A set of 24 in-vessel saddle coils is planned for MHD control experiments in ASDEX Upgrade. These coils can produce static and alternating error fields for suppression of Edge Localised Modes, locked mode rotation control and, together with additional conducting wall elements, resistive wall mode excitation and feedback stabilisation experiments. All of these applications address critical physics issues for the operation of ITER. This extension is implemented in several stages, starting with two poloidally separated rings of eight toroidally distributed saddle coils above and below the outer midplane. In stages 2 and 3, eight midplane coils around the large vessel access ports and 12 AC power converters are added, respectively. Finally (stage 4), the existing passive stabilising loop (PSL), a passive conductor for vertical growth rate reduction, will be complemented by wall elements that allow helical current patterns to reduce the RWM growth rate for active control within the accessible bandwidth. The system is capable of producing error fields with toroidal mode number n = 4 for plasma edge ergodisation with core island width well below the neoclassical tearing mode seed island width even without rotational shielding. Phase variation between the three toroidal coil rings allows to create or avoid resonances with the plasma safety factor profile, in order to test the importance of resonances for ELM suppression.
A power-balance model, with radiation losses from impurities and neutrals, gives a unified description of the density limit (DL) of the stellarator, the L-mode tokamak, and the reversed field pinch (RFP). The model predicts a Sudo-like scaling for the stellarator, a Greenwald-like scaling, , for the RFP and the ohmic tokamak, a mixed scaling, , for the additionally heated L-mode tokamak. In a previous paper (Zanca et al 2017 Nucl. Fusion 57 056010) the model was compared with ohmic tokamak, RFP and stellarator experiments. Here, we address the issue of the DL dependence on heating power in the L-mode tokamak. Experimental data from high-density disrupted L-mode discharges performed at JET, as well as in other machines, are taken as a term of comparison. The model fits the observed maximum densities better than the pure Greenwald limit.
Active feedback control of resistive wall modes (RWMs) has been demonstrated on the EXTRAP T2R reversed-field pinch experiment. The control system includes a sensor consisting of an array of magnetic coils (measuring mode harmonics) and an actuator consisting of a saddle coil array (producing control harmonics). Closed-loop (feedback) experiments using a digital controller based on a real time Fourier transform of sensor data have been studied for cases where the feedback gain was constant and real for all harmonics (intelligent-shell) and cases where the feedback gain could be set for selected harmonics, with both real or complex values (targeted-harmonics). The growth of the dominant RWMs can be suppressed by feedback for both the intelligent-shell and targeted-harmonic control systems. Because the number of toroidal positions of saddle coils in the array is half the number of sensors, it is predicted and observed experimentally that the control harmonic spectrum has sidebands. As a result, each control harmonic has to control simultaneously two mode harmonics. Real gains can stabilize non-rotating RWMs, while complex gains give better results for (slowly) rotating RWMs. In addition open loop experiments have been used to observe the effects of resonant field errors applied to unstable, marginally stable and robustly stable modes. The observed effects of field errors are consistent with the thin-wall model, where mode growth is proportional to the resonant field error amplitude and the wall penetration time for that mode harmonic.
A two-dimensional array of saddle coils at M c poloidal and N c toroidal positions is used on the EXTRAP T2R reversed-field pinch (Brunsell P R et al 2001 Plasma Phys. Control. Fusion 43 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 | = N c . Pairs of coupled unstable RWMs are present in feedback experiments with an array of M c ×N c = 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 M c × N c = 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.
An active feedback system is required for long pulse operation of the reversed field pinch (RFP) device to suppress resistive wall modes (RWMs). A general feature of a feedback system using a discrete active coil array is a coupling effect which arises when a set of side band modes determined by the number of active coils is produced. Recent results obtained on the EXTRAP T2R RFP demonstrated the suppression of independent m = 1 RWMs using an active feedback system with a two-dimensional array of discrete active coils in the poloidal and toroidal directions. One of the feedback algorithms used is the intelligent shell feedback scheme. Active feedback systems having different number of active coils in the poloidal (M c ) and toroidal (N c ) directions (M c ×N c = 2×32 and M c ×N c = 4×16) are studied. Different side band effects are seen for these configurations. A significant prolongation of the plasma discharge is achieved for the intelligent shell feedback scheme using the 2 × 32 active coil configuration. This is attributed to the side band sets including only one of the dominant unstable RWMs and avoiding coupling to resonant modes. Analog proportional-integral-derivative controllers are used in the feedback system. Regimes with different values of the proportional gain are studied. The requirement of the proportional-integral control for low proportional gain and proportional-derivative control for high proportional gain is seen in the experiments.
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