| 1. |
- Fridström, Richard, 1985-
(author)
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Resonant magnetic perturbation effect on the tearing mode dynamics : Novel measurements and modeling of magnetic fluctuation induced momentum transport in the reversed-field pinch
- 2017
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Doctoral thesis (other academic/artistic)abstract
- 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.
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| 2. |
- Fridström, Richard, 1985-
(author)
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Tearing mode dynamics in the presence of resonant magnetic perturbations
- 2016
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Licentiate thesis (other academic/artistic)abstract
- 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.
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| 3. |
- Olofsson, K Erik J, 1982-
(author)
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Nonaxisymmetric experimental modal analysis and control of resistive wall MHD in RFPs : System identification and feedback control for the reversed-field pinch
- 2012
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Doctoral thesis (other academic/artistic)abstract
- 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.
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| 4. |
- Schmuck, Stefan, 1980-
(author)
-
Bayesian Inference for Microwave Diagnostics at Joint European Torus
- 2022
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Doctoral thesis (other academic/artistic)abstract
- The major goal of this thesis is to perform Bayesian inference jointly for electron kinetic profiles, a toroidal magnetic field correction, diagnostic sensitivities, and wall reflection properties given noisy measurements of four microwave diagnostics at the tokamak JET. Besides the measurements, this kind of inference considers prior knowledge, like profile length-scales, to update objectively the information about the physics parameters. Such a probabilistic update, i.e. a posterior probability distribution or posterior, states the plausibility of parameter combinations and captures parameter uncertainties and correlations. The already existing Bayesian framework Minerva was used to carry out the inference.Contrary to standard approaches, plasma physics and diagnostic models and physics parameters are used to make predictions which are compared objectively with the data provided by one reflectometer and three electron cyclotron emission (ECE) diagnostics; two broadband Martin-Puplett interferometers and one heterodyne radiometer. In addition, these models represent reality more closely, for instance: (i) the smoothnesses of temperature and density profiles are modelled and estimated by length-scale parameters, (ii) the models SPECE and ECEPT, predicting each broadband ECE spectra, take into account relativistic and density effects like the finite optical thickness, (iii) the working principle and measurement uncertainty of each diagnostic are considered. As an example for the latter point, the two interferometers supply convoluted ECE spectra over several harmonic ranges up to 500 GHz and in mainly ordinary and extra-ordinary wave mode polarisations. The uncertainties on these spectra originate mostly from absolute calibrations for which a dedicated, robust and reliable procedure had to be established during this thesis.Further intermediate achievements of this thesis are for example: (i) the analytical derivation of the generalised square-exponential covariance function, enabling the estimation of multiple length-scales for electron temperature and density profiles in the plasma core and edge domains, (ii) the already existing ray-tracer SPECE, which predicts accurately but slowly ECE spectra, was parallelised successfully by a client-server approach, (iii) the derivation of the model ECEPT to predict quickly and sufficiently accurately broadband ECE spectra for an Ohmically heated plasma, and (iv) the extension of the multi-reflection model to allow different properties for the high-field and low-field side walls of a fusion device, affecting substantially the predictions of ECE spectra at frequencies for which the plasma has a low optical thickness.For a low temperature and low density plasma, the joint inference of more than 200 parameters was carried out for a given flux surface geometry, using either SPECE or ECEPT as predictor for the measured ECE spectra from 50 GHz to 280 GHz (first three harmonic ranges at least) with contributions from the ordinary and extra-ordinary wave-modes. For the ECEPT case, the shape of the joint posterior could be explored numerically. Related findings are, for example, smooth electron temperature and density profiles with values at the centre of 1.5 keV and 1.75x1e19 m^-3 and at the separatrix of 80 eV and 2x1e18 m^-3 with uncertainties of the order of 10 eV and few 1e17 m^-3. Furthermore, the smoothness of each core and edge profile originates in the inferred length-scale. These results were confirmed by the most likely parameter combination of the posterior when the more accurate predictor SPECE is used. The only exceptions are the correction to the magnetic field, which increased from 1.4% to 2%, and the reflectivity of the ITER-like wall, which elevated from 0.72 to 0.92.With ECEPT in use, multiple posterior correlation features could be revealed of which many could be explained. For instance, each profile smoothness, due to the estimated length-scale, implies considerable correlationsbetween nearby locations. In addition, a global correlation feature is evidentfor edge and core density profiles, likely caused by the measurement principle of the reflectometer.The second part of this thesis focusses on Bayesian inference about spectra in the field of Fourier transform spectroscopy. An example application has been carried out for the calibration data measured with one of the Martin-Puplett interferometers at JET. Compared to standard analysis techniques, more information could be extracted about the spectra from the so-called double-, single- and zero-sided data domains. The spectra have been modelled as Brownian bridge processes a priori, by which the global trend of the data located in double- and single-sided domains is modelled. This enables the estimation of the posterior uncertainties of the spectra due to non-probed data domains, especially the zero-sided domain. Such consideration is not made in any form by conventional techniques, because no method has been developed to estimate the seemingly lost information contained in the zero-sided domain. The lower and upper limits of the spectra have been estimated by (33+/-1.7) GHz and (913+/-2.9) GHz. These limits are rated to be more likely by a factor of 1e277 than the limits at 0 GHz and 3747 GHz (Nyquist frequency) assumed by conventional analysis approaches but never checked for plausibility.
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| 5. |
- Setiadi, Agung Chris, 1986-
(author)
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Model predictive control of resistive wall modes in the reversed-field pinch
- 2015
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Licentiate thesis (other academic/artistic)abstract
- The reversed-field pinch (RFP) is a magnetic confinement fusion (MCF) device. It exhibits a variety of unstable modes that can be explained by magnetohydrodynamic (MHD) theory. A particular unstable mode that is treated in this work is the resistive wall mode (RWM), which occurs when the shell of the device has finite conductivity. Application of control engineering tools appears to be important for the operation of the RFP. A model-based control approach is pursued to stabilize the RWM. The approach consists of experimental modeling of RWM using a class of system identification techniques. The obtained model is then used as a basis for Mode Predictive Control (MPC) design. The MPC employs the model to build predictions of the system and find a control input that optimizes the predicted behavior of the system. It is shown that the formulation of the MPC allows the user to incorporate several physics relevant phenomena aside from RWMