On the Effect of Two-Dimensional Plasma Inhomogeneity in a Magnetic Island on the Parametric Excitation Threshold of Trapped Upper Hybrid Waves and the Level of Anomalous Absorption in ECRH Experiments

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The effect of two-dimensional localization of an upper hybrid (UH) wave in a magnetic island is found. The influence of this effect on the threshold and saturation level of the absolute parametric decay instability of an extraordinary wave, which results in the excitation of two two-dimensional localized UH waves, is investigated.

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作者简介

A. Popov

Ioffe Institute

编辑信件的主要联系方式.
Email: a.popov@mail.ioffe.ru
俄罗斯联邦, St. Petersburg

E. Gusakov

Ioffe Institute

Email: a.popov@mail.ioffe.ru
俄罗斯联邦, St. Petersburg

N. Teplova

Ioffe Institute

Email: a.popov@mail.ioffe.ru
俄罗斯联邦, St. Petersburg

参考

  1. Sagdeev R.Z., Galeev A.A. // In Nonlinear Physics Plasma Theory / Ed. by T. M. O’ Neil and D. L. Book. New York: Benjamin, 1969.
  2. Davidson B.C. // Methods in Nonlinear Plasma Theory. New York: Academic, 1972.
  3. Hasegawa A. // Plasma Instabilities and Nonlinear Effects. Berlin: Springer, 1975.
  4. Силин В.П. // ЖЭТФ. 1964. Т. 47. С. 2254–2265.
  5. Горбунов Л.М., Силин В.П. // ЖЭТФ. 1965. Т. 49. С. 1973.
  6. Jackson E.A. // Phys. Rev. 1967. V. 153. P. 255.
  7. Bers A., Kaup D.J., Reiman A. // Phys. Rev. Lett. 1976. V. 37. P. 182.
  8. Kaup D.J., Reiman A., Bers A. // Reviews of Modern Physics. 1979. V. 51. P. 275.
  9. Силин В.П. // ЖЭТФ. 1966. Т. 51. С. 1842.
  10. Horton W. // Reviews of Modern Physics. 1999. V. 71. P. 735.
  11. Piliya A.D. // Proc. 10th Conf. Phenomena in Ionized Gases (Oxford, UK, 13–18 September 1971). P. 320.
  12. Пилия А.Д. // ЖЭТФ. 1973. Т. 64. С. 1237.
  13. Rosenbluth M.N. // Phys. Rev. Lett. 1972. V. 29. P. 565.
  14. Reiman A. // Reviews of Modern Physics. 1979. V. 51. P. 331.
  15. Bers A. Basic Plasma Physics. Handbook of Plasma Physics by A.A. Galeev and R.N. Sudan. Elsevier Science Ltd, 1985.
  16. Гусаков Е.З., Федоров В.И. // Физика плазмы. 1979. Т. 5. С. 827.
  17. Popov A.Yu., Gusakov E.Z. // Plasma Phys. Control. Fusion. 2015. V. 57. P. 025022.
  18. Popov A. Yu., Gusakov E. Z. // Europhys. Lett. 2016. V. 116. P. 45002.
  19. Попов А.Ю., Гусаков Е.З. // Письма в ЖЭТФ. 2017. Т. 105. С. 64–69.
  20. Гусаков Е.З., Попов А.Ю. // УФН. 2020. Т. 190. P. 396.
  21. Hansen S.K., Nielsen S.K., Stober J., Rasmussen J., Stejner M., Hoelzl M., Jensen T. // Nucl. Fusion. 2020. V. 60. P. 106008.
  22. Hansen S.K., Jacobsen A.S., Willensdorfer M., Nielsen S.K., Stober J., Höfler K., Maraschek M., Fischer R., Dunne M. // Plasma Phys. Control. Fusion. 2021. V. 63. P. 095002.
  23. Tancetti A., Nielsen S.K., Rasmussen J., Gusakov E.Z., Popov A.Y., Moseev D., Stange T., Senstius M.G., Killer C., Vecsei M., Jensen T., Zanini M., Abramovic I., Stejner M., Anda G., Dunai D., Zoletnik S., Laqua H. // Nuclear Fusion. 2022. V. 62. P. 074003.
  24. Tancetti A., Nielsen S.K., Rasmussen J., Moseev D., Stange T., Marsen S., Vecséi M., Killer C., Wurden G.A., Jensen T., Stejner M., Anda G., Dunai D., Zoletnik S., Rahbarnia K., Brandt C., Thomsen H., Hirsch M., Hoefel U., Chaudhary N., Winters V., Kornejew P., Harris J., Laqua H.P. and the W7-X Team // Plasma Phys. Control. Fusion. 2023. V. 65. P. 015001.
  25. Gusakov E.Z., Popov A.Yu. // Physics of Plasmas. 2016. V. 23. P. 082503.
  26. Гусаков Е.З., Попов А.Ю. // Физика плазмы. 2023. Т. 49. С. 128.
  27. Гусаков Е.З., Попов А.Ю. // Физика плазмы. 2023. Т. 49. C. 753.
  28. Westerhof E., Nielsen S.K., Oosterbeek J.W., Salewski M., de Baar M.R., Bongers W.A., Bürger A., Hennen B.A., Korsholm S.B., Leipold F., Moseev D., Stejner M., Thoen D.J. // Phys. Rev. Lett. 2009. V. 103. P. 125001.
  29. Nielsen S.K., Salewski M., Westerhof E., Bongers W., Korsholm S.B., Leipold F., Oosterbeek J.W., Moseev D., Stejner M. // Plasma Phys. Control. Fusion. 2013. V. 55. P. 115003.
  30. Gusakov E.Z., Popov A.Yu., Tretinnikov P.V. // Nucl. Fusion. 2019. V. 59. 106040.
  31. Gusakov E.Z., Popov A.Yu. // Plasma Phys. Control. Fusion. 2020. V. 62. P. 025028.
  32. Gusakov E.Z., Popov A.Yu. // Nucl. Fusion. 2020. V. 60. P. 076018.
  33. Altukhov A.B., Arkhipenko V.I., Gurchenko A.D., Gusakov E.Z., Popov A.Yu., Simonchik L.V., Usachonak M.S. // Europhys. Lett. 2019. V. 126. P. 15002.
  34. Мещеряков А.И., Вафин И.Ю., Гришина И.А. // Физика плазмы. 2021. Т. 47. С. 22.
  35. Dnestrovskij Yu.N., Danilov A.V., Dnestrovskij A.Yu., Lysenko S.E., Melnikov A.V., Nemets A.R., Nurgaliev M.R., Subbotin G.F., Solovev N.A., Sychugov D.Yu., Cherkasov S.V. // Plasma Phys. Control. Fusion. 2021. V. 63. P. 055012.
  36. Abdullaev S.S., Finken K.H., Jakubowski M.W., Kasilov S.V., Kobayashi M., Reiser D., Reiter D., Runov A.M. and Wolf R. // Nucl. Fusion. 2003. V. 43. P. 299.
  37. Koslowski H.R., Westerhof E., de Bock M., Classen I., Jaspers R., Kikuchi Y., Krämer-Flecken A., Lazaros A., Liang Y., Löwenbrück K., Varshney S., von Hellermann M., Wolf R., Zimmermann O. and the TEXTOR team // Plasma Phys. Control. Fusion. 2006. V. 48. P. B53.
  38. Бейтман Г. // МГД-неустойчивости. M.: Энергоиздат, 1982.
  39. Kantor M.Yu., Donne A.J.H., Jaspers R., van der Meiden H. and TEXTOR Team // Plasma Phys. Control. Fusion. 2009. V. 51. P. 055002.
  40. Kantor M.Y., Bertschinger G., Bohm P., Buerger A., Donné A.J.H., Jaspers R., Krämer-Flecken A., Mann S., Soldatov S., Zang Qing // Proc. 36th EPS Conference on on Plasma Phys. (Sofia, Bulgaria) ECA 33E (2009) P-1.184.
  41. Ахиезер А.И., Ахиезер И.А., Половин Р.В., Ситенко А.Г., Степанов К.Н. Электродинамика плазмы. М.: Наука, 1974.
  42. Gusakov E.Z., Popov A.Yu., Saveliev A.N. // Plasma Phys. Control. Fusion. 2014. V. 56. P. 015010.
  43. Pustovalov V.V., Silin V.P. Theory of Plasmas. Consultants Bureau, 1975.
  44. Larsson J. // J. Plasma Physics. 1988. V. 40. P. 385.
  45. Gusakov E.Z., Popov A.Yu., Tretinnikov P.V. // Plasma Phys. Control. Fusion. 2019. V. 61. P. 085008.
  46. Cohen B.I., Cohen R.H., Nevins W.M., Rognlien T.D. // Rev. Mod. Phys. 1991. V. 63. P. 949.
  47. Гусаков Е.З., Попов А.Ю. // Письма в ЖЭТФ. 2022. Т. 116. С. 41.
  48. Петвиашвили В.И. // Письма в ЖЭТФ. 1976. Т. 23. С. 682.
  49. Некрасов А.К. // Физика плазмы. 1986. Т. 12. С. 971.

