×

Optimization of energy confinement in the \(1/\nu \) regime for stellarators. (English) Zbl 1159.82322

For certain conditions the stellarator magnetic field can be originally obtained in the real space coordinates and there is no necessity in its transformation to magnetic coordinates. A procedure working in real space coordinates is presented for maximizing the plasma energy content, based on reducing the most unfavorable \(1/\nu\) neoclassical transport. Preliminary results for the heliac-type stellarator TJ-II are presented showing a configuration with almost twice the stored energy of the standard TJ-II configuration.

MSC:

82D10 Statistical mechanics of plasmas

Software:

MPI/MPICH
Full Text: DOI

References:

[1] Nührenberg, J.; Zille, R., Quasi-helically symmetric toroidal stellarators, Phys. Lett. A, 129, 2, 113-117 (1988)
[2] Garren, D. A.; Boozer, A. H., Existence of quasihelically symmetric stellarators, Phys. Fluids B, 3, 10, 2822-2843 (1991)
[3] Isaev, M. Yu.; Mikhailov, M. I.; Shafranov, V. D., Quasi-symmetrical toroidal magnetic systems, Plasma Phys. Rep., 20, 4, 319-335 (1994)
[4] M.I. Mikhailov, M. Yu. Isaev, J. Nuehrenberg, A.A. Subbotin, W.A. Cooper, M.F. Heyn, V.N. Kalyuzhnyj, S.V. Kasilov, W. Kernbichler, V.V. Nemov, M.A. Samitov, V.D. Shafranov, Topology of magnetic field strength surfaces and particle confinement in mirror-type stellarators, in: C. Silva, C. Varandas, D. Campbell (Eds.), 28th EPS Conference on Controlled Fusion and Plasma Physics, Funchal, 18-22 June 2001, vol. 25A of ECA, European Physical Society, 2001, pp. 757-760.; M.I. Mikhailov, M. Yu. Isaev, J. Nuehrenberg, A.A. Subbotin, W.A. Cooper, M.F. Heyn, V.N. Kalyuzhnyj, S.V. Kasilov, W. Kernbichler, V.V. Nemov, M.A. Samitov, V.D. Shafranov, Topology of magnetic field strength surfaces and particle confinement in mirror-type stellarators, in: C. Silva, C. Varandas, D. Campbell (Eds.), 28th EPS Conference on Controlled Fusion and Plasma Physics, Funchal, 18-22 June 2001, vol. 25A of ECA, European Physical Society, 2001, pp. 757-760.
[5] Mikhailov, M. I.; Shafranov, V. D.; Subbotin, A. A.; Isaev, M. Yu.; Nührenberg, J.; Zille, R.; Cooper, W. A., Improved \(α\)-particle confinement in stellarators with poloidally closed contours of the magnetic field strength, Nucl. Fusion, 42, L23-L26 (2002)
[6] A.A. Subbotin, W.A. Cooper, M. Yu. Isaev, M.I. Mikhailov, J. Nührenberg, M.F. Heyn, V.N. Kalyuzhnyj, S.V. Kasilov, W. Kern-bichler, V.V. Nemov, M.A. Samitov, V.D. Shafranov, R. Zille, Quasi-isodynamical configurations without transitional particle orbits, in: B. Duval (Ed.), 29th EPS Conference on Plasma Physics Controlled Fusion, Montreux, 17-21 June 2002, vol. 26B of ECA, European Physical Society, 2002, p. P-5.086.; A.A. Subbotin, W.A. Cooper, M. Yu. Isaev, M.I. Mikhailov, J. Nührenberg, M.F. Heyn, V.N. Kalyuzhnyj, S.V. Kasilov, W. Kern-bichler, V.V. Nemov, M.A. Samitov, V.D. Shafranov, R. Zille, Quasi-isodynamical configurations without transitional particle orbits, in: B. Duval (Ed.), 29th EPS Conference on Plasma Physics Controlled Fusion, Montreux, 17-21 June 2002, vol. 26B of ECA, European Physical Society, 2002, p. P-5.086.
