Skip to main content
Log in

Geodesic Acoustic Mode in an Elliptic Cylinder

  • Methodological Notes
  • Published:
Plasma Physics Reports Aims and scope Submit manuscript

Abstract

Using equations for small plasma oscillations in an elliptic current-carrying cylinder, it is demonstrated that, in a configuration with magnetic surfaces and geodesic curvature, excitation of a longitudinal displacement with a poloidal mode number determined by the geodesic curvature is accompanied by the appearance of a zero angular harmonic in the transverse displacement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. H. Diamond, S.-I. Itoh, K. Itoh, and T. S. Hahm, Plasma Phys. Controlled Fusion 47, R35 (2005).

    Google Scholar 

  2. A. V. Melnikov, L. G. Eliseev, S. E. Lysenko, M. V. Ufimtsev, and V. N. Zenin, Nucl. Fusion 57, 115001 (2017).

    Article  ADS  Google Scholar 

  3. N. Winsor, J. L. Johnson, and J. M. Dawson, Phys. Fluids 11, 2448 (1968).

    Article  ADS  Google Scholar 

  4. B. B. Kadomtsev, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Consultants Bureau, New York, 1966), Vol. 2, p. 153.

    Google Scholar 

  5. A. V. Melnikov, L. I. Krupnik, L. G. Eliseev, J. M. Barcala, A. Bravo, A. A. Chmyga, G. N. Deshko, M. A. Drabinskij, C. Hidalgo, P. O. Khabanov, S. M. Khrebtov, N. K. Kharchev, A. D. Komarov, A. S. Kozachek, J. Lopez, et al., Nucl. Fusion 57, 072004 (2017).

    Article  ADS  Google Scholar 

  6. E. Z. Gusakov, A. B. Altukhov, V. V. Bulanin, A. D. Gurchenko, J. A. Heikkinen, S. J. Janhunen, S. Leerink, L. A. Esipov, M. Yu. Kantor, T. P. Kiviniemi, T. Korpilo, D. V. Kouprienko, S. I. Lashkul, A. V. Petrov, and N. V. Teplova, Plasma Phys. Controlled Fusion 55, 124034 (2013).

    Article  ADS  Google Scholar 

  7. A. D. Gurchenko, E. Z. Gusakov, A. B. Altukhov, E. P. Selyunin, L. A. Esipov, M. Yu. Kantor, D. V. Kouprienko, S. I. Lashkul, A. Yu. Stepanov, and F. Wagner, Plasma Phys. Controlled Fusion 55, 085017 (2013).

    Article  ADS  Google Scholar 

  8. A. V. Melnikov, L. G. Eliseev, S. V. Perfilov, S. E. Lysenko, R. V. Shurygin, V. N. Zenin, S. A. Grashin, L. I. Krupnik, A. S. Kozachek, R. Yu. Solomatin, A. G. Elfimov, A. I. Smolyakov, and M. V. Ufimtsev, Nucl. Fusion 55, 063001 (2015).

    Article  ADS  Google Scholar 

  9. A. V. Melnikov, L. G. Eliseev, S. E. Lysenko, S. V. Perfilov, R. V. Shurygin, L. I. Krupnik, A. S. Kozachok, and A. I. Smolyakov, JETP Lett. 100, 555 (2015).

    Article  ADS  Google Scholar 

  10. K. Itoh, S.-I. Itoh, P. H. Diamond, A. Fujisawa, M. Yagi, T. Watari, Y. Nagashima, and A. Fukuyama, Plasma Fusion Res. Rapid Commun. 1, 037 (2006).

    Article  ADS  Google Scholar 

  11. A. B. Mikhailovskii, A. I. Smolyakov, A. P. Churicov, and V. D. Pustovitov, Plasma Phys. Controlled Fusion 51, 075010 (2009).

    Article  ADS  Google Scholar 

  12. V. I. Ilgisonis, V. P. Lakhin, A. I. Smolyakov, and E. A. Sorokina, Plasma Phys. Controlled Fusion 53, 065008 (2011).

    Article  ADS  Google Scholar 

  13. V. I. Ilgisonis, L. V. Konoval’tseva, V. P. Lakhin, and E. A. Sorokina, Plasma Phys. Rep. 40, 843 (2014).

    Article  ADS  Google Scholar 

  14. C. Wahlberg and J. P. Graves, Plasma Phys. Controlled Fusion 58, 075014 (2016).

    Article  ADS  Google Scholar 

  15. A. F. Aleksandrov and A. A. Rukhadze, Course of Electrodynamics of Plasmalike Media (Mosk. Gos. Univ., Moscow, 1999) [in Russian].

    Google Scholar 

  16. L. S. Solov’ev, in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Consultants Bureau, New York, 1967), Vol. 3, p. 277.

    Google Scholar 

  17. A. B. Mikhailovskii, Instabilities in a Confined Plasma (Atomizdat, Moscow, 1978; IOP, Bristol, 1998).

    Google Scholar 

  18. D. A. Frank-Kamenetskii, Sov. Phys. Tech. Phys. 5, 847 (1961).

    MathSciNet  Google Scholar 

  19. G. Wang, W. A. Peebles, T. L. Rhodes, M. E. Austin, Z. Yan, G. R. McKee, R. J. La Haye, K. H. Burrell, E. J. Doyle, J. C. Hillesheim, M. J. Lanctot, R. Nazikian, C. C. Petty, L. Schmitz, S. Smith, et al., Phys. Plasmas 20, 092501 (2013).

    Article  ADS  Google Scholar 

  20. C. A. de Meijere, S. Coda, Z. Huang, L. Vermare, T. Vernay, V. Vuille, S. Brunner, J. Dominski, P. Hennequin, A. Krämer-Flecken, G. Merlo, L. Porte, and L. Villard, Plasma Phys. Controlled Fusion 56, 072001 (2014).

    Article  ADS  Google Scholar 

  21. A. V. Melnikov, V. A. Vershkov, L. G. Eliseev, S. A. Grashin, A. V. Gudozhnik, L. I. Krupnik, S. E. Lysenko, V. A. Mavrin, S. V. Perfilov, D. A. Shelukhin, S. V. Soldatov, M. V. Ufimtsev, A. O. Urazbaev, G. Van Oost, and L. G. Zimeleva, Plasma Phys. Controlled Fusion 48, S87 (2006).

    Google Scholar 

  22. J. Seidl, J. Krbec, M. Hron, J. Adamek, C. Hidalgo, T. Markovic, A. V. Melnikov, J. Stockel, V. Weinzettl, M. Aftanas, P. Bilkova, O. Bogar, P. Bohm, L. G. Eliseev, P. Hacek, et al., Nucl. Fusion 57, 126048 (2017).

    Article  ADS  Google Scholar 

  23. V. A. Rozhanskii, Plasma Theory (Lan’, St. Petersburg, 2012) [in Russian].

    Google Scholar 

  24. V. I. Ilgisonis, Classical Problems in the Physics of Hot Plasma (Izd. dom MEI, Moscow, 2015) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Skovoroda.

Additional information

Original Russian Text © A.A. Skovoroda, E.A. Sorokina, 2018, published in Fizika Plazmy, 2018, Vol. 44, No. 11, pp. 925–934.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Skovoroda, A.A., Sorokina, E.A. Geodesic Acoustic Mode in an Elliptic Cylinder. Plasma Phys. Rep. 44, 1076–1084 (2018). https://doi.org/10.1134/S1063780X18110107

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063780X18110107

Navigation