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Open Access Publications from the University of California

Contour dynamics method for solving the Grad-Shafranov equation with applications to high beta equilibria

  • Author(s): Gourdain, P A
  • Leboeuf, J.-N.
  • et al.

Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of a plasma confined by an axisymmetric magnetic field. Nevertheless, they are limited to low beta or small plasma pressure. Combining a nonconservative variational principle with a contour dynamics approach, the approach presented in this paper converges for extreme high beta configurations. By reducing the dimension of the problem from two to one, a compact and efficient numerical algorithm can be developed, and a wide range of boundary shapes can be utilized. Furthermore, the iterative nature of this technique greatly facilitates convergence at high beta while minimizing computation times.

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