<p>A wide range of unstable current driven MHD modes is present in the re- versed τeld pinch (RFP) conτguration. An ideally conducting wall facing the plasma can stabilize the ideal MHD modes. In the presence of a resistive wall characterized by the wall time τw, fast mode rotation with the frequency exceeding the inverse wall time gives stabilization for resistive MHD modes. The ideal MHD modes in the RFP are non-rotating modes and can not be stabilized by the resistive wall. Instead they are converted into resistive wall modes (RWM) growing with a growth rate proportional to the inverse of the wall time τw. EXTRAP T2R is an RFP device equipped with a thin resistive wall having the wall time shorter than the plasma pulse duration τw < τp. This feature allows the study of non-resonant non-rotating resistive wall modes. Resistive wall modes dynamics has been studied in EXTRAP T2R . RWM growth rates has been measured and compared with linear MHD stability calculations. Quantitative agreement is observed. In the case τw < τp the RWM can cause discharge degradation and should be stabilized. Active feedback is the way to stabilize the RWM in the RFP. An intelligent shell scheme is one possible feedback scenario. An active feed- back system including a set of sensors and discrete active coils is installed in EXTRAP T2R. The intelligent shell tries to keep the magnetic flux zero at the positions of the sensor. The analog PID controller for the intelligent shell feedback scheme has been studied. A model of the active control system was developed and comparison with the experimental results showed good agree- ment. Encouraging experimental results on the active feedback stabilization of multiple RWMs in the RFP plasmas were obtained.</p>

A wide range of unstable current driven MHD modes is present in the re- versed τeld pinch (RFP) conτguration. An ideally conducting wall facing the plasma can stabilize the ideal MHD modes. In the presence of a resistive wall characterized by the wall time τw, fast mode rotation with the frequency exceeding the inverse wall time gives stabilization for resistive MHD modes. The ideal MHD modes in the RFP are non-rotating modes and can not be stabilized by the resistive wall. Instead they are converted into resistive wall modes (RWM) growing with a growth rate proportional to the inverse of the wall time τw. EXTRAP T2R is an RFP device equipped with a thin resistive wall having the wall time shorter than the plasma pulse duration τw &lt; τp. This feature allows the study of non-resonant non-rotating resistive wall modes. Resistive wall modes dynamics has been studied in EXTRAP T2R . RWM growth rates has been measured and compared with linear MHD stability calculations. Quantitative agreement is observed. In the case τw &lt; τp the RWM can cause discharge degradation and should be stabilized. Active feedback is the way to stabilize the RWM in the RFP. An intelligent shell scheme is one possible feedback scenario. An active feed- back system including a set of sensors and discrete active coils is installed in EXTRAP T2R. The intelligent shell tries to keep the magnetic flux zero at the positions of the sensor. The analog PID controller for the intelligent shell feedback scheme has been studied. A model of the active control system was developed and comparison with the experimental results showed good agree- ment. Encouraging experimental results on the active feedback stabilization of multiple RWMs in the RFP plasmas were obtained.

The reversed-field pinch (RFP) is a device for magnetic confinement of fusion plasmas. The main objective of fusion plasma research is to realise cost-effective thermonuclear fusion power plants. The RFP is highly unstable as can be explained by the theory of magnetohydrodynamics (MHD). Feed-back control technology appears to enable a robustly stable RFP operation.  Experimental control and identification of nonaxisymmetric multimode MHD is pursued in this thesis. It is shown that nonparametric multivariate identification methods can be utilised to estimate MHD spectral characteristics from plant-friendly closed-loop operational input-output data. It is also shown that accurate tracking of the radial magnetic field boundary condition is experimentally possible in the RFP. These results appear generically useful as tools in both control and physics research in magnetic confinement fusion. / <p>QC 20120508</p>

Control of MHD instabilities using a conducting wall together with external magnetic fields is an important route to improved performance and reliability in fusion devices. Active control of MHD modes is of interest for both the Advanced Tokamak and the Reversed Field Pinch (RFP) configurations. A wide range of unstable, current driven MHD modes is present in the RFP. An ideally conducting wall facing the plasma can in principle provide stabilization to these modes. However, a real, resistive wall characterized by a wall field diffusion time, cannot stabilize the ideal MHD modes unless they rotate with Alfvénic velocity, which is usually not the case. With a resistive wall, the ideal modes are converted into resistive wall modes (RWM) with growth rates comparable to the inverse wall time. Resistive wall modes have been studied in the EXTRAP T2R thin shell RFP device. Growth rates have been measured and found in agreement with linear MHD stability calculations. An advanced system for active control has been developed and installed on the EXTRAP T2R device. The system includes an array of 128 active saddle coils, fully covering the torus surface. Experiments on EXTRAP T2R have for the first time demonstrated simultaneous active suppression of multiple independent RWMs. In experiments with a partial array, coupling of different modes due to the limited number of feedback coils has been observed, in agreement with theory. Different feedback strategies, such as the intelligent shell, the rotating shell, and mode control have been studied. Further, feedback operation with different types of magnetic field sensors, measuring either the radial or the toroidal field components have been compared / QC 20100929

