed for rational planning of the fusion program.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 515810606
Copyright
© Cambridge University Press 2015 

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References

Bauer, F., Betancourt, O. & Garabedian, P. 1984 Magnetohydrodynamic Equilibrium and Stability of Stellarators. Springer.Google Scholar
Boozer, A. H. 1983 Evaluation of the structure of ergodic fields. Phys. Fluids 26, 1288–1291.Google Scholar
Boozer, A. H. 2015 Non-axisymmetric magnetic fields and toroidal plasma confinement. Nucl. Fusion 55, 025001.Google Scholar
Boozer, A. H. & Ku, L. P. 2011 Control of stellarator properties illustrated by a Wendelstein7-X equilibrium. Phys. Plasmas 18, 052501.Google Scholar
Breslau, J.2015 Unpublished report on the COILOPT++ code.Google Scholar
Bromberg, L., Zarnstorff, M., Meneghini, O., Brown, T., Heitzenroeder, P., Neilson, G. H., Minervini, J. V. & Boozer, A. 2011 Stellarator configuration improvement using high temperature superconducting monoliths. Fusion Sci. Technol. 60, 643–647.Google Scholar
Brown, T., Pomphrey, N., Breslau, J. & Zolfaghari, A.2014 Unpublished report on modified NCSX coils.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, 056107.Google Scholar
Cary, J. R. & Shasharina, S. G. 1997 Omnigeneous stellarators. Plasma Phys. Rep. 23, 509–511.Google Scholar
Chodura, R., Dommaschk, W., Herrnegger, F., Lotz, W., Nührenberg, J. & Schlüter, A. 1981 Theoretical optimization of stellarators. IEEE Trans. Plasma Sci. 9, 221–228.Google Scholar
Evans, T., Yu, J., Jakubowski, M., Schmitz, O., Watkins, J. & Moyer, R. 2009 A conceptual model of the magnetic topology and nonlinear dynamics of ELMs. J. Nucl. Mater. 390–391, 789–792.Google Scholar
Evans, T. E., Roeder, R. K. W, Carter, J. A. & Rapoport, B. I. 2004 Homoclinic tangles, bifurcations and edge stochasticity in diverted tokamaks. Contrib. Plasma Phys. 44, 235–240.CrossRefGoogle Scholar
Feder, T. 2008 US Stellarator aborted. Phys. Today 61 (7), 25.Google Scholar
Feng, Y., Frerichs, H., Kobayashi, M., Bader, A., Effenberg, F., Harting, D., Hoelbe, H., Huang, J., Kawamura, G., Lore, J. D. et al. 2014 Recent improvements in the EMC3-Eirene code. Contrib. Plasma Phys. 54, 426–431.Google Scholar
Feng, Y., Sardei, F., Grigull, P., McCormick, K., Kisslinger, J. & Reiter, D. 2006 Physics of island divertors as highlighted by the example of W7-AS. Nucl. Fusion 46, 807–819.Google Scholar
Feng, Y., Sardei, F., Kisslinger, J. & Grigull, P. 1997 3D Monte Carlo code for plasma transport in island divertors. J. Nucl. Mater. 241, 930–934.Google Scholar
Garabedian, P. R. 1996 Stellarators with the magnetic symmetry of a tokamak. Phys. Plasmas 3, 2483–2485.Google Scholar
Greene, J. M. 1979 Method of determining a stochastic transition. Math. Phys. 20, 1183–1201.Google Scholar
Helander, P. 2014 Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys. 77, 087001.CrossRefGoogle ScholarPubMed
Hirshman, S. P. & Whitson, J. C. 1983 Steepest-descent moment method for 3-dimensional magnetohydrodynamic equilibria. Phys. Fluids 26, 3553–3568.Google Scholar
Kerst, D. W. 1962 The influence of errors on plasma-confining magnetic fields. J. Nucl. Energy C 4, 253–262.Google Scholar
Ku, L. P. & Boozer, A. H. 2010a New classes of quasi-helically symmetric stellarators. Nucl. Fusion 51, 013004.Google Scholar
Ku, L. P. & Boozer, A. H. 2010b Stellarator coil design and plasma sensitivity. Phys. Plasmas 17, 122503.CrossRefGoogle Scholar
Landreman, M. & Catto, P. J. 2012 Omnigenity as generalized quasisymmetry. Phys. Plasmas 19, 056103.Google Scholar
Mau, T. K., Kaiser, T. B., Grossman, A. A., Raffray, A. R., Want, X. R., Lyon, J. F., Maingi, R., Ku, L. P., Zarnstorff, M. C.& ARIES-CS Team 2008 Divertor Configuration and heat load studies for the ARIES-CS fusion power plant. Fusion Sci. Technol. 54, 771–786.Google Scholar
Meiss, J. D. 2015 Thirty years of turnstiles and transport. Chaos 25, 097602.CrossRefGoogle ScholarPubMed
Merkel, P. 1987 Solution of stellarator boundary-value-problems with external currents. Nucl. Fusion 27, 867–871.CrossRefGoogle Scholar
Mikhailov, M. I., Drevlak, M., Nührenberg, J. & Shafranov, V. D. 2012 Medium-beta free-boundary equilibria of a quasi-isiodynamic stellarator. Plasma Phys. Rep. 38, 439–442.Google Scholar
