The paper extends and augments earlier research concerning the effect that a finitely conducting wall has on the linear stability of various plasma models. If a plasma is stable to a particular mode when surrounded by a perfect wall but unstable to it when the wall is removed, then theory indicates that surrounding the plasma with an imperfect wall can lead to instability of that mode on the long time constant of the wall. Analysis of this effect requires that the various modes possible be classified as to whether the plasma is regarded as ideal or resistive, and whether the pitch of the perturbation resonates with that of the equilibrium. The effect of both bulk plasma rotation and mode rotation (plasma diamagnetism) on these various modes is discussed.

A number of possible designs of external and in-vessel coils generating resonant magnetic perturbations (RMPs) for Type I edge localized modes (ELMs) control in ITER are analysed for the reference scenarios (H-mode, Hybrid and Steady-State) taking into account physical, technical and spatial constraints. The level of stochasticity (Chirikov parameter ∼1 at ψ1/2 ∼ 0.95) generated by the I-coils in the DIII-D experiments on ELMs suppression was taken as a reference. Designs with a toroidal symmetry n = 3 were considered to avoid lower n numbers producing larger central islands, a potential trigger of MHD instabilities. The evaluation of RMP coils designs is done with respect to the RMPs spectrum that should produce enough edge ergodisation and minimum central perturbations at minimum current. The proposed designs include in-vessel, mid-ports and external coils. Changes in the equilibrium due to changes in the internal inductance l i, the poloidal beta βp and the edge magnetic shear in a reasonable range for ITER scenarios were demonstrated to have a small effect on the edge ergodisation. Present estimations were done without margins and for vacuum fields neglecting plasma response on RMPs. The validity of the vacuum approach was estimated analytically in the visco-resistive linear response regime using [1]. The typical radial magnetic field amplitudes produced by RMP coils in DIII-D and ITER are an order of magnitude or slightly above the critical values for the ‘downward’ bifurcation to the reconnected stage indicating the possibility of the islands formation in the pedestal region. Central islands (from the top of the pedestal) are expected to be screened.

An analytical, large aspect ratio, calculation of the drift-kinetic energy perturbation is carried out for the resistive wall mode, due to the mode resonance with the magnetic precession drifts of trapped thermal ions and electrons. Four asymptotic cases are identified and analyzed in detail. Generally, a partial stabilization of the mode is possible thanks to the kinetic correction to the perturbed plasma energy. A complete stabilization can occur only in a narrow space of the plasma equilibrium parameters. Kinetic destabilization of the mode is also possible due to a finite pressure correction to the precession drift frequency.