Equilibrium in an actopole Tokamak without conducting shell

A numerical method is described for solving free boundary problems in an axially symmetric toroidal configuration. Approximate solutions for equilibrium plasmas are given for a fixed external magnetic field. The equilibrium plasma in the multipole configuration consisting of a uniform vertical magnetic field and a shaping field is discussed. A shift of the equilibrium position leads to a change of the cross-section shape from rectangular to a D- or a tear-drop type. The plasma equilibria with the D-shaped cross section are horizontally unstable and an off-centre equilibrium is obtained. The safety factor and the well depth are increased by adding the shaping magnetic field.