Feedback control of dynamo tearing modes in a reversed field pinch: comparison between out-vessel and in-vessel active coils

Abstract

In the framework of innovative feedback schemes for control of dynamo tearing modes (TMs) in reversed field pinch (RFP) devices, the possibility of placing active coils between a non-conducting first wall and the vacuum vessel is investigated with a MHD based model. In this formulation the vacuum vessel plays the role of a stabilizing shell. With active coils placed outside the vacuum vessel and magnetic sensors located inside it, a previous study (Zanca 2009 Plasma Phys. Control. Fusion 51 015006) has shown that the ratio between the TM radial field amplitudes at the sensors' radius and at the resonant surface can be made close to but not smaller than the ideal-shell limit. This analysis considered a continuous-time modelling of the feedback. The same model admits a very appealing solution when applied to the in-vessel coil configuration: for high gains the radial field measured by sensors located between the first wall and the coils is reduced virtually to zero and the TM rotation frequency approaches the unperturbed natural value. In this case the feedback would mimic the stabilizing action of an ideal shell placed at the sensor radius. An improvement which makes the model closer to a realistic digital feedback is also presented. This is realized by introducing a discrete-time feedback action which includes a non-zero latency time. Unfortunately, the nice solution for in-vessel coils becomes unstable for realistic TM amplitudes when passing to the discrete-time feedback. In contrast the feedback of out-vessel coils is robust to time discretization, except when the vacuum vessel time constant becomes very small. This analysis indicates that future RFPs should rely on feedback systems of out-vessel coils.