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Tokamak-like Vlasov equilibria

  • Henri Tasso
  • George ThroumoulopoulosEmail author
Regular Article
Part of the following topical collections:
  1. Topical issue: Theory and Applications of the Vlasov Equation

Abstract

Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, some toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, the two cases considered here are produced by means of either a Heaviside step function or an exponential function. The resulting Grad-Shafranov-like equations are established explicitly.

Keywords

Magnetic Axis Vlasov Equation Electron Distribution Function Heaviside Step Function Pressure Gradient Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    P.J. Channell, Phys. Fluids 19, 1541 (1976)ADSCrossRefGoogle Scholar
  2. 2.
    S.M. Mahajan, Phys. Fluids B 1, 43 (1989)ADSCrossRefMathSciNetGoogle Scholar
  3. 3.
    N. Attico, F. Pegoraro, Phys. Plasmas 6, 767 (1999)ADSCrossRefMathSciNetGoogle Scholar
  4. 4.
    F. Mottez, Phys. Plasmas 10, 2501 (2003)ADSCrossRefMathSciNetGoogle Scholar
  5. 5.
    C. Montagna, F. Pegoraro, Phys. Plasmas 14, 042103 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    C.R. Stark, T. Neukirch, Phys. Plasmas 19, 012115 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    G. Belmont, N. Aunai, R. Smets, Phys. Plasmas 19, 022108 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    S.A. Lazerson, J. Plasma Phys. 77, 31 (2011)CrossRefGoogle Scholar
  9. 9.
    H.E. Mynick, W.M. Sharp, A.N. Kaufman, Phys. Fluids 22, 1478 (1979)ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    K. Schindler, Physics of space plasma activity (Cambridge University Press, 2007)Google Scholar
  11. 11.
    G.N. Throumoulopoulos, H. Tasso, arxiv:0909.1745v2 [physics.plasm-ph]Google Scholar
  12. 12.
    H. Tasso, G.N. Throumoulopoulos, J. Phys. A 40, F631 (2007)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    J.P. Freidberg, in Ideal Magnetohydrodynamics (Plenum Press, 1987), p. 108Google Scholar
  14. 14.
    E.W. Weinstein, The CRC concise encyclopedia of mathematics (CRC Press LLC, 1999)Google Scholar
  15. 15.
    R. Courant, D. Hilbert, Methods of mathematical physics (Interscience Publishers, 1966), Vol. 2, p. 372Google Scholar
  16. 16.
    G.N. Throumoulopoulos, H. Tasso, Phys. Plasmas 10, 2382 (2003)ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Max-Planck-Institut für PlasmaphysikGarching bei MünchenGermany
  2. 2.Department of PhysicsUniversity of Ioannina, Association Euratom-Hellenic RepublicIoanninaGreece

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