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.
Similar content being viewed by others
References
Mercier C.: Nucl. Fusion1 (1960) 47.
Morozov A. I., Solovev L. S.: Reviews of Plasma Physics, Vol. 2. Gosatomizdat, Moscow, 1963 (in Russian).
Rome J. A., Peng Y. K. M.: Nucl. Fusion19 (1979) 1193.
Hinton F. L.: Plasma Physics23 (1981) 1143.
Boozer A. H.: Phys. Fluids25 (1982) 520.
Wong H. V.: Phys. Fluids25 (1982) 1811.
Schep T. J., Braams B. J., Pegoraro F.: Phys. Fluids25 (1982) 1871.
Rogister A., Hasselberg G.: Plasma Physics27 (1985) 193.
Lacina J.: Czech. J. Phys. B14 (1964) 5.
Krlín L.: Czech. J. Phys. B17 (1967) 112.
Krlín L.:in Internal Report of the Institute of Plasma Physics, Czechosl. Acad. Sci., No.6, 1982.
Gášek Z.: Diploma Thesis. Faculty of Mathematics and Physics, Charles University, Prague, 1985.
Krall N. A., Trivelpiece A. W.: Principles of Plasma Physics. Mir, Moscow, 1975 (in Russian)
Status of the Tokamak Research (ed. J. M. Rawls) DOE/ER-0034, UC-20. US Department of Energy, Washington, D. C., 20 585, 1979.
Dnestrovskii Yu. N., Kostomarov D. D.: Mathematical Modelling of Plasmas. Nauka, Moscow, 1982 (in Russian).
Ohnishi M., Wakabayashi N.: Nucl. Fusion18 (1978) 859.
Krlín L., Pavlo P., Tlučhoř Z.: Czech. J. Phys. B35 (1985) 133.
Gradstein I. S., Ryzhik I. M.: The Tables of Integrals, Sumsand Productions. Fizmatgiz, Moscow, 1962 (in Russian).
Karney C. F. F.: Phys. Fluids21 (1978) 1584.
Elfimov A. G. et al.:in Proceedings of the All-Union Conference on RF Heating of Plasma, Gorkii, 1983, p. 211 (in Russian).
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.
Lichtenberg A. J., Lieberman M. A.: Regular and stochastic motion. Springer Verlag, Berlin, 1983.
Chirikov B. V.:in Proceedings of Int. Conf. Plasma Physics, Lausanne 1984, Vol. 2, p. 761,
Ter Haar D.: Elements of Hamiltonian Mechanics. North-Holland Publishing Company, Amsterodam, 1961.
Chirikov B. V.: Physics Reports52 (1979) 263.
Zaslavskii G. M.: Stochasticity of Dynamic Systems. Nauka, Moscow, 1984 (in Russian).
Escade D. F.: Stochasticity in Classical Hamiltonian Systems. Report DOE-ET-53088-147 Institute for Fusion Studies, The University of Texas at Austin, 1984.
Krlín L.: J. Plasma Physics12 (1974) 365.
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.
Casati G., Lazzaro E.: Phys. Fluids24 (1981) 1570.
Janke E., Emde F., Lösch F.: Tafeln Höherer Funktionen. Nauka, Moscow, 1964 (in Russian).
Whang K. W., Morales G. J.: Nucl. Fusion23 (1983) 481.
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.
Kaufman A. N.: Phys. Fluids15 (1972) 1603.
Hitchcock D. A., Hazeltine R. D., Mahajan S. M.: Phys. Fluids26 (1983) 2603.
Mahajan S. M., Chen. C. Y.: Phys. Fluids28 (1985) 3538.
Author information
Authors and Affiliations
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
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01597187