Active control of resistive wall modes and error field compensation in reversed field pinch devices

QC 20251031

Abstract

The advanced tokamak scenario relevant for steady state operation require a conductive shell to stabilize the ideal Magneto Hydro Dynamic (MHD) modes with fast growth rate on the Alfvén time scale. However, for pulse lengths τp longer than the shell time τw , the finite conductivity of the shell introduces the Resistive Wall Mode (RWM) instability. In the absence of plasma rotation, RWMs can be controlled using magnetic feedback and model-based control algorithms have potential advantages for RWM feedback control. In this work, a white-box physics model has been used to characterize the RWM plasma response. The RWM plasma response has been experimentally validated by the excitation of nonaxisymmetric perturbation magnetic fields utilizing an array of control coils on the Reversed Field Pinch (RFP) device EXTRAP T2R. EXTRAP T2R is equipped with an extended sensor array, enabling a wide spectrum of RWMs to be resolved and experimentally validated. A model-based optimal control method for multi-mode RWM feedback stabilization has been designed, implemented and tested in plasma experiments at EXTRAP T2R. EXTRAP T2R utilizes a feedback controller that is designed to address challenges that arise in connection with RWM magnetic feedback stabilization systems that rely on discrete control coil and sensor arrays in tokamak and RFP devices. In these devices, the systems for multi-mode control capabilities is limited due to coupling of modes induced by the control system. The coupling arises from the generation of side-band control field harmonics and from the aliasing of multiple harmonics in the sensor measurements, resulting in a Multi Input, Multiple Output (MIMO) control problem. To adress this, the MIMO control problem can be Fourier-decoupled into a set of Single Input, Multiple Output (SIMO) systems using the Discrete Fourier Transform (DFT). This decoupling enables the design of a controller with enhanced multi-mode control capabilities compared to previous controller designs. The controller design allows for prioritizing suppression of one of the multiple magnetic field Fourier harmonics produced by a given control current DFT component. Plasma experiments at the EX-TRAP T2R device, utilizing the extended sensor array and the enhanced capabilities for multiple RWM feedback stabilization have demonstrated the effectiveness of the controller in achieving multiple RWM feedback stabilization. The RWM feedback stabilization has been implemented using a linear physics model-based Linear Quadratic (LQ) optimal control algorithm that has been extended to include Error Field (EF) correction. The EF correction is based on a scheme known in control engineering as disturbance estimation and rejection. The new RWM control algorithm is implemented and tested in EXTRAP T2R plasma experiments that performs real-time EF estimation and feedforward EF compensation in parallel with feedback stabilization. The EF correction leads to improved performance of the RFP plasma, indicated by lower plasma resistance and sustained, less perturbed intrinsic tearing mode rotation, visible as a reduction of the temporal fluctuations in the mode rotation frequency. The estimated spatial and temporal structure of the EF provides useful information for identification of the EF sources in the EX-TRAP T2R device.

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