Demetrio Gregoratto

Feedback control of resistive wall modes in reversed field pinches

Feedback stabilization of magnetohydrodynamical modes in reversed field pinches is studied in cylindrical geometry, taking into account a finite number of coils, both in poloidal and toroidal directions. The robustness and stability of the feedback scheme is analysed by means of Nyquist diagrams for different arrangements of the feedback coils and magnetic sensors. The feedback can be adversely affected by the coupling of different Fourier components from the discrete coils, and configurations are sought where this coupling does not seriously degrade the performance. The requirements on the feedback system are discussed for different cases and low gain solutions are identified.

Active control of resistive wall modes in the large-aspect-ratio tokamak

The large-aspect-ratio model for current-driven external kinks is applied to study control of non-axisymmetric resistive wall modes in tokamaks. Comparison with toroidal computations indicates that the cylindrical instabilities react in similar ways to feedback as the pressure-driven toroidal modes, when the feedback and sensor coils are placed on the low-field side of the torus. However, higher gain is required in the cylindrical case. The cylindrical model is used to gain insights into design issues concerning a feedback system for ITER, with a double wall and superconducting coils. Good control performance and acceptable coil voltages are found in an initial value problem, where the initial conditions correspond to expected noise levels, when sensors for the poloidal field are placed inside the first wall. This can be accomplished with a PI (proportional plus integral) controller from the voltages of the sensor loops to the voltage over the active coils. The two-wall structure of ITER makes control somewhat more demanding than for tokamaks with a single wall. Adequate control can be achieved also when poloidal sensors are placed outside a single wall, but this requires additional derivative action (PID) and the resulting voltages are significantly higher.

Physics and control of resistive wall modes

Active feedback stabilization of resistive wall modes in tokamaks is studied both analytically, using large aspect ratio theory, and by means of toroidal computations. Extensive studies show that robust stabilization, with respect to variations in plasma current, pressure and flow velocity, can be achieved with a simple control system using poloidal sensors inside the first wall. The required coil voltages are modest, even for the two-wall structure of a tokamak reactor.

Influence of rotation profiles on stabilization of resistive wall modes

The influence of non-uniform toroidal plasma rotation on the stability of resistive wall modes is analysed for high-β advanced tokamak equilibria, using toroidal ideal MHD. For advanced tokamak equilibria with qmin in the range of 1.6-2.1, a main role is played by the rotation at the resonance where q2. A rotation frequency of at least 3% of the central Alfven frequency is required around at the q2 resonance in order to raise the ideal β limit significantly above the no-wall value. Certain types of rotation profiles do not lead to stabilization at any rotation velocity. Comparison with experimental results from DIII-D indicates that ideal MHD thresholds are in reasonable agreement with experiment.

Optimization of resistive wall mode control in reversed field pinches

Feedback stabilization of magnetohydrodynamic modes in reversed field pinches is analysed for a set of discrete coils driven by voltage control. It is found that the resistive wall mode can be stabilized with a very simple controller structure and with acceptable voltages in the coils. These results are obtained by using a sufficient number of active coils and either sensors for the radial field or sensors for the poloidal or toroidal field placed inside the resistive wall. The result is robust with respect to variations in the plasma equilibrium. Poloidal and toroidal sensors placed outside the wall require a more complicated controller and very high voltages, and do not allow as good control performance as internal sensors.

Physics and stabilization of resistive wall modes in tokamaks

The theory of resistive wall modes (RWMs) is discussed and compared with experimental results. Special attention is given to the possibilities of stabilizing the RWM by plasma rotation and active feedback. A simple cylindrical model is used to illustrate various aspects of active control. Fully toroidal computations are also presented, including predictions for RWM stabilization in ITER. According to ideal MHD, robust control of RWM should be straightforward. Theory for stabilization by rotation is discussed, and a semikinetic model is introduced, which compares favourably with experiment. The semikinetic model produces somewhat lower rotation thresholds than previous models.

Feedback control of resistive wall modes in toroidal devices

Feedback control of nonaxisymmetric resistive wall modes is studied analytically for cylindrical plasmas and computationally for high beta tokamaks. Internal poloidal sensors give superior performance to radial sensors, for instance in terms of the highest achievable plasma pressure. A single poloidal array of feedback coils allows robust control with respect to variations in plasma pressure, current and rotation velocity. The control analysis is applied to advanced scenarios for ITER. Configurations with multiple poloidal coils and feedback systems for nonresonant MHD instabilities in reversed field pinches are also studied. The control study was carried out using the assumption of ideal amplifiers.