Skip to main content
Log in

On the dynamics of particles in tokamak magnetic field and in RF fields

  • Published:
Czechoslovak Journal of Physics B Aims and scope

Abstract

The motion of magnetically trapped particles and their interaction with RF field is discussed; for the description, suitable canonical formalism is used. The chosen form of the Hamiltonian enables us to investigate in a relatively simple way the effect of RF fields on the change of the parallel and perpendicular velocities of particles, and, consequently, on the form of the banana and on its radial displacement. Special attention is devoted to the stochastic instability regime. Simple numerical discussion of the interaction of Alfvén waves with banana-trapped particles is presented, together with the estimation of the stochastic instability threshold.

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. Mercier C.: Nucl. Fusion1 (1960) 47.

    Google Scholar 

  2. Morozov A. I., Solovev L. S.: Reviews of Plasma Physics, Vol. 2. Gosatomizdat, Moscow, 1963 (in Russian).

    Google Scholar 

  3. Rome J. A., Peng Y. K. M.: Nucl. Fusion19 (1979) 1193.

    Google Scholar 

  4. Hinton F. L.: Plasma Physics23 (1981) 1143.

    Google Scholar 

  5. Boozer A. H.: Phys. Fluids25 (1982) 520.

    Google Scholar 

  6. Wong H. V.: Phys. Fluids25 (1982) 1811.

    Google Scholar 

  7. Schep T. J., Braams B. J., Pegoraro F.: Phys. Fluids25 (1982) 1871.

    Google Scholar 

  8. Rogister A., Hasselberg G.: Plasma Physics27 (1985) 193.

    Google Scholar 

  9. Lacina J.: Czech. J. Phys. B14 (1964) 5.

    Google Scholar 

  10. Krlín L.: Czech. J. Phys. B17 (1967) 112.

    Google Scholar 

  11. Krlín L.:in Internal Report of the Institute of Plasma Physics, Czechosl. Acad. Sci., No.6, 1982.

  12. Gášek Z.: Diploma Thesis. Faculty of Mathematics and Physics, Charles University, Prague, 1985.

    Google Scholar 

  13. Krall N. A., Trivelpiece A. W.: Principles of Plasma Physics. Mir, Moscow, 1975 (in Russian)

    Google Scholar 

  14. Status of the Tokamak Research (ed. J. M. Rawls) DOE/ER-0034, UC-20. US Department of Energy, Washington, D. C., 20 585, 1979.

    Google Scholar 

  15. Dnestrovskii Yu. N., Kostomarov D. D.: Mathematical Modelling of Plasmas. Nauka, Moscow, 1982 (in Russian).

    Google Scholar 

  16. Ohnishi M., Wakabayashi N.: Nucl. Fusion18 (1978) 859.

    Google Scholar 

  17. Krlín L., Pavlo P., Tlučhoř Z.: Czech. J. Phys. B35 (1985) 133.

    Google Scholar 

  18. Gradstein I. S., Ryzhik I. M.: The Tables of Integrals, Sumsand Productions. Fizmatgiz, Moscow, 1962 (in Russian).

    Google Scholar 

  19. Karney C. F. F.: Phys. Fluids21 (1978) 1584.

    Google Scholar 

  20. Elfimov A. G. et al.:in Proceedings of the All-Union Conference on RF Heating of Plasma, Gorkii, 1983, p. 211 (in Russian).

  21. Belikov V. S. et al.:in Proceedings of the 12th European Conference on Controlled Fusion and Plasma Physics, Part II (ed. L. Pócz, A. Montvai), p. 206.

  22. Lichtenberg A. J., Lieberman M. A.: Regular and stochastic motion. Springer Verlag, Berlin, 1983.

    Google Scholar 

  23. Chirikov B. V.:in Proceedings of Int. Conf. Plasma Physics, Lausanne 1984, Vol. 2, p. 761,

    Google Scholar 

  24. Ter Haar D.: Elements of Hamiltonian Mechanics. North-Holland Publishing Company, Amsterodam, 1961.

    Google Scholar 

  25. Chirikov B. V.: Physics Reports52 (1979) 263.

    Google Scholar 

  26. Zaslavskii G. M.: Stochasticity of Dynamic Systems. Nauka, Moscow, 1984 (in Russian).

    Google Scholar 

  27. Escade D. F.: Stochasticity in Classical Hamiltonian Systems. Report DOE-ET-53088-147 Institute for Fusion Studies, The University of Texas at Austin, 1984.

    Google Scholar 

  28. Krlín L.: J. Plasma Physics12 (1974) 365.

    Google Scholar 

  29. Casati G., Lazzaro E., Nowak S.:in International Workshop on Intrinsic Stochasticity in Plasmas (ed. G. Laval and D. Gresillon). Edition de Physique, Orsay, 1979.

    Google Scholar 

  30. Casati G., Lazzaro E.: Phys. Fluids24 (1981) 1570.

    Google Scholar 

  31. Janke E., Emde F., Lösch F.: Tafeln Höherer Funktionen. Nauka, Moscow, 1964 (in Russian).

    Google Scholar 

  32. Whang K. W., Morales G. J.: Nucl. Fusion23 (1983) 481.

    Google Scholar 

  33. Parail V. V., Yushmanov P. N.:in Proceedings of the 12th European Conference on Controlled Fusion and Plasma Physics, Part I (ed. L. Pócz, A. Montvai), p. 98.

  34. Kaufman A. N.: Phys. Fluids15 (1972) 1603.

    Google Scholar 

  35. Hitchcock D. A., Hazeltine R. D., Mahajan S. M.: Phys. Fluids26 (1983) 2603.

    Google Scholar 

  36. Mahajan S. M., Chen. C. Y.: Phys. Fluids28 (1985) 3538.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The authors are indebted to Dr. V. V. Parail for the help in the formulation of the problem of the interaction of Alfvén waves with particles in the intrinsic stochasticity regime and to Dr. P. N. Yushmanov for valuable discussions. The authors also would like to thank Dr. J. Horáček and Dr. P. Pavlo for numerical help and stimulating discussions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gášek, Z., Krlín, L. & Tlučhoř, Z. On the dynamics of particles in tokamak magnetic field and in RF fields. Czech J Phys 37, 571–595 (1987). https://doi.org/10.1007/BF01597187

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01597187

Keywords

Navigation