It is relatively straightforward to establish equilibrium inmagnetically confined plasmas, but the plasma is frequentlysucceptible to a variety of instabilities that are driven bythe free energy in the magnetic field or in the pressuregradient. These unstable modes exhibit effects that affect theparticle, momentum and heat confinement properties of theconfiguration. Studies of the dynamics of several of the mostimportant modes are the subject of this thesis. The studies arecarried out on plasmas in the reversed field pinch (RFP)configuration. One phenomenon commonly observed in RFPs is mode walllocking. The localized nature of these phase- and wall lockedstructures results in localized power loads on the wall whichare detrimental for confinement. A detailed study of the walllocked mode phenomenon is performed based on magneticmeasurements from three RFP devices. The two possiblemechanisms for wall locking are investigated. Locking as aresult of tearing modes interacting with a static field errorand locking due to the presence of a non-ideal boundary. Thecharacteristics of the wall locked mode are qualitativelysimilar in a device with a conducting shell system (TPE-RX)compared to a device with a resistive shell (Extrap T2). Atheoretical model is used for evaluating the threshold valuesfor wall locking due to eddy currents in the vacuum vessel inthese devices. A good correlation with experiment is observedfor the conducting shell device. The possibility of succesfully sustaining discharges in aresistive shell RFP is introduced in the recently rebuiltdevice Extrap T2R. Fast spontaneous mode rotation is observed,resulting in low magnetic fluctuations, low loop voltage andimproved confinement. Wall locking is rarely observed. The lowtearingmode amplitudes allow for the theoretically predictedinternal nonresonant on-axis resistive wall modes to beobserved. These modes have not previously been distinguisheddue to the formation of wall locked modes. The internal andexternal nonresonant resistive wall modes grow on the timescale of the shell penetration time. These growth rates dependon the RFP equilibrium. The internal nonresonant resistive wallmodes dominate in Extrap T2R, especially for shallow reverseddischarges. The external nonresonant modes grow solely in deepreversal discharges. <b>Keywords</b>Nuclear fusion, reversed field pinch, resistiveinstabilities, wall locked modes, tearing modes, resistiveshell modes, field errors, EXTRAP-T2, EXTRAP-T2R, TPE-RX

<p>It is relatively straightforward to establish equilibrium inmagnetically confined plasmas, but the plasma is frequentlysucceptible to a variety of instabilities that are driven bythe free energy in the magnetic field or in the pressuregradient. These unstable modes exhibit effects that affect theparticle, momentum and heat confinement properties of theconfiguration. Studies of the dynamics of several of the mostimportant modes are the subject of this thesis. The studies arecarried out on plasmas in the reversed field pinch (RFP)configuration.</p><p>One phenomenon commonly observed in RFPs is mode walllocking. The localized nature of these phase- and wall lockedstructures results in localized power loads on the wall whichare detrimental for confinement. A detailed study of the walllocked mode phenomenon is performed based on magneticmeasurements from three RFP devices. The two possiblemechanisms for wall locking are investigated. Locking as aresult of tearing modes interacting with a static field errorand locking due to the presence of a non-ideal boundary. Thecharacteristics of the wall locked mode are qualitativelysimilar in a device with a conducting shell system (TPE-RX)compared to a device with a resistive shell (Extrap T2). Atheoretical model is used for evaluating the threshold valuesfor wall locking due to eddy currents in the vacuum vessel inthese devices. A good correlation with experiment is observedfor the conducting shell device.</p><p>The possibility of succesfully sustaining discharges in aresistive shell RFP is introduced in the recently rebuiltdevice Extrap T2R. Fast spontaneous mode rotation is observed,resulting in low magnetic fluctuations, low loop voltage andimproved confinement. Wall locking is rarely observed. The lowtearingmode amplitudes allow for the theoretically predictedinternal nonresonant on-axis resistive wall modes to beobserved. These modes have not previously been distinguisheddue to the formation of wall locked modes. The internal andexternal nonresonant resistive wall modes grow on the timescale of the shell penetration time. These growth rates dependon the RFP equilibrium. The internal nonresonant resistive wallmodes dominate in Extrap T2R, especially for shallow reverseddischarges. The external nonresonant modes grow solely in deepreversal discharges.</p><p><b>Keywords</b>Nuclear fusion, reversed field pinch, resistiveinstabilities, wall locked modes, tearing modes, resistiveshell modes, field errors, EXTRAP-T2, EXTRAP-T2R, TPE-RX</p>