MHD stability analysis of force-free reversed field pinch configurations

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Abstract
The MHD current driven instabilities of Reversed Field Pinch (RFP) configurations are analysed for a plasma in contact with a perfectly conducting wall. The equilibrium distributions are obtained on the basis of a model which allows a parametric variation of the value of the safety factor on the axis, q(0), and of the current density distribution. – The RFP is found to be stable in a wide range of parameters. However, when the toroidal field reversal becomes too deep, unstable modes, resonant outside the reversal surface, are found in analogy to the stability limit at θ = 1.56 for the Taylor's theoretical, fully relaxed states. Nevertheless, it is shown that these modes are not very significant in that they arise in a region of the parameters space which is only rarely approached in experiments. On the other hand, for peaked current density distributions, new unstable tearing and kink modes are found when q(0) drops below the limit q(0) ≈ 2a/(3R). These modes are resonant inside the reversal surface and may include the mode resonant on the axis. – The results of the MHD stability for the internal modes and in particular the limit on the value of q on axis that has been found are discussed in connection with experimental observations on mean field profiles and related oscillations.