A new method to obtain the radial profile of the magnetic perturbation in a toroidal force-free plasma having a circular cross section is developed. The toroidal geometry produces poloidal harmonics in the equilibrium quantities (at the leading order m = ±1, n=0), which act as mediators between perturbations with the same toroidal number and different poloidal numbers. The approach proposed here, based on the contravariant representation of the magnetic field in flux co-ordinates, is formally simple and rigorous and maintains a nice similarity with the cylindrical treatment. The method is quite general and can be applied to any circular low-beta plasma. In this work we describe its application to the Reversed Field eXperiment (RFX) plasma. It is customary in reversed field pinches to approach the analysis of MHD instabilities by using a cylindrical geometry. Nonetheless, the effect of a more realistic toroidal geometry can play an important role, and indeed we found that the toroidal effects on the magnetic perturbations are not negligible.
Analysis of MHD equilibria by toroidal multipolar expansions