Closed-loop direct parametric identification of magnetohydrodynamic normal modes spectra in EXTRAP-T2R reversed-field pinch

The reversed-field pinch (RFP) EXTRAP-T2R (T2R) is a plasma physics experiment with particular relevance for magnetic confinement fusion (MCF) research. T2R is very well equipped for investigations of magnetohydrodynamic (MHD) instabilities known as resistive-wall modes (RWMs), growing on a time-scale set by a surrounding non-perfectly conducting shell. The RWM instability is also subject of intense research in tokamak experiments (another MCF configuration). Recently, multiple RWMs have been stabilized in T2R using arrays of active (current-carrying) and sensor (voltage-measuring) coils equidistributed on the shell. In this paper, the MHD normal modes dynamics is probed in the required feedback operation by simultaneously, and pseudo-randomly, exciting the spectrum in the spatial sense. Spectra are then extracted by prediction-error minimization based on an observer that tracks dynamically aliased modes and the results thus obtained are related, and compared, to established linear MHD stability theory. This pioneer study at T2R is, arguably, appealling both to plasma physicists and automatic control staff.