Variational principles related to the equilibrium shape of a plasma in an axisymmetric torus

Considers the equilibrium shape of a plasma confined in an axisymmetric torus with a perfectly conducting shell of arbitrary cross-section and with (or without) control field coils. This problem leads to a non-classical, free boundary value problem for the flux function psi . A variational, non-linear eigenvalue problem is proposed whose solution defines the function psi in the whole cavity, giving at the same time the boundary of the plasma and the values of psi inside the plasma and in the vacuum. This approach is useful for the analytical study of the problem and also for its numerical solution.