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>

La description magnétohydrodynamique est utilisée pour étudier les plasmas de fusion par confinement magnétique dans deux configurations: tokamak et reversed field pinch. Une méthode de Fourier pseudo-spectrale et une technique de pénalisation en volume sont employées pour résoudre les équations. La méthode de pénalisation permet d’introduire des conditions aux limites de Dirichlet et donc de faire varier facilement la géométrie considérée. Les simulations dans des géométries toroïdales de type tokamak montrent l’apparition spontanée de vitesses. Une importante composante toroïdale se développe si le système est peu dissipatif. Il est aussi montré que la brisure de symétrie dans la forme de la section du tore fait apparaitre un moment angulaire toroïdal. Pour le Reversed Field Pinch on montre l’émergence de structures hélicoïdales. La forme de ces structures varie en fonction des coefficients de transport ainsi que du paramètre de pincement du champ magnétique imposé. Pour compléter l’étude on compare les résultats du tore aux calculs dans un cylindre périodique. Les différences dans la dynamique des deux cas sont mises en avant. Finalement les simulations sont confrontées à des expériences et un meilleur accord est observé entre simulation et expérience pour la géométrie toroïdale que pour la géométrie cylindrique. / A magnetohydrodynamic description is used to study magnetic fusion plasmas in two different configurations: tokamak and reversed field pinch. A Fourier pseudo-spectral method with a volume penalization technique are used to solve the system of equations. The penalization method is used to introduce Dirichlet boundary conditions and it al- lows to easily modify the consider geometry. The simulations of a tokamak configuration in a toroidal geometry show the spontaneous appearance of velocities. These velocities are dominated by their toroidal component if the system is little dissipative. It is also shown that the symmetry breaking of the cross section of the torus causes a toroidal angular momentum to develop. For the Reversed Field Pinch configuration we show the appearance of helical structures. The shape of these structures varies with the value of the transport coefficients and with the pinch ratio parameter of the imposed magnetic field. To complete the study, we compare the results of simulations obtained in toroidal and in periodic cylindrical geometries. The differences in the dynamics of these two cases are highlighted. Finally, simulations are compared to experimental data and a significant better agreement is observed between the simulation and the experiment for the toroidal geometry than for the cylindrical case.

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

Over the past decade, fusion research has showed the potential of being a main candidate for energy production for future generations. Further advances in improved fusion performance are therefore vital. This thesis focuses on advanced fusion plasma scenarios and their diagnostic requirements. In particular the design of a motional Stark effect (MSE) diagnostic at the MAST spherical tokamak and the analysis of magneto-hydrodynamic mode feedback control and pulsed poloidal current drive (PPCD) at the reversed field pinch (RFP) experiment EXTRAP T2R are discussed. The MSE diagnostic is important for the determination of the plasma current profile, information that is necessary for studies in advanced confinement scenarios like reversed shear profiles or current holes. The MAST MSE system has two channels and selects the spectral components using 1Å FWHM interference filters. The diagnostic has been commissioned during the fall of 2006 and the results show the feasibility of the technique with rms-noise ~0.5° using a time resolution of 1 ms. Investigations of mirror labyrinths for the future ITER MSE diagnostic highlight the need for careful calibration considerations. Feedback control and PPCD are techniques for improved confinement. Feedback control dramatically decreases impurity influx at the end of discharges while transport in the bulk plasma is largely unaffected. During PPCD the transport is seen to decrease and it is demonstrated that PPCD and feedback control can be employed simultaneously. New and innovative techniques for fusion spectroscopy are furthermore described. This includes the use of correlations in line integrated signals to determine ion emission profiles in poloidally symmetric environments. Good agreement with other diagnostic methods is obtained. The assessment of electron temperature profiles using measured differences between Thomson scattering and vacuum ultra-violet spectroscopy is also shown. / QC 20100907

<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>

La description magnétohydrodynamique est utilisée pour étudier les plasmas de fusion par confinement magnétique dans deux configurations: tokamak et reversed field pinch. Une méthode de Fourier pseudo-spectrale et une technique de pénalisation en volume sont employées pour résoudre les équations. La méthode de pénalisation permet d'introduire des conditions aux limites de Dirichlet et donc de faire varier facilement la géométrie considérée. Les simulations dans des géométries toroïdales de type tokamak montrent l'apparition spontanée de vitesses. Une importante composante toroïdale se développe si le système est peu dissipatif. Il est aussi montré que la brisure de symétrie dans la forme de la section du tore fait apparaitre un moment angulaire toroïdal. Pour le Reversed Field Pinch on montre l'émergence de structures hélicoïdales. La forme de ces structures varie en fonction des coefficients de transport ainsi que du paramètre de pincement du champ magnétique imposé. Pour compléter l'étude on compare les résultats du tore aux calculs dans un cylindre périodique. Les différences dans la dynamique des deux cas sont mises en avant. Finalement les simulations sont confrontées à des expériences et un meilleur accord est observé entre simulation et expérience pour la géométrie toroïdale que pour la géométrie cylindrique.

