Infinite symmetries of the ideal MHD equilibrium equations

2001 ◽  
Vol 291 (4-5) ◽  
pp. 256-264 ◽  
Author(s):  
Oleg I. Bogoyavlenskij
Keyword(s):  
Equilibrium Equations ◽  
Mhd Equilibrium ◽  
Ideal Mhd ◽  
Infinite Symmetries ◽  
The Ideal

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

1979 ◽  
Vol 21 (1) ◽  
pp. 177-182 ◽  
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.

scholarly journals Magnetic Braking and Protostellar Disk Formation: The Ideal MHD Limit

2008 ◽  
Vol 681 (2) ◽  
pp. 1356-1376 ◽  
Author(s):  
Richard R. Mellon ◽  
Zhi‐Yun Li
Keyword(s):  
Disk Formation ◽  
Ideal Mhd ◽  
Magnetic Braking ◽  
The Ideal

Toroidal plasma configuration with non-planar magnetic axis

1984 ◽  
Vol 32 (2) ◽  
pp. 179-196
Author(s):  
Hussain M. Rizk
Keyword(s):  
Cross Section ◽  
Ohmic Heating ◽  
Circular Cross Section ◽  
Magnetic Axis ◽  
Toroidal Plasma ◽  
Mhd Equilibrium ◽  
Special Cases ◽  
Magnetic Surfaces ◽  
Plasma Configuration ◽  
The Ideal

The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.

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