Fourier–Bessel Series Solutions of the Axisymmetrical Grad–Shafranov Equation for Plasma Confinement

The axisymmetrical Grad–Shafranov equation is solved by separating the radial and axial variables and expressing the azimuthal plasma current density via series of sinusoidal or exponentially decaying functions of the axial variable. In these conditions, the flux function, exact solution of the axisymmetrical Grad–Shafranov equation, is described by double series involving Bessel functions of the radial coordinate and sinusoidal or exponential functions of the axial coordinate.