STRUCTURE OF FORCE-FREE MAGNETIC-FIELDS IN EQUILIBRIUM OF TOROIDAL PLASMA IN HIGH BETA-TOKAMAK

For a sharp boundary equilibrium model of an axisymmetrical-toroidal dense plasma surrounded by a pressureless plasma with force-free fields, structure of force-free magnetic fields is studied by using analytical solutions of the Helmholtz equation for toroidal coordinates and Fourier decomposition. Geometrical form of the magnetic surfaces inside the separatrix surrounding the dense plasma is revealed for the poloidal beta βp and the aspect ratio of the dense plasma Rp/rp=cosh σp which are characteristic of a high β tokamak. A condition of the equilibrium is determined and the maximum βp is given by βp=¼ (Rp/rp +rp/Rp) + ¼. The magnetic field equation ▼ × H=αH is reduced to the Helmholtz equation (▼2 =0 for the condition α=constant, which is solved without the approximation of the expansion about the inverse aspect ratio. The force-free magnetic fields can be evaluated in a high accuracy under the equilibrium condition of the toroidal dense plasma. For the force-free magnetic surfaces similar to the vacuum magnetic ones, by increasing —α or Rp/rp=cosh σp the separatrix surrounding the dense plasma is expanded and the layers of the magnetic surfaces inside the separatrix are increased. Thus, by decreasing Rp/rp for the fixed separatrix, the layers of the magnetic surfaces inside the separatrix are increased with the increase of —α. © 1979, Atomic Energy Society of Japan. All rights reserved.