The tearing mode (TM) is a resistive instability that can arise in magnetically confined plasmas. The TM can be driven unstable by the gradient of the plasma current. When the mode grows it destroys the magnetic field symmetry and reconnects the magnetic field in the form of a so-called magnetic island. The TMs are inherent to a type of device called the reversed-field pinch (RFP), which is a device for toroidal magnetic confinement of fusion plasmas. In the RFP, TMs arise at several resonant surfaces, i.e. where the field lines and the perturbation have the same pitch angle. These surfaces are closely spaced in the RFP and the neighboring TM islands can overlap. Due to the island overlap, the magnetic field lines become tangled resulting in a stochastic magnetic field, i.e. the field lines fill a volume instead of lying on toroidal surfaces. Consequently, a stochastic field results in an anomalously fast transport in the radial direction. Stochastic fields can also arise in other plasmas, for example, the tokamak edge when a resonant magnetic perturbation (RMP) is applied by external coils. This stochastization is intentional to mitigate the edge-localized modes. The RMPs are also used for control of other instabilities. Due to the finite number of RMP coils, however, the RMP fields can contain sidebands that decelerate and lock the TMs via electromagnetic torques. The locking causes an increased plasma-wall interaction. And in the tokamak, the TM locking can cause a plasma disruption which is disastrous for future high-energy devices like the ITER. In this thesis, the TM locking was studied in two RFPs (EXTRAP T2R and Madison Symmetric Torus) by applying RMPs. The experiments were compared with modern mode-locking theory. To determine the viscosity in different magnetic configurations where the field is stochastic, we perturbed the momentum via an RMP and an insertable biased electrode. In the TM locking experiments, we found qualitative agreement with the mode-locking theory. In the model, the kinematic viscosity was chosen to match the experimental locking instant. The model then predicts the braking curve, the short timescale dynamics, and the mode unlocking. To unlock a mode, the RMP amplitude had to decrease by a factor ten from the locking amplitude. These results show that mode-locking theory, including the relevant electromagnetic torques and the viscous plasma response, can explain the experimental features. The model required viscosity agreed with another independent estimation of the viscosity. This showed that the RMP technique can be utilized for estimations of the viscosity. In the momentum perturbation experiments, it was found that the viscosity increased 100-fold when the magnetic fluctuation amplitude increased 10-fold. Thus, the experimental viscosity exhibits the same scaling as predicted by transport in a stochastic magnetic field. The magnitude of the viscosity agreed with a model that assumes that transport occurs at the sound speed -- the first detailed test of this model. The result can, for example, lead to a clearer comparison between experiment and visco-resistive magnetohydrodynamics (MHD) modeling of plasmas with a stochastic magnetic field. These comparisons had been complicated due to the large uncertainty in the experimental viscosity. Now, the viscosity can be better constrained, improving the predictive capability of fusion science. / <p>QC 20171122</p>

Magnetically confined fusion (MCF) plasmas are typically subject to several unstable modes. The growth of one mode can limit the plasma energy confinement and might cause a termination of the plasma. Externally applied resonant magnetic perturbations (RMPs) are used to control and to mitigate some of the unstable modes. Examples are, mitigation of edge localized modes and steering of neoclassical tearing mode position for stabilization by electron cyclotron current drive. Consequently, use of RMPs are considered necessary in planned future fusion machines. There are however negative consequences, the RMP interaction with a tearing mode (TM) of the same resonance can cause deceleration of the TM and possibly wall-locking. If a TM is non-rotating relative the machine-wall, it can grow and degrade fusion plasma performance and lead to a plasma disruption. Thus, all fusion confinement machines want to avoid wall-locked modes. Resonant magnetic fields can also be present in the form of machine-error-fields, which can produce the same effects. Clearly, it is of importance to understand the TM-RMP interaction. Typically, the modes with long wavelength are described by magnetohydrodynamic (MHD) theory. Considering the finite plasma resistivity, MHD predicts a mode that tears and reconnects magnetic field lines, called a tearing mode (TM). TMs occur at surfaces where the magnetic field lines close on themselves after a number of (m) toroidal and (n)poloidal turns. These surfaces are resonant in the sense that magnetic field and helical current perturbation has the same helicity, which minimize stabilizing effect of magnetic field line bending. In this thesis, the mechanisms of TM locking and unlocking due to external resonant magnetic perturbations (RMPs) are experimentally studied. The studies are conducted in two MCF machines of the type reversed-field pinch (RFP): EXTRAP T2R and Madison Symmetric Torus (MST). The studied machines exhibit multiple rotating TMs under normal operation. In EXTRAP T2R TM locking and unlocking are studied by application of a single harmonic RMP. Observations show that after the TM is locked, RMP amplitude has to be reduced significantly in order to unlock the TM. In similar studies in MST unlocking is not observed at all after turn-off of the RMP. Hence, in both machines, there is hysteresis in the locking and subsequent unlocking of a tearing mode. Results show qualitative agreement with a theoretical model of the TM evolution when subjected to an RMP. It is shown that the RMP cause a reduction of TM and plasma rotation at the resonant surface. The velocity reduction is opposed by a viscous torque from surrounding plasma. After TM locking, relaxation of the whole plasma rotation is observed, due to the transfer of velocity reduction via viscosity. This results in a reduced viscous resorting torque, which explains the observed hysteresis. The hysteresis is further deepened by the increase in amplitude of a locked mode. / <p>QC 20160111</p>