Magnetic ripple and the modeling of lower-hybrid current drive in tokamaks

Physics of Plasmas

Volumn 3, Issue 10, 1996, Pages 3668-3688

  Peysson, Yves ^a   Arslanbekov, Robert ^a   Basiuk, Vincent ^a   Carrasco, Joël ^a   Litaudon, Xavier ^a   Moreau, Didier ^a   Bizarro, João P ^b  

^a IRFM   (France)

^b INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001194958     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.871960     Document Type: Article

References (51)

1. T. E. Stringer, Nucl. Fusion 12, 689 (1972).
2. A. H. Boozer, Phys. Fluids 11, 2283 (1980).
3. R. J. Goldston and H. H. Towner, J. Plasma Phys. 26, 283 (1981).
4. Equipe TFR, in Proceedings of the 11th Conference on-Plasma Physics and Controlled Nuclear Fusion Research, Kyoto (International Atomic Energy Agency, Vienna, 1987), Vol. I, Paper IAEA-CN-47/A-III-5, p. 179.
5. M. Tuszewski and J. P. Roubin, Nucl. Fusion 28, 499 (1988).
6. Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 105, Paper IAEA-CN-60/A1-5. For design parameters and history of the machines mentioned in the paper, see: ASDEX: M. Keilhacker, D. B. Albert, K. Behringer, R. Behrisch, W. Engelhart, G. Fussmann, J. Gernhardt, E. Clock, G. Haas, G. Herppich, Y. Shie, F. Karger, O. Klücker, M. Kornherr, K. Lackner, G. Lisitano, Ch. Liu, H. M. Mayer, D. Meiser, R. Müller, H. Murmann, H. Nidermeyer, W. Poschenrieder, H. Rapp, S. Rossnagel, J. Roth, N. Ruhs, B. Scherzer, F. Schneider, S. Sesnic, G. Siller, P. Staib, G. Staudenmaier, F. Wagner, K. Wang, H. Wedler, and F. Wesner, Proceedings, 8th International Conference on Plasma Physics and Controlled Nuclear Fusion, Brussels, 1980 (International Atomic Energy Agency, Vienna, 1981), Vol. 2, p. 351. JET: P.M. Rebut, R. J. Bicherton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985). TORE SUPRA: Equipe Tore Supra, Proceedings, 12th International Conference on Plasma Physics and Controlled Nuclear Fusion, Nice, 1988 (International Atomic Energy Agency, Vienna, 1989), vol. 1, p. 9.
7. Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 105, Paper IAEA-CN-60/A1-5. For design parameters and history of the machines mentioned in the paper, see: ASDEX: M. Keilhacker, D. B. Albert, K. Behringer, R. Behrisch, W. Engelhart, G. Fussmann, J. Gernhardt, E. Clock, G. Haas, G. Herppich, Y. Shie, F. Karger, O. Klücker, M. Kornherr, K. Lackner, G. Lisitano, Ch. Liu, H. M. Mayer, D. Meiser, R. Müller, H. Murmann, H. Nidermeyer, W. Poschenrieder, H. Rapp, S. Rossnagel, J. Roth, N. Ruhs, B. Scherzer, F. Schneider, S. Sesnic, G. Siller, P. Staib, G. Staudenmaier, F. Wagner, K. Wang, H. Wedler, and F. Wesner, Proceedings, 8th International Conference on Plasma Physics and Controlled Nuclear Fusion, Brussels, 1980 (International Atomic Energy Agency, Vienna, 1981), Vol. 2, p. 351. JET: P.M. Rebut, R. J. Bicherton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985). TORE SUPRA: Equipe Tore Supra, Proceedings, 12th International Conference on Plasma Physics and Controlled Nuclear Fusion, Nice, 1988 (International Atomic Energy Agency, Vienna, 1989), vol. 1, p. 9.
8. Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 105, Paper IAEA-CN-60/A1-5. For design parameters and history of the machines mentioned in the paper, see: ASDEX: M. Keilhacker, D. B. Albert, K. Behringer, R. Behrisch, W. Engelhart, G. Fussmann, J. Gernhardt, E. Clock, G. Haas, G. Herppich, Y. Shie, F. Karger, O. Klücker, M. Kornherr, K. Lackner, G. Lisitano, Ch. Liu, H. M. Mayer, D. Meiser, R. Müller, H. Murmann, H. Nidermeyer, W. Poschenrieder, H. Rapp, S. Rossnagel, J. Roth, N. Ruhs, B. Scherzer, F. Schneider, S. Sesnic, G. Siller, P. Staib, G. Staudenmaier, F. Wagner, K. Wang, H. Wedler, and F. Wesner, Proceedings, 8th International Conference on Plasma Physics and Controlled Nuclear Fusion, Brussels, 1980 (International Atomic Energy Agency, Vienna, 1981), Vol. 2, p. 351. JET: P.M. Rebut, R. J. Bicherton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985). TORE SUPRA: Equipe Tore Supra, Proceedings, 12th International Conference on Plasma Physics and Controlled Nuclear Fusion, Nice, 1988 (International Atomic Energy Agency, Vienna, 1989), vol. 1, p. 9.
9. Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 105, Paper IAEA-CN-60/A1-5. For design parameters and history of the machines mentioned in the paper, see: ASDEX: M. Keilhacker, D. B. Albert, K. Behringer, R. Behrisch, W. Engelhart, G. Fussmann, J. Gernhardt, E. Clock, G. Haas, G. Herppich, Y. Shie, F. Karger, O. Klücker, M. Kornherr, K. Lackner, G. Lisitano, Ch. Liu, H. M. Mayer, D. Meiser, R. Müller, H. Murmann, H. Nidermeyer, W. Poschenrieder, H. Rapp, S. Rossnagel, J. Roth, N. Ruhs, B. Scherzer, F. Schneider, S. Sesnic, G. Siller, P. Staib, G. Staudenmaier, F. Wagner, K. Wang, H. Wedler, and F. Wesner, Proceedings, 8th International Conference on Plasma Physics and Controlled Nuclear Fusion, Brussels, 1980 (International Atomic Energy Agency, Vienna, 1981), Vol. 2, p. 351. JET: P.M. Rebut, R. J. Bicherton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985). TORE SUPRA: Equipe Tore Supra, Proceedings, 12th International Conference on Plasma Physics and Controlled Nuclear Fusion, Nice, 1988 (International Atomic Energy Agency, Vienna, 1989), vol. 1, p. 9.
10. J. P. Roubin, D. Guilhem, G. Martin, B. Pégourié, and Y. Peysson, in Proceedings of the 18th European Conference on Controlled Fusion and Plasma Physics, Berlin, edited by P. Bachman and D. C. Robinson (European Physical Society, Petit-Lancy, Switzerland, 1991), Vol. 15C, Part I, P. 53.
11. G. Sadler, P. Barabaschi, E. Bertolini, S. Conroy, E. Deksnis, J. Dietz, B. de Esch, B. Green, M. Huart, M. Huguet, J. Jacquinot, O. N. Jarvis, A. Khudoleev, M. J. Loughlin, R. König, J. Last, A. Maas, M. Petrov, S. Putvinskii, C. Sborchia, D. Stork, B. Tubbing, and P. V. Belle, Proceedings of the 19th European Conference on Controlled Fusion and Plasma Physics, Innsbrück, edited by W. Freysinger, K. Lackner, R. Schrittwieser, and W. Lindinger (European Physical Society, Petit-Lancy, Switzerland, 1992), Vol. 16C, Part I, p. 167.
12. J. G. Wégrowe, in Proceedings of the 14th European Conference on Controlled Fusion and Plasma Physics, Madrid, edited by F. Engelmann and J. L. Alvarez-Rivas (European Physical Society, Petit-Lancy, Switzerland, 1987), Vol. 11D, Part III, p. 911.
13. J. G. Wégrowe, in Proceedings of the 8th Topical Conference on Radio-Frequency Power in Plasmas, Irvine, edited by R. McWilliams, AIP Conf. Proc. 190 (American Institute of Physics, New York, 1989), p. 182), 182.
14. P. T. Bonoli and R. C. Englade, Phys. Fluids 29, 2937 (1986).
15. D. Moreau, J. M. Rax, and A. Samain, Plasma Phys. Controlled Fusion 31, 1895 (1989).
16. A. R. Esterkin and A. D. Piliya, Plasma Phys. Controlled Fusion 34, 1954 (1992).
17. K. Kupfer and D. Moreau, Nucl. Fusion 32, 1845 (1992).
18. J. P. Bizarro and D. Moreau, Phys. Fluids B 5, 1227 (1993).
19. J. P. Bizarro, Nucl. Fusion 33, 831 (1993).
20. K. Kupfer, D. Moreau, and X. Litaudon, Phys. Fluids B 5, 4391 (1993).
21. R. Arslanbekov, J. P. Bizarro, J. S. Ferreira, Y. Peysson, V. Basiuk, J. Carrasco, G. T. Hoang, X. Litaudon, and D. Moreau, in Proceedings of the 21th European Conference on Controlled Fusion and Plasma Physics, Montpellier, edited by E. Joffrin, P. Platz, and P. E. Stott (European Physical Society, Petit-Lancy, Switzerland, 1994), Vol. 18B, Part III, p. 1046.
22. J. P. Bizarro, J. S. Ferreira, P. Rodrigues, R. Arslanbekov, and Y. Peysson, Phys. Rev. Lett. 7, 1308, 3780 (1995).
23. J. P. Bizarro, Y. Peysson, P. T. Bonoli, J. Carrasco, T. Dudok de Wit, V. Fuchs, G. T. Hoang, X. Litaudon, D. Moreau, C. Pocheau, and I. P. Shkarofsky, Phys. Fluids B 5, 3276 (1993).
