Some remarks on computing axisymmetric equilibria

Abstract Some aspects of the computation of diffuse axisymmetric equilibria by means of the HBT code, exploiting conformal mapping, are elaborated. A general method of profile parametrization is developed which provides a unique way of prescribing the shape of equilibrium profiles and the magnitude of global parameters. This method and the associated scaling is illustrated by means of the Soloviev equilibrium and a generalized Haas equilibrium. The results of a comparison of the HBT code, the EMEQ code, and approximate analytical solutions are presented. Some possible generalizations of the use of conformal mappings for the computation of MHD equilibria are indicated.

[1]  M. S. Chance,et al.  Study of the MHD spectrum of an elliptic plasma column , 1977 .

[2]  R. Gajewski.  Magnetohydrodynamic Equilibrium of an Elliptical Plasma Cylinder , 1972 .

[3]  J. P. Goedbloed.  Free‐boundary high‐beta tokamaks. III. Free‐boundary stability , 1982 .

[4]  J. P. Goedbloed.  Conformal mapping methods in two-dimensional magnetohydrodynamics , 1981 .

[5]  J. Freidberg.  Ideal magnetohydrodynamic theory of magnetic fusion systems , 1982 .

[6]  J. Manickam,et al.  Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria , 1979 .

[7]  John L. Johnson,et al.  Long‐wavelength kink instabilities in low‐pressure, uniform axial current, cylindrical plasmas with elliptic cross sections , 1974 .

[8]  F. Haas.  Sharp‐Boundary Model of a High‐Pressure Tokamak , 1972 .

[9]  W. Kerner.  Numerical study of the MHD spectrum in tokamaks with a non-circular cross-section , 1976 .

[10]  J. P. Goedbloed,et al.  High‐beta tokamaks surrounded by force‐free fields , 1978 .

[11]  Glenn Bateman,et al.  Magnetohydrodynamic stability of flux-conserving tokamak equilibria , 1977 .

[12]  W. Schneider,et al.  Erato Stability Code , 1984 .

[13]  Free‐boundary high‐beta tokamaks. II. Mathematical intermezzo: Hilbert transforms and conformal mapping , 1982 .

[14]  F. Troyon,et al.  Numerical study of the unstable MHD spectrum of a small aspect ratio, flat current, non-circular tokamak , 1980 .

[15]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[16]  L. Lao,et al.  Variational moment solutions to the Grad–Shafranov equation , 1981 .