Active control of multiple resistive wall modes

A two-dimensional array of saddle coils at Mc poloidal and Nc toroidal positions is used on the EXTRAP T2R reversed-field pinch (Brunsell P R et al2001 Plasma Phys. Control. Fusion43 1457) to study active control of resistive wall modes (RWMs). Spontaneous growth of several RWMs with poloidal mode number m = 1 and different toroidal mode number n is observed experimentally, in agreement with linear MHD modelling. The measured plasma response to a controlled coil field and the plasma response computed using the linear circular cylinder MHD model are in quantitive agreement. Feedback control introduces a linear coupling of modes with toroidal mode numbers n, n' that fulfil the condition |n − n'| = Nc. Pairs of coupled unstable RWMs are present in feedback experiments with an array of Mc × Nc = 4 × 16 coils. Using intelligent shell feedback, the coupled modes are generally not controlled even though the field is suppressed at the active coils. A better suppression of coupled modes may be achieved in the case of rotating modes by using the mode control feedback scheme with individually set complex gains. In feedback with a larger array of Mc × Nc = 4 × 32 coils, the coupling effect largely disappears, and with this array, the main internal RWMs n = −11, −10, +5, +6 are all simultaneously suppressed throughout the discharge (7–8 wall times). With feedback there is a two-fold extension of the pulse length, compared to discharges without feedback.