[7] V.D. Shafranov, W.A. Cooper, M.F. Heyn, M. Yu. Isaev, V.N. Kalyuzhnyj, S.V. Kasilov, W. Kernbichler, M.I. Mikhailov, V.V. Nemov, C. Nührenberg, J. Nührenberg, M.A. Samitov, A.A. Skovoroda, A.A. Subbotin, R. Zille, Results of integrated optimization of \(n\); V.D. Shafranov, W.A. Cooper, M.F. Heyn, M. Yu. Isaev, V.N. Kalyuzhnyj, S.V. Kasilov, W. Kernbichler, M.I. Mikhailov, V.V. Nemov, C. Nührenberg, J. Nührenberg, M.A. Samitov, A.A. Skovoroda, A.A. Subbotin, R. Zille, Results of integrated optimization of \(n\)
[8] Grieger, G.; Lotz, W.; Merkel, P.; Nührenberg, J.; Sapper, J.; Strumberger, E.; Wobig, H.; Burhenn, R.; Erckmann, V.; Gasparino, U.; Giannone, L.; Hartfuss, H. J.; Jaenicke, R.; Kiihner, G.; Ringler, H.; Weller, A.; Wagner, F., Physics optimization of stellarators, Phys. Fluids B, 4, 7, 2081-2091 (1992)
[9] Almagri, A. F.; Anderson, D. T.; Anderson, F. S.B.; Probert, P. H.; Shohet, J. L.; Talmadge, J. N., A helically symmetric stellarator (HSX), IEEE Trans. Plasma Sci., 27, 1, 114-115 (1999)
[10] Reiman, A.; Ku, L.; Monticello, D.; Hirshman, S.; Hudson, S.; Kessel, C.; Lazarus, E.; Mikkelsen, D.; Zarnstorff, M.; Berry, L. A.; Boozer, A.; Brooks, A.; Cooper, W. A.; Drevlak, M.; Fredrickson, E.; Fu, G.; Goldston, R.; Hatcher, R.; Isaev, M.; Jun, C.; Knowlton, S.; Lewandowski, J.; Lin, Z.; Lyon, J. F.; Merkel, P.; Mikhailov, M.; Miner, W.; Mynick, H.; Neilson, G.; Nelson, B. E.; Nührenberg, C.; Pomphrey, N.; Redi, M.; Reiersen, W.; Rutherford, P.; Sanchez, R.; Schmidt, J.; Spong, D.; Strickler, D.; Subbotin, A.; Valanju, P.; White, R., Recent advances in the design of quasiax-isymmetric stellarator plasma configurations, Phys. Plasmas, 8, 5, 2083-2094 (2001)
[11] Zarnstorff, M. C.; Berry, L. A.; Brooks, A.; Fredrickson, E.; Fu, G. Y.; Hirshman, S.; Hudson, S.; Ku, L. P.; Lazarus, E.; Mikkelsen, D.; Monticello, D.; Neilson, G. H.; Pomphrey, N.; Reiman, A.; Spong, D.; Strickler, D.; Boozer, A.; Cooper, W. A.; Goldston, R.; Hatcher, R.; Isaev, M.; Kessel, C.; Lewandowski, J.; Lyon, J. F.; Merkel, P.; Mynick, H.; Nelson, B. E.; Nuehrenberg, C.; Redi, M.; Reiersen, W.; Rutherford, P.; Sanchez, R.; Schmidt, J.; White, R. B., Physics of the compact advanced stellarator NCSX, Plasma Phys. Contr. Fusion, 43, A237-A249 (2001)
[12] Spong, D. A.; Hirshman, S. P.; Berry, L. A.; Lyon, J. F.; Fowler, R. H.; Strickler, D. J.; Cole, M. J.; Nelson, B. N.; Williamson, D. E.; Ware, A. S.; Alban, D.; Sanchez, R.; Fu, G. Y.; Monticello, D. A.; Miner, W. H.; Valanju, P. M., Physics issues of compact drift optimized stellarators, Nucl. Fusion, 41, 6, 711-716 (2001)
[13] Spong, D. A.; Hirshman, S. P.; Lyon, J. F.; Berry, L. A.; Strickler, D. J., Recent advances in quasi-poloidal stellarator physics issues, Nucl. Fusion, 45, 918-925 (2005)
[14] Nemov, V. V.; Kasilov, S. V.; Kernbichler, W.; Heyn, M. F., Evaluation of \(1/ν\) neoclassical transport in stellarators, Phys. Plasmas, 6, 12, 4622-4632 (1999)
