Numerical solution of the MHD equilibrium equation for an axially symmetric free-boundary plasma in a torus with arbitrary cross-section

The rectilinear flow of an incompressible viscous fluid along a duct of uniform cross section due to an oscillating pressure gradient has been considered by a number of investigators. The duct of circular cross .section has been treated by Richardson and Tyler and Sexl, the elliptic case by Khamrui, and the rectangular case by Drake and Fan and Chao. Recently Jeng has discussed the importance of this type of flow and has given a procedure for calculating a numerical solution for a duct of arbitrary cross-section. An interesting feature of these flows is that, at large frequencies when the flow is of boundary-layer type, the velocity at any instant has its maximum near the walls, the velocity overshooting its almost uniform distribution at the centre of the duct.

Download Full-text

Some uniqueness theorems for the ideal MHD equilibrium of a cylindrical tokamak

Journal of Plasma Physics ◽

10.1017/s0022377800021735 ◽

1979 ◽

Vol 21 (1) ◽

pp. 177-182 ◽

Cited By ~ 2

Author(s):

C.LL. Thomas

Keyword(s):

Free Boundary ◽

Uniqueness Theorem ◽

Current Density ◽

Equilibrium Equation ◽

Uniqueness Theorems ◽

Total Current ◽

Mhd Equilibrium ◽

Ideal Mhd ◽

Boundary Equilibrium ◽

The Ideal

The cylindrical MHD equilibrium equation is formulated in a manner suitable for numerical computations which require the application of a constraint. In this formulation a uniqueness theorem is proved for a free boundary equilibrium with a specified total current. Uniqueness is independent of the details of the current density and merely requires that the total current is compatible with the current density. Two uniqueness theorems for diffuse plasmas are also presented. Four free boundary examples are studied with a variety of constraints applied.

Download Full-text

Axialsymmetrische Lösungen der magnetohydrostatischen Gleichung mit Oberflächenströmen II

Zeitschrift für Naturforschung A ◽

10.1515/zna-1958-0701 ◽

1958 ◽

Vol 13 (7) ◽

pp. 493-498 ◽

Cited By ~ 7

Author(s):

K. Jörgens

Keyword(s):

Magnetic Field ◽

Cross Section ◽

Circular Cross Section ◽

Arbitrary Cross Section ◽

Axially Symmetric ◽

Equilibrium Configurations ◽

Circular Case ◽

Axis Of Symmetry ◽

Hydrodynamic Equilibrium ◽

The Magnetic Field

Axially symmetric magneto-hydrodynamic equilibrium configurations are considered where the plasma is contained in a torus of arbitrary cross-section and electric currents flow in the surface of the plasma only. It is shown that the magnetic field is uniquely determined by the values of the total current in azimuthal and in meridional direction respectively and by the gas pressure. A method is given to compute the location of discontinuities of the magnetic field outside of the torus. The singularities are found explicitly in the case of elliptic or circular cross-section. In the circular case only the magnetic field is regular everywhere outside except on the axis of symmetry.

Download Full-text