Advertisement

The European Physical Journal D

, Volume 48, Issue 1, pp 95–109 | Cite as

Modelling of Lévy walk kinetics of charged particles in edge electrostatic turbulence in tokamaks

  • L. KrlínEmail author
  • R. Paprok
  • V. Svoboda
Plasma Physics

Abstract.

We model and discuss the possible types of motion that charged particles may undergo in a stationary and spatially periodic electrostatic potential and a homogeneous magnetic field. The model is considered to be the simplest approximation of more complex phenomena of plasma edge turbulence in tokamaks. Therein, low frequency turbulence appears in the plasma edge, resulting in a fluctuation of the electron density, and also in the generation of a turbulent electrostatic field. Typical parameters of this turbulent electrostatic field are an electrical potential amplitude of 10–100 V and wave numbers k≈103 m-1. In our model, we consider these regimes, together with a homogeneous magnetic field with a magnitude of 1 T. We investigate the dynamics of singly-ionized carbon ions – a typical plasma impurity – with kinetic energies on the order of 10 eV. Besides the obvious Larmor and drift motions, a motion of random-walk and of Lévy walk character appear therein. All of these types of motion can play an important role in the modelling of the anomalous diffusion of particles from the plasma edge turbulence region. The dynamics mentioned will cause an inevitable escape of energetic particles and thus of power loss from the thermonuclear reactor. Moreover, Lévy walk kinetics represents a very interesting kind of kinetics, currently of great interest, which was previously not so often discussed.

PACS.

52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.) 52.65.Cc Particle orbit and trajectory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.J. Lichtenberg, M.A. Lieberman, Regular and Stochastic Motion (Springer Verl., Berlin, 1983). Druhé vydání, Regular and Chaotic Dynamics, 1992 Google Scholar
  2. V. Naulin, A.H. Nielsen, J.J. Rasmussen, Phys. Plasmas 6, 4574 (1999) CrossRefADSMathSciNetGoogle Scholar
  3. A. Hasegawa, K. Mima, Phys. Fluids 21, 87 (1978) CrossRefADSMathSciNetzbMATHGoogle Scholar
  4. A. Hasegawa, M. Wakatani, Phys. Rev. Lett. 50, 682 (1983) CrossRefADSGoogle Scholar
  5. L. Krlín, J. Stöckel, V. Svoboda, Plasma Phys. Control. Fusion 41, 339 (1999) CrossRefADSGoogle Scholar
  6. L. Krlín, J. Stöckel, V. Svoboda, Czech. J. Phys. 48, S2 301 (1998) Google Scholar
  7. L. Krlín, J. Stöckel, V. Svoboda, M. Tendler, Phys. Scripta T 84, 221 (2000) CrossRefADSGoogle Scholar
  8. G.M. Zaslavsky, Hamiltonian chaos and fractional dynamics (Oxford, University Press, 2005) Google Scholar
  9. M. Tendler, L. Krlín, J. Stöckel, V. Svoboda, Proc. 26th EPS Conf. on Plasma Phys. Control. Fusion P4 (1999) 060 Google Scholar
  10. L. Krlín et al., Proc. 27 EPS Conf. on Control. Fusion and Plasma Phys. Budapest (2000) Conference Abstracts 24B, 45 Google Scholar
  11. L. Krlín et al., Proc. 28th EPS Conf. on Control. Fusion and Plasma Phys. Madeira (2001) Conference Abstracts 25A, 269 Google Scholar
  12. Ju.G.M. Zaslavskij, Statistical irreversibility in nonlinear systems (in Russian) (Nauka, Moscow, 1970) Google Scholar
  13. G.M. Zaslavskij, Stochasticity of dynamical systems (in Russian) (Nauka, Moscow, 1984) Google Scholar
  14. J. Wagenhuber, T. Geisel, P. Niebauer, G. Obermair, Phys. Rev. B 45, 4372 (1992) CrossRefADSGoogle Scholar
  15. D.A. Rakhlin, Phys. Rev. E 63, 011112 (2000) CrossRefADSGoogle Scholar
  16. J. Kucera, P. Streda, R.R. Gerhardts, Phys. Rev. B 14, 439 (1997) Google Scholar
  17. P.M. Bellan, Plasma Phys. Control. Fusion 35, 169 (1993) CrossRefADSGoogle Scholar
  18. M.F. Shlesinger et al., Nature 363, 3 (1993) Google Scholar
  19. R. Paprok, Diploma Thesis, Charles University 2007 Google Scholar
  20. R. Balescu, Aspects of Anomalous Transport in Plasmas (IOP, Bristol, 2005) Google Scholar
  21. L. Krlín, V. Svoboda, M. Zápotocký, Czech. J. Phys. 54, 759 (2004) CrossRefADSGoogle Scholar
  22. R. Pánek, L. Krlín, M. Tendler, D. Tskhakaya, S. Kuhn, V. Svoboda, R. Klíma, P. Pavlo, J. Stöckel, V. Petržílka, Phys. Scripta 72, 327 (2005) CrossRefGoogle Scholar
  23. K. Dyabilin, R. Klíma, I. Duran, J. Horácek, M. Hron, P. Pavlo, J. Stöckel, F. Žácek, Czech. J. Phys. 51, 1107 (2001) CrossRefADSGoogle Scholar
  24. S.V. Annibaldi, G. Manfredi, R.O. Dendy, Phys. Plasmas 9, 791 (2002) CrossRefADSGoogle Scholar
  25. R. Jha, P.K. Kaw, D.R. Kulkarni, J.C. Parikh, Phys. Plasmas 10, 699 (2003) CrossRefADSGoogle Scholar
  26. G. Zimbardo, Plasma Phys. Control. Fusion 47, B755 (2005) Google Scholar
  27. V.P. Budaev, S. Takamura, N. Ohno, S. Masuzaki, Nucl. Fusion 46, S181 (2006) Google Scholar
  28. A. Fujisawa et al., Plasma Phys. Control. Fusion 48, S205 (2006) Google Scholar
  29. J.H. Misguich, R. Nakach, Phys. Rev. A 44, 3869 (1991) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institute of Plasma Physics, Academy of Sciences of the Czech RepublicPrague 8Czech Republic
  2. 2.Faculty of Mathematics and Physics, Charles UniversityPragueCzech Republic
  3. 3.Faculty of Nuclear Engineering, Czech Technical UniversityPragueCzech Republic

Personalised recommendations