[15] Alejaldre, C.; Alonso, J.; Almoguera, L.; Ascasibar, E.; Baciero, A.; Balbin, R.; Blaumoser, M.; Botija, J.; Branas, B.; de la Cal, E.; Cappa, A.; Carrasco, R.; Castejon, F.; Cepero, J. R.; Cremy, C.; Doncel, J.; Dulya, C.; Estrada, T.; Fernandez, A.; Frances, M.; Fuentes, C.; Garcia, A.; Garcia-Cortes, I.; Guasp, J.; Herranz, J.; Hidalgo, C.; Jimenez, J. A.; Kirpitchev, I.; Krivenski, V.; Labrador, I.; Lapayese, F.; Likin, K.; Liniers, M.; Lopez-Fraguas, A.; Lopez-Sanchez, A.; de la Luna, E.; Martin, R.; Martinez, A.; Medrano, M.; Mendez, P.; McCarthy, K.; Medina, F.; van Milligen, B.; Ochando, M.; Pacios, L.; Pastor, I.; Pedrosa, M. A.; de la Peiia, A.; Portas, A.; Qin, J.; Rodriguez-Rodrigo, L.; Salas, A.; Sanchez, E.; Sanchez, J.; Tabares, F.; Tafalla, D.; Tribaldos, V.; Zurro, B.; Vega, J.; Akulina, D.; Fedyanin, O. I.; Grebenshchicov, S.; Kharchev, N.; Meshcheryakov, A.; Barth, R.; van Dijk, G.; van der Meiden, H.; Petrov, S., First plasmas in the TJ-II flexible Heliac, Plasma Phys. Contr. Fusion, 41, A539-A548 (1999)
[16] Mynick, H. E.; Pomphrey, N., Control-matrix approach to stellarator design and control, Phys. Plasmas, 7, 12, 4960-4971 (2000)
[17] Mynick, H. E.; Pomphrey, N.; Ethier, S., Exploration of stellarator configuration space with global search methods, Phys. Plasmas, 9, 3, 869-876 (2002)
[18] Hirshman, S. P.; van Rij, W. I.; Merkel, P., Three-dimensional free boundary calculations using a spectral Green’s function method, Comp. Phys. Commun., 43, 143-155 (1986)
[19] B. Seiwald, V.V. Nemov, V.N. Kalyuzhnyj, S.V. Kasilov, and W. Kernbichler, Optimization of neoclassical transport in URAGAN-2M, In: 31st EPS Conference on Plasma Physics London, 28 June-2 July 2004, vol. 28G of ECA, European Physical Society, 2004, p. P-5.118.; B. Seiwald, V.V. Nemov, V.N. Kalyuzhnyj, S.V. Kasilov, and W. Kernbichler, Optimization of neoclassical transport in URAGAN-2M, In: 31st EPS Conference on Plasma Physics London, 28 June-2 July 2004, vol. 28G of ECA, European Physical Society, 2004, p. P-5.118. · Zbl 1159.82322
[20] Hirshman, S. P.; Shaing, K. C.; van Rij, W. I.; Beasley, C. O.; Crume, E. C., Plasma transport coefficients for nonsymmetric toroidal confinement systems, Phys. Fluids, 29, 9, 2951-2959 (1986) · Zbl 0601.76053
[21] van Rij, W. I.; Hirshman, S. P., Variational bounds for transport coefficients in three-dimensional toroidal plasmas, Phys. Fluids B, 1, 3, 563-569 (1989)
[22] Reiman, A. H.; Greenside, H. S., Numerical solution of three-dimensional magnetic differential equations, J. Comput. Phys., 75, 423-443 (1988) · Zbl 0652.76070
[23] Harafuji, K.; Hayashi, T.; Sato, T., Computational study of three-dimensional magnetohydrodynamic equilibria in toroidal helical systems, J. Comput. Phys., 81, 1, 169-192 (1989) · Zbl 0662.76146
[24] Suzuki, Y.; Nakajima, N.; Watanabe, K.; Nakamura, Y.; Hayashi, T., Development and application of HINT2 to helical system plasmas, Nucl. Fusion, 46, 11, L19-L24 (2006)
[25] B. Seiwald, V.V. Nemov, S.V. Kasilov, and W. Kernbichler, Optimization of stellarators with respect to neoclassical transport in real space, in: B. Duval, (Ed.), 29th EPS Conference on Plasma Physics and Controlled Fusion, Montreux, 17-21 June 2002, vol. 26B of ECA, European Physical Society, 2002, p. P-4.099.; B. Seiwald, V.V. Nemov, S.V. Kasilov, and W. Kernbichler, Optimization of stellarators with respect to neoclassical transport in real space, in: B. Duval, (Ed.), 29th EPS Conference on Plasma Physics and Controlled Fusion, Montreux, 17-21 June 2002, vol. 26B of ECA, European Physical Society, 2002, p. P-4.099.
