Perturbed plasma equilibria

The force balance, or equilibrium, of an axisymmetric toroidal plasma with a scalar pressure can be relatively simply calculated. However, equilibrium calculations present fundamental difficulties when either the geometry or the plasma forces are more complicated. Many of these issues, such as the loss of magnetic surfaces and complicated plasma forces, can be addressed by perturbation theory using ideal magnetohydrodynamics stability codes. This paper outlines the procedure for carrying out such calculations and demonstrates the method by applying it to a problem with a known solution, an axisymmetric tokamak in which the pressure is increased by 15%.