  A new method to obtain the radial profile of the magnetic perturbation in a
toroidal force-free plasma having circular cross section is developed. The
method is quite general and can be applied to any circular low-beta plasma once
suitable boundary conditions are imposed. In particular, due to its
characteristics, it is appropriate for describing the Reversed Field Pinch
(RFP) configuration. The curvilinear metric of the toroidal geometry is
described by adopting flux co-ordinates, and the magnetic field is expressed by
the contravariant representation with two independent potentials. The method
leads to a system of Newcomb-like equations in the two independent potentials
for modes with the same toroidal n-number and poloidal mode number m coupled by
toroidicity. The advantage of this description is that the potentials together
with the metric coefficients can be related in a straightforward manner to the
magnetic field. Moreover it is formally simple and maintains a similarity with
the cylindrical treatment. Indeed it is customary in RFPs to approach the
analysis of MHD instabilities by using cylindrical geometry. Nonetheless the
effect of a more realistic toroidal geometry can play an important role, and
indeed by applying the method to the Reversed Field eXperiment (RFX) plasma we
found that the toroidal effects on the magnetic perturbations are not
negligible.
