Bifurcated Tokamak equilibria with vanishing edge current density

Abstract Tokamak equilibria with canonical profiles of current density and pressure are obtained by minimisation of the total plasma energy under the constraint of a constant total plasma current. It is shown that there are an infinite number of solutions when there is a vacuum region between a free plasma boundary and a conducting wall. For the case with fixed boundary a finite multiplicity of solutions exists. Canonical profiles are obtained also in the case of an average current density vanishing at the boundary. The bifurcation of solutions, similar to an L to H transition, is briefly discussed.