24. J. Carrasco, V. Basiuk, R. Arslanbekov, G. T. Hoang, X. Litaudon, G. Martin, D. Moreau, and Y. Peysson, in Proceedings of the 21th European Conference on Controlled Fusion and Plasma Physics, Montpellier, edited by E. Joffrin, P. Platz and P. E. Stott (European Physical Society, Petit-Lancy, Switzerland, 1994), Vol. 18B. Part I. p. 278.
25. S. V. Shchepetov, Nucl. Fusion 34, 369 (1994).
26. t[p], where the subscript t[p], stands for toroidal [poloidal].
27. P. N. Yushmanov, in Reviews of Plasma Physics, edited by B. B. Kadomtsev (Consultants Bureau, New York, 1990). Vol. 16. p. 117.
28. M. Abramowitz and I. E. Stegun, in Handbook of Mathematical Functions (Dover, New York, 1972).
29. J. M. Ané, in Proceedings of the 18th Symposium on Fusion Technology, Karlsruhe, edited by K. Herschbach, U. Maurer, and J. E. Vetter (Elsevier, Amsterdam, 1995), p. 723.
30. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, in Numerical Recipes (Cambridge University, Cambridge, 1986).
31. N. J. Fisch, Rev. Mod. Phys. 59, 175 (1982).
32. M. Brambilla and A. Cardinali, Plasma Phys. 24, 1187 (1982).
33. It is worth noting that the expression of the toroidal ripple depth for TORE SUPRA as given by (24) differs from approximate and usually phenomenological expressions previously published (Refs. 5 and 31). Though they give very similar results within few percent throughout the plasma and especially in the high ripple region, they are not fully consistent with the condition ▽·B=O, up to the order of the ripple perturbation. The fact that the equilibrium magnetic field is not divergence-free up to the first order in the ripple corrections may introduce additional errors in the calculation of the ray trajectory, which can become significant if the ray path is followed over a long distance with respect to the ripple scale length.
34. P. Grua, Ph.D. thesis, Aix-Marseille I University, 1989.
35. v)cos θ in expressions (22)-(24), and (28).
36. S. S. Abdullaev and G. M. Zaslavskii, Sov. Phys. Usp. 34, 645 (1991).
37. J. M. Wersinger, E. Ott, and J. M. Finn, Phys. Fluids 21, 2263 (1978).
38. P. T. Bonoli and E. Ott, Phys. Fluids 25, 359 (1982).
39. D. A. Ehst, C. F. F. Karney, Nucl. Fusion 31, 1933 (1991).
40. X. Litaudon and D. Moreau, Nucl. Fusion 30, 471 (1990).
41. D. W. Ignat, E. J. Valeo, and S. C. Jardin, Nucl. Fusion 34, 837 (1994).
42. Y. Peysson, Plasma Phys. Controlled Fusion 35, B253 (1993).
43. Y. Baranov, M. Brusati, A. Ekedahl, P. Froissard, C. Gormezano, M. Lennholm, and F. Rimini, in Proceedings of the 20th European Conference on Controlled Fusion and Plasma Physics, Lisbon, edited by J. A. Costa Cabrai, M. E. Manso, F. M. Serra, and F. C. Schüller (European Physical Society, Petit-Lancy, Switzerland, 1993), Vol. 17C, Part III, p. 881.
44. S. Jones, J. Kesner, S. Luckhardt, F. Paoletti, S. von Goeler, S. Bernabei, R. Kaita, G. Giruzzi, and the PBX-M Team, Phys. Plasmas 2, 1548 (1995).
45. E. Joffrin (private communication, 1995).
46. C. B. Forrest, K. Kupfer, T. C. Luce, P. A. Politzer, L. L. Lao, M. R. Wade, D. G. Whyte, and D Wròblewski, Phys. Rev. Lett. 73, 2444 (1994).
47. V. Basiuk, J. P. Roubin, A. Bécoulet, J. Carrasco, G. Martin, D. Moreau, and B. Saoutic, Proceedings of the 19th European Conference on Controlled Fusion and Plasma Physics, Innsbrück, edited by W. Freysinger, K. Lackner, R. Schrittwieser, and W. Lindinger (European Physical Society, Petit-Lancy, Switzerland, 1992), Vol. 16C, Part I, p. 175.
48. G. Vahala, L. Vahala and P. T. Bonoli, Phys. Fluids B 4, 4033 (1992).
49. ITER Concept Definition (International Atomic Energy Agency, Vienna, 1989), Vol. 3, p. 52, IAEA/ITER/DS/3.
50. J. M. Rax, Ph.D. thesis, Paris-Sud University, Orsay Center, 3261, 1987.
51. S. G. Shasharina and J. R. Cary, Nucl. Fusion 33, 648 (1993).