Exact solutions to the Grad-Shafranov equation for magnetically confined plasmas

A class of exact analytic solutions to the Grad-Shafranov equation (GSE), in cylindrical geometry under assumption of axial symmetry is obtained. For this configuration all the physical quantities are invariant under rotations about a fixed direction, which we take it to be the direction Oz of a cylindrical polar coordinate system (r, θ, z). The obtained solutions can be employed to describe isothermal magnetostatic atmosphere.