The non-axisymmetric analysis of the vacuum magnetic surface in a toroidal device is discussed assuming that the deviation from axisymmetry is a perturbation. The problem is particularly relevant to study the locked-mode phenomena due to internally resonant resistive magnetohydrodynamic (MHD) modes in reversed field pinch experiments. The general expressions which can be used for the magnetic reconstruction are derived according to two types of formalism: the flux function reconstruction and the magnetic scalar potential representation of the magnetic field. The measurements necessary to obtain a suitable magnetic reconstruction are discussed. In particular, it is found that a sufficient set of Br measurements is key information in obtaining the non-axisymmetric flux function. Such a set of measurements is presently lacking in the RFX reversed field pinch device. Nevertheless, based on an approximate solution of the Laplace equation for the magnetic scalar potential in the vacuum region outside the plasma, a method is derived by which the helical perturbation of the plasma magnetic surface can be computed with sufficient accuracy in RFX based on the measurements of a twin array of B coils only.
Equilibrium configurations of reverse field pinch plasma with a helical magnetic axis