Mioduszewski, P. K., Owen, L. W., Spong, D. A., Fenstermacher, M. E., Koniges, A. E., Rognlien, T. D., Umansky, M. V., Grossman, A. & Kugel, H. W. 2007 Power and particle handling and wall conditioning in NCSX. Fusion Sci. Technol. 51, 238–260.Google Scholar
Neilson, G. H., Heitzenroeder, P. J., Nelson, B. E., Reiersen, W. T., Brooks, A., Brown, T. G., Chrzanowski, J. H., Cole, M. J., Dahlgren, F., Dodson, T. et al. 2009 Engineering accomplishments in the construction of NCSX. Fusion Sci. Technol. 56, 485–492.Google Scholar
Nemov, V. V., Kasilov, S. V., Kernbichler, W. & Heyn, M. F. 1999 Evaluation of 1/nu neodclassical trasport in stellarators. Phys. Plasmas 6, 4622–4632.Google Scholar
Nührenberg, C., Boozer, A. H. & Hudson, S. R. 2009 Magnetic surface quality in non-axisymmetric plasma equililbria. Phys. Rev. Lett. 102, 235001.Google Scholar
Nührenberg, C., Mikhailov, M. I., Nührenberg, J. et al. 2010 Quasi-helical symmetry at finite aspect ratio. Plasma Phys. Rep. 36, 558–562.Google Scholar
Nührenberg, J. 2006 Critical issues and comparison of optimized stellarators. Fusion Sci. Technol. 50, 146–157.Google Scholar
Nührenberg, J. 2010 Development of quasi-isodynamic stellarators. Plasma Phys. Control. Fusion 52, 124003.Google Scholar
Nührenberg, J., Lotz, W. & Gori, S. 1994 Quasi-axisymmetric Tokamaks. In Theory of Fusion Plasmas (ed. Sindoni, E., Tryon, E. & Vaclavik, J.), vol. 15, p. 3. Editrice Copositori.Google Scholar
Nührenberg, J., Lotz, W., Merkel, P., Nührenberg, C., Schwenn, U., Strumberger, E. & Hayashi, T. 1995 Overview on Wendelstein 7-X theory. Fusion Technol. 27, 71–78; (Supplement S).Google Scholar
Nührenberg, J. & Strumberger, E. 1992 Development of divertor concept for optimized stellarators. Contrib. Plasma Phys. 32, 204–211.CrossRefGoogle Scholar
Nührenberg, J. & Zille, R. 1988 Stable stellarators with medium-beta and aspect ratio. Phys. Lett. A 129, 113–117.Google Scholar
Park, J.-K., Schaffer, M. J., Menard, J. E. & Boozer, A. H. 2007 Control of asymmetric magnetic perturbations in tokamaks. Phys. Rev. Lett. 99, 195003.Google Scholar
Park, J.-K., Boozer, A. H., Menard, J. E. & Schaffer, M. J. 2008 Error field correction in ITER. Nucl. Fusion 48, 045006.CrossRefGoogle Scholar
Poincaré, H. 1899 Les Méthodes Nouvelles de la Mécanique Céleste, vol. 3. Gauthier-Villars.Google Scholar
Punjabi, A. & Boozer, A. 2014 Homoclinic tangle in tokamak divertors. Phys. Lett. A 378, 2410.Google Scholar
Reiman, A., Fu, G., Hirshman, S., Ku, L., Monticello, D., Mynick, H., Redi, M., Spong, D., Zarnstorff, M., Blackwell, B. et al. 1999 Physics design of a high-beta QA stelllarator. Plasma Phys. Control. Fusion 41, B273–B283.CrossRefGoogle Scholar
Risse, K.& W7-X Team 2009 Experiences from design and production of Wendelstein 7-X magnets. Fusion Engng Des. 84, 1619–1622.CrossRefGoogle Scholar
Shafranov, V. D. 2001 Some theoretical problems of the toroidal plasma equilibrium. Plasma Phys. Control. Fusion 12A, A1–A10; Supplement.Google Scholar
Shafranov, V. D., Mikhailov, M. I. & Skovoroday, A. A. 1999 Quasisymmetrical stellarators and mirrors. Fusion Technol. 35, 67–76.Google Scholar
Shafranov, V. D. & Zakharov, L. 1972 Use of virtual-casing principle in calculating containing magnetic-field in toroidal plasma systems. Nucl. Fusion 12, 599–601.Google Scholar
Strickler, D. J., Berry, L. A. & Hirshman, S. P. 2002 Designing coils for compact stellarators. Fusion Sci. Technol. 41, 107–115.Google Scholar
Strikler, D. J., Hirshman, S. P., Spong, D. A., Cole, M. J., Lyon, J. F., Nelson, B. E., Williamson, D. E. & Ware, A. S. 2004 Development of a robust quasi-poloidal compact stellarator. Fusion Sci. Technol. 45, 15–26.Google Scholar
Strumberger, E. 1992 Magnetic field diversion in Helias stellarator configurations. Nucl. Fusion 32, 737–744.Google Scholar
Strumberger, E. 1996 SOL studies for W7-X based on the island divertor concept. Nucl. Fusion 36, 891–908.CrossRefGoogle Scholar
Velikhov, E. P., Gibson, A. G., Zakharov, V. E., Zelenyi, L. M., Imshennik, V. S., Kraraś, V. I., Clark, J., Coppi, B., Litvak, A. G., Ryutov, D. D. et al. 2014 In memory of Vitaly Dmitrievich Shafranov. Phys. Uspekhi 57, 1244–1245.Google Scholar