[26] Hazeltine, R. D.; Meiss, J. D., Plasma Confinement, Front. Physics, vol. 86 (1992), Addison Wesley
[27] Galeev, A. A.; Sagdeev, R. Z., Reviews of Plasma Physics, vol. 7 (1979), Consultants Bureau: Consultants Bureau New York
[28] Lotz, W.; Nührenberg, J., Monte Carlo computations of neoclassical transport, Phys. Fluids, 31, 10, 2984-2991 (1988) · Zbl 0657.76046
[29] Maaßberg, H.; Brakel, R.; Burhenn, R.; Gasparino, U.; Grigull, P.; Kick, M.; Kühner, G.; Ringler, H.; Sardei, F.; Stroth, U.; Weller, A., Transport in stellarators, Plasma Phys. Contr. Fusion, 35, B319-B332 (1993)
[30] Maaßberg, H.; Beidler, C. D.; Simmet, E. E., Density control problems in large stellarators with neoclassical transport, Plasma Phys. Contr. Fusion, 41, 1135-1153 (1999)
[31] Ida, K.; Osakabe, M.; Tanaka, K.; Minami, T.; Nishimura, S.; Okamura, S.; Fujisawa, A.; Yamazaki, K.; Yoshimura, Y.; Kubo, S.; Akiyama, R.; Darrow, D. S.; Idei, H.; Iguchi, H.; Isobe, M.; Kado, S.; Kondo, T.; Lee, S.; Matsuoka, K.; Morita, S.; Nomura, I.; Ohdachi, S.; Sasao, M.; Shimizu, A.; Takagi, S.; Takahashi, C.; Takayama, S.; Takechi, M.; Toi, K.; Tsumori, K.; Watari, T., Transition from l mode to high ion temperature mode in CHS heliotron/torsatron plasmas, Nucl. Fusion, 39, 11Y, 1649-1658 (1999)
[32] Motojima, O.; Ohyabu, N.; Komori, A.; Kaneko, O.; Yamada, H.; Kawahata, K.; Nakamura, Y.; Ida, K.; Akiyama, T.; Ashikawa, N.; Cooper, W. A.; Ejiri, A.; Emoto, M.; Ezumi, N.; Funaba, H.; Fukuyama, A.; Goncharov, P.; Goto, M.; Idei, H.; Ikeda, K.; Inagaki, S.; Isobe, M.; Kado, S.; Kawazome, H.; Khlopenkov, K.; Kobuchi, T.; Kondo, K.; Kostrioukov, A.; Kubo, S.; Kumazawa, R.; Liang, Y.; Lyon, J. F.; Mase, A.; Masuzaki, S.; Minami, T.; Miyazawa, J.; Morisaki, T.; Morita, S.; Murakami, S.; Muto, S.; Mutoh, T.; Nagaoka, K.; Nagayama, Y.; Nakajima, N.; Nakamura, K.; Nakanishi, H.; Narihara, K.; Narushima, Y.; Nishimura, K.; Nishino, N.; Noda, N.; Notake, T.; Nozato, H.; Ohdachi, S.; Oka, Y.; Okada, H.; Okamura, S.; Osakabe, M.; Ozaki, T.; Peterson, B. J.; Sagara, A.; Saida, T.; Saito, K.; Sakakibara, S.; Sakamoto, M.; Sakamoto, R.; Sasao, M.; Sato, K.; Sato, M.; Seki, T.; Shimozuma, T.; Shoji, M.; Suzuki, H.; Takeiri, Y.; Takeuchi, N.; Tamura, N.; Tanaka, K.; Tanaka, M. Y.; Teramachi, Y.; Toi, K.; Tokuzawa, T.; Tomota, Y.; Torii, Y.; Tsumori, K.; Watanabe, K. Y.; Watari, T.; Xu, Y.; Yamada, I.; Yamamoto, S.; Yamamoto, T.; Yokoyama, M.; Yoshimura, S.; Yoshimura, Y.; Yoshinuma, M.; Asakura, N.; Fujita, T.; Fukuda, T.; Hatae, T.; Higashijima, S.; Isayama, A.; Kamada, Y.; Kubo, H.; Kusama, Y.; Miura, Y.; Nakano, T.; Ninomiya, H.; Oikawa, T.; Oyama, N.; Sakamoto, Y.; Shinohara, K.; Suzuki, T.; Takenaga, H.; Ushigusa, K.; Hino, T.; Ichimura, M.; Takase, Y.; Sano, F.; Zushi, H.; Satow, T.; Imagawa, S.; Mito, T.; Ohtake, I.; Uda, T.; Itoh, K.; Ohkubo, K.; Sudo, S.; Yamazaki, K.; Matsuoka, K.; Hamada, Y.; Fujiwara, M., Recent advances in the LHD experiment, Nucl. Fusion, 43, 1674-1683 (2003)
