MHD spectra and coordinate transformations in toroidal systems

A fully geometric approach is used to study the mutual spectral properties of different classes of MHD equilibria with symmetries defined by action-angle coordinates. We refer mostly to the helical equilibria of tokamak and reversed field pinch plasmas compared to the axisymmetric counterpart. Based on the existence of different coordinate systems, we show how the magnetic field and the vector potential are correspondingly evaluated, and how their spectral decompositions may largely vary. Most notably, a monochromatic perturbation in a reference frame can appear with a rich spectrum in another frame. The consequences on the interpretation of the measurements and the implications on the effectiveness of the externally applied magnetic fields on the plasma are discussed with practical examples.