Analytical Solution Of The Tokamak Equilibrium. I. The Fixed-Boundary Case

This article presents an analytical method to evaluate the equilibrium of plasmas in axisymmetric, nested magnetic configurations relevant for tokamak experiments. The emphasis is in the use of spectral representations of the magnetic flux surfaces and variational methods to solve the Grad-Shafranov equation. Approximate solutions are obtained based on power series expansions of the variational moment equations and sectionally continuous representations of the Fourier amplitudes. The method is applied to an up-down asymmetric configuration of an ITER-like tokamak in a fixed-boundary equilibrium. The free-boundary case is treated in the Paper II [G.O. Ludwig, Phys. Plasma 24, 092503 (2017)]. Published by AIP Publishing.