Perturbed solutions of fixed boundary MHD equilibria

In this study, the fixed boundary plasma MHD equilibrium problem is solved by the finite element method; then, by perturbing the flux at the plasma boundary nodes, linear formulae are derived linking the variation of several plasma parameters of interest to the variation of the currents flowing in the external circuits. On the basis of these formulae it is shown how it is possible to efficiently solve two central problems in plasma engineering, namely (1) the optimization of the currents in a given set of coils necessary to maintain a specified equilibrium configuration and (2) the derivation of a linear dynamic model describing the plasma axisymmetric displacement (n = 0 mode) about a given magnetic configuration. A case study-based on the ITER reference equilibrium magnetic configuration at burn-is analysed both in terms of equilibrium currents optimality as well as axisymmetric stability features. The results obtained by these formulae are also compared with the predictions of a non-linear free boundary code and of a linear, dynamic model. As shown, the formulae derived here are in good agreement with such predictions, confirming the validity of the present approach. (author)