Advertisement

Magnetohydrodynamic equilibrium calculations using multigrid

  • B. J. Braams
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1228)

Abstract

The multigrid method has been applied to the solution of the two-dimensional elliptic equation that governs axisymmetric ideal magnetohydrodynamic equilibrium. The possibility of applying multigrid to the computation of axisymmetric equilibria in the ‘inverse coordinates’ formulation and to three-dimensional equilibrium and evolution calculations is investigated.

Keywords

Equilibrium Problem Multigrid Method Grid Generation Magnetic Confinement Force Balance Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Brandt, Multi-Level Adaptive Solutions to Boundary Value Problems, Math. Comp. 31 (1977), 333–390.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    A. Brandt, Guide to Multigrid Development, in “Multigrid Methods”, Proceedings of the Conference held at Köln-Porz, Nov. 1981 (W. Hackbusch, U. Trottenberg, Eds.), Lecture Notes in Mathematics, Springer, Berlin, 1982.Google Scholar
  3. 3.
    G. Bateman, “MHD Instabilities”, The MIT Press, Cambridge, Mass., 1978.Google Scholar
  4. 4.
    J.P. Freidberg, Ideal Magnetohydrodynamic Theory of Magnetic Fusion Systems, Rev. Mod. Phys. 54 (1982), 801–902.CrossRefGoogle Scholar
  5. 5.
    B.B. Kadomtsev and V.D. Shafranov, Magnetic Plasma Confinement, Sov. Phys. Usp. 26 (1983), 207–227; Usp. Fiz. Nauk (USSR) 139 (1983), 399–434.CrossRefGoogle Scholar
  6. 6.
    R.M. Kulsrud, MHD Description of Plasma, in “Handbook of Plasma Physics”, Vol. 1: Basic Plasma Physics I, (A.A. Galeev and R.N. Sudan, Eds.), Elsevier, Amsterdam, 1984, pp. 115–145.Google Scholar
  7. 7.
    V.D. Shafranov, On Magnetohydrodynamical Equilibrium Configurations, Sov. Phys. JETP 6 (1958), 545–554; J. Exper. Theor. Phys. 33 (1957), 710–722.MathSciNetzbMATHGoogle Scholar
  8. 8.
    R. Lüst and A. Schlüter, Axialsymmetrische Magnetohydrodynamische Gleichgewichtskonfigurationen, Z. Naturforsch. 12a (1957), 850–854.MathSciNetzbMATHGoogle Scholar
  9. 9.
    H. Grad and H. Rubin, Hydromagnetic Equilibria and Force-Free Fields, in “Proceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy”, Geneva, 1958.Google Scholar
  10. 10.
    K. Lackner, Computation of Ideal MHD Equilibria, Comput. Phys. Commun. 12 (1976), 33–44.CrossRefGoogle Scholar
  11. 11.
    L.E. Zakharov and V.D. Shafranov, Equilibrium of Current-Carrying Plasmas in Toroidal Systems, in “Reviews of Plasma Physics”, vol. 11, Energoisdat, Moscow, 1982 (Russian, translation not yet available).Google Scholar
  12. 12.
    P.N. Vabishchevich, L.M. Degtyarev and A.P. Favorskii, Variable-Inversion Method in MHD-Equilibrium Problems, Sov. J. Plasma Phys. 4 (1978), 554–556, Fiz. Plazmy 4 (1978), 995–1000.Google Scholar
  13. 13.
    J. DeLucia, S.C. Jardin and A.M.M. Todd, An Iterative Metric Method for Solving the Inverse Tokamak Equilibrium Problem, J. Comput. Phys. 37 (1980), 183–204.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    H.R. Hicks, R.A. Dory and J.A. Holmes, Inverse Plasma Equilibria, Comput. Phys. Reports 1 (1984), 373–388.CrossRefGoogle Scholar
  15. 15.
    L.M. Degtyarev and V.V. Drozdov, An Inverse Variable Technique in the MHD-Equilibrium Problem, Comput. Phys. Reports 2 (1985), 341–387.CrossRefGoogle Scholar
  16. 16.
    J.F. Thompson (Ed.), “Numerical Grid Generation”, North Holland, New York, 1982.zbMATHGoogle Scholar
  17. 17.
    J.F. Thompson, Z.U.A. Warsi and C.W. Mastin, Boundary-Fitted Coordinate Systems for Numerical Solution of Partial Differential Equations—A Review, J. Comput. Phys. 47 (1982), 1–108.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    R. Chodura and A. Schlüter, A 3D Code for MHD Equilibrium and Stability, J. Comput. Phys. 41 (1981), 68–88.CrossRefzbMATHGoogle Scholar
  19. 19.
    F. Troyon, R. Gruber, H. Saurenmann, S. Semenzato and S. Succi, MHD-Limits to Plasma Confinement, 11th European Conference on Controlled Fusion and Plasma Physics, Aachen, 1983, Plasma Phys. Contr. Fusion 26 (1984), 209–215.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • B. J. Braams
    • 1
    • 2
  1. 1.F.O.M. Instituut voor PlasmafysicaNieuwegeinThe Netherlands
  2. 2.Max-Planck-Institut für PlasmaphysikGarching bei MünchenFed. Rep. Germany

Personalised recommendations