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2. Fig. 1. The trajectory of the upper hybrid wave (solid line, fm = 69.71 GHz, mx = 45) is shown in the poloidal section of the TEXTOR tokamak [29]. The magnetic surfaces are shown as dashed lines. The zoomed-in window shows the trajectory of the VG-wave in the magnetic island

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3. Fig. 2. The trajectory of the upper hybrid wave (solid line, fm = 69.71 GHz, mx = 45) is shown in the magnetic surface plane of the TEXTOR tokamak [29]. The magnetic force lines are shown as dashed lines

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4. Fig. 3. The wave vector component qx(x) obtained numerically by the ray-tracing procedure is indicated by the arrow. The analytical solution is shown by dots and indicated by the arrow

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5. Fig. 4. The wave vector component qζ(ζ) obtained numerically from ray tracing is indicated by the arrow. The analytical solution is shown by the dashed curve and indicated by the arrow

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6. Fig. 5. The wave number of the VG-wave fm = 69.71 GHz, qξmn = 0.43 cm-1, m = (40.3), shifted down by the value of the wave number of the extraordinary wave, is the solid line. The wave number of the second VG wave is the dashed line. The VG-frequency profile is the thick solid curve. Te = 700 eV, Ti = 350 eV - on the discharge axis. B = 2.1T - in the magnetic island

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7. Fig. 6. Sum of the wave numbers of the primary (fn = 70.29 GHz, n = (12.4)) and secondary (fl = 69.67 GHz, qξnp = 0.52 cm-1, l = (47.3)) WG-waves - solid line. The wave number of the secondary IB wave fI = 0.62 GHz, qIξ = 0.09 cm-1 is the dashed curve. The VG-frequency profile is the thick solid curve. The parameters are the same as in Fig. 4

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8. Fig. 7. Temporal evolution of the energies of the primary HG waves and the secondary HG wave in the beam spot. The dependences are indicated by arrows. The thin horizontal lines give the saturation levels predicted by equations (18)-(20). P0 = 1 MW, w = 1 cm

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9. Fig. 8. Dependence of the primary instability increment on the pumping power. The solid line shows the analytical dependence (16). Symbols are the result of numerical solution of equations (13). The zoomed-in window shows the dependence in the vicinity of the threshold power

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10. Fig. 9. Time dependence of the energy of all VG-waves within the box in the region of WΣ calculation in the saturation mode for different pumping power

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11. Fig. 10. Dependence of the anomalous absorption level on the pump power. The symbols show the result of the numerical solution ΔP = dWΣ/dt. The solid line shows the analytical dependence (21)

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