Journal of Fusion Energy

, Volume 32, Issue 1, pp 71–77 | Cite as

Ergodic Magnetic Limiter with Barrier

Original Research

Abstract

A barrier is produced to radial diffusion of chaotic field lines and consequently increasing the particles confinement time. The chaotic layer near the plasma edge is created by perturbed Hamiltonian (of order ε) of an ergodic magnetic limiter (EML). Adding a control term of order ε 2 to this perturbed Hamiltonian revives invariant tori acting as barriers against plasma particles diffusion. The location of the barrier could be chosen in the chaotic zone of EML at a given place near the edge of plasma column. The chaotic behavior of the magnetic field lines around the barrier is studied by utilizing the maximal Lyapunov exponent, average square displacement (diffusion) and invariant manifolds. The effect of changing the number of EML rings on the barrier is investigated. A barrier is also generated by considering special modes in the Fourier expansion of the perturbed Hamiltonian.

Keywords

Hamiltonian chaos Transport barrier Ergodic magnetic limiter Symplectic maps Tokamak 

References

  1. 1.
    A. Boozer, Rev. Mod. Phys. 76, 1071 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    R. Balescu, Aspects of anomalous transport in plasmas (Taylor and Francis, London, 2005)CrossRefGoogle Scholar
  3. 3.
    W. Horton, Rev. Mod. Phys. 71, 735 (1999)ADSCrossRefGoogle Scholar
  4. 4.
    A.F. Marcus, T. Kroetz, M. Roberto, I.L. Caldas, E.C. da Silva, R.L. Viana, Z.O. Guimares-Filho, Nucl. Fusion 48, 024018 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    M.W. Jakubowski et al., Phys. Rev. Lett. 96, 35004 (2006)ADSCrossRefGoogle Scholar
  6. 6.
    T.E. Evans et al., J. Nucl. Mater. 337, 691 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    S.C. McCool et al., Nucl. Fusion 29, 547 (1989)CrossRefGoogle Scholar
  8. 8.
    T.E. Evans et al., Nature Phys. 2, 419 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    T.E. Evans et al., Nucl. Fusion 45, 595 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    T.E. Evans et al., Phys. Rev. Lett. 92, 235003 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    J.R. Cary, J.D. Hanson, Phys. Fluids 29, 2464 (1986)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    J.D. Hanson, Nucl. Fusion 34, 441 (1994)ADSCrossRefGoogle Scholar
  13. 13.
    S.R. Hudson, R.L. Dewar, Phys. Lett. A 226, 85 (1997)ADSCrossRefGoogle Scholar
  14. 14.
    S.R. Hudson, R.L. Dewar, Phys. Lett. A 247, 246 (1998)ADSCrossRefGoogle Scholar
  15. 15.
    P.C. Stangeby, The Plasma Boundary of Magnetic Fusion Devices (Institure of Physics Publishing, Bristol, 2000)CrossRefGoogle Scholar
  16. 16.
    R. Parker, G. Janeschitz, H.D. Pacher, D.E. Post, S. Chiocchio, G. Federici, P. Ladd, J. Nucl. Mater. 241, 241–243 (1997)Google Scholar
  17. 17.
    R.C. Wolf, Plasma Phys. Control. Fusion 45, R1–R91 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    K.H. Finken, T.E. Evans, D. Reiter, K.H. Spatschek, W. Suttrop, Nucl. Fusion 48, 020201 (2008)ADSCrossRefGoogle Scholar
  19. 19.
    F.M. Levinton et al., Phys. Rev. Lett. 75, 4417 (1995)ADSCrossRefGoogle Scholar
  20. 20.
    E.J. Strait et al., Phys. Rev. Lett. 75, 4421 (1995)ADSCrossRefGoogle Scholar
  21. 21.
    F.A. Marcus, I.L. Caldas, Z.O. Guimaraes-Filho, P.J. Morrison, W. Horton, Y.K. Kuznetsov, I.C. Nascimento, Phys. Plasma 15, 112304 (2008)ADSCrossRefGoogle Scholar
  22. 22.
    K.H. Spatschek, Plasma Phys. Control. Fusion 50, 124027 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    T. Kroetz, M. Roberto, E.C. da Silva, I.L. Caldas, R.L. Viana, Phys. Plasmas 15, 092310 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    T.J. Martin, J.B. Taylor, Plasma Phys. Control. Fusion 26, 321 (1984)ADSCrossRefGoogle Scholar
  25. 25.
    K. Ullman, I.L. Caldas, Chaos. Solit. & Fract. 11, 2129 (2000)CrossRefGoogle Scholar
  26. 26.
    E.C. da Silva, I.L. Caldas, R.L. Viana, Phys. Plasmas 8, 2855 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    E.C. da Silva, I.L. Caldas, L.V. Ricardo, IEEE Trans. Plasma Sci. 29(4), 617 (2001)ADSCrossRefGoogle Scholar
  28. 28.
    A.J. Lichtenberg, M.A. Lieberman, Regular and Chaotic Dynamics, 2nd edn. (Springer, New York, 1992)MATHGoogle Scholar
  29. 29.
    J.D. Meiss, Rev. Mod. Phys. 64, 795 (1992)MathSciNetADSMATHCrossRefGoogle Scholar
  30. 30.
    A.R. Sohrabi, S.M. Jazayeri, M. Mollabashi, J. Plasma Phys. 76, 777 (2010)ADSCrossRefGoogle Scholar
  31. 31.
    G. Ciraolo, C. Chandre, R. Lima, M. Vittot, M. Pettini, C. Figarella, P. Ghendrih, J. Phys. A: Math. Gen. 37, 3589 (2004)MathSciNetADSMATHCrossRefGoogle Scholar
  32. 32.
    G. Ciraolo et al., Phys. Rev. E 69 (2004) 056213-1-16Google Scholar
  33. 33.
    M. Vittot, J. Phys. A: Math. Gen. 37, 6337 (2004)MathSciNetADSMATHCrossRefGoogle Scholar
  34. 34.
    C. Chandre, G. Ciraolo, F. Doveil, R. Lima, A. Macor and M.Vittot, Phys. Rev. Lett. 94 (2005) 074101-1-4Google Scholar
  35. 35.
    C. Chandre et al., Nucl. Fusion 46, 33 (2006)ADSCrossRefGoogle Scholar
  36. 36.
    M. Y. Kucinski, I. L. Caldas, Naturforsch Z 42a (1987) 1124Google Scholar
  37. 37.
    M.Y. Kucinski, I.L. Caldas, L.H.A. Monteiro, V. Okano, J. Plasma Phys. 44, 303 (1990)ADSCrossRefGoogle Scholar
  38. 38.
    J. Aguirre, R.L. Viana, M.A.F. Sanjuan, Rev. Mod. Phys. 81, 333 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of PhysicsIran University of Science and TechnologyTehranIran

Personalised recommendations