**Theory of Perturbed Equilibria for Solving the Grad-Shafranov Equation**

Authors: L.E. Zakharov and A. Pletzer

**Date:** July 14, 1999

**Submitted:** Plasma of Physics

The theory of perturbed magnetohydrodynamic equilibria is presented for different formulations of the tokamak equilibrium problem. For numerical codes, it gives an explicit Newton scheme for solving the Grad-Shafranov equation subject to different constraints. The problem of stability of axisymmetric modes is shown to be a particular case of the equilibrium perturbation theory.