Free-boundary high-beta tokamaks. I. Free-boundary equilibrium

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Abstract
The free-boundary problem of a sharp-boundary high-β tokamak plasma inside a conducting shell is solved. This problem is reduced to solving Laplace’s equation on a domain with an unknown inner boundary. Centering this boundary with respect to the center of the shell is effected by means of a Moebius transformation which facilitates the use of the fast Fourier transformation. The method exploits Green’s theorem for the linear part of the problem which is the solution of Laplace’s equation with given boundaries. The nonlinear part consists of moving the plasma boundary until pressure balance is obtained. Fast convergence to accurate results is obtained through the use of a judiciously chosen damping factor determining the response of the plasma shape to changes in the poloidal field pressure. This allows for a complete scan of the two-dimensional parameter space characterized by the plasma shift Δ and the plasma thickness a. Expressions are derived for the maximum permissible value of the poloidal beta.