[33] Kovrizhnykh, L. M., Neoclassical theory of transport processes in toroidal magnetic confinement systems, with emphasis on non-axisymmetric configurations, Nucl. Fusion, 24, 7, 851-936 (1984)
[34] Beidler, C. D.; Hitchon, W. N.G.; van Rij, W. I.; Hirshman, S. P.; Shohet, J. L., Unified theory of ripple transport in stellarators, Phys. Rev. Lett, 58, 17, 1745-1747 (1987)
[35] Boozer, A. H., Plasma equilibrium with rational magnetic surfaces, Phys. Fluids, 24, 11, 1999-2003 (1981) · Zbl 0471.76130
[36] V.V. Nemov, S.V. Kasilov, W. Kernbichler, and M.F. Heyn. Evaluation of an effective ripple in stellarators, in: C. Silva, C. Varandas, and D. Campbell, (Eds.), 28th EPS Conference on Controlled Fusion and Plasma Physics, Funchal, 18-22 June 2001, vol. 25A of ECA, European Physical Society, 2001, pp. 1985-1988.; V.V. Nemov, S.V. Kasilov, W. Kernbichler, and M.F. Heyn. Evaluation of an effective ripple in stellarators, in: C. Silva, C. Varandas, and D. Campbell, (Eds.), 28th EPS Conference on Controlled Fusion and Plasma Physics, Funchal, 18-22 June 2001, vol. 25A of ECA, European Physical Society, 2001, pp. 1985-1988.
[37] Nemov, V. V., Calculations of the magnetic surface function gradient and associated quantities in a torsatron, Nucl. Fusion, 28, 10, 1727-1736 (1988)
[38] Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P., Optimization by Simulated Annealing, Science, 220, 4598, 671-680 (1983) · Zbl 1225.90162
[39] Aarts, E.; Korst, J., Simulated Annealing and Boltzmann Machines (1989), Wiley · Zbl 0674.90059
[40] (Vidal, R. V.V., Applied Simulated Annealing (1993), Springer-Verlag) · Zbl 0789.90064
[41] Seiwald, B.; Kalyuzhnyj, V. N.; Kasilov, S. V.; Kernbichler, W.; Nemov, V. V., Neoclassical transport in Uragan-2M for the \(1/ν\) regime, Fusion Sci. Technol., 50, 3, 447-456 (2006)
[42] Gropp, W.; Lusk, E., User’s Guide for MPICH, a Portable Implementation of MPI, Argonne National Laboratory, Mathematics and Computer Science Division (1999)
[43] MPICH webpage: <http://www-unix.mcs.anl.gov/mpi/>; MPICH webpage: <http://www-unix.mcs.anl.gov/mpi/>
[44] Alejaldre, C.; Gozalo, J. J.A.; Botija Perez, J.; Castejón Magaña, F.; Cepero Diaz, J. R.; Guasp Perez, J.; López-Fraguas, A.; García, L.; Krivenski, V. I.; Martín, R.; Navarro, A. P.; Perea, A.; Rodriguez-Yunta, A.; Sorolla Ayza, M.; Varias, A., TJ-II project: a flexible heliac stellarator, Fusion Technol., 17, 131-139 (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.