Using the techniques of Hilbert transforms and conformal mapping, the stability problem of a toroidal free‐boundary high‐β tokamak equilibrium with a skin current is reduced to a one‐dimensional problem for which a new variational principle is derived. The minimization is carried out numerically and a complete scan of parameter space is carried out. The stability limit is qualitatively different from the one obtained in the usual fixed‐boundary model without a wall. Rather than a more severe, a less severe limitation on the plasma current is obtained. It is shown that the Kruskal–Shafranov limit may be surpassed when the value of β is sufficiently high and the wall is sufficiently close to the plasma.
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