Some problems of axisymmetric toroidal equilibria in orthogonal flux coordinates

Formulations of axisymmetric equilibrium problems are presented in orthogonal flux coordinates with boundary conditions that do not assume fixation of the boundary shape for both levitron-type traps with a plasma-embedded conductor and conductor-free configurations, including a tokamak. Illustrative examples of numerical solutions of these problems are presented. For traps with a conductor, it is demonstrated how the geometry of the equilibrium with an isodynamic magnetic surface can be found using flux coordinates.