Analytic Examples of Force-Free Toroidal MHD Equilibria

Analytically described toroidal (axisymmetric and three-dimensional) equilibrium magnetic field configurations with a “flat” current density, j = (lambda)B((lambda)=const), are proposed. Such configurations are superpositions of several force-free two-dimensional configurations with plane, axial, or helical coordinate symmetry. Each of them is generated by an exact partial solution to the corresponding Grad–Shafranov equation. A variety of toroidal configurations thus obtained allows one to model topological changes of magnetic surfaces, such as magnetic axis splitting (doublets) in axisymmetric equilibrium configurations and the appearance and interaction of magnetic islands and ergodic lines in three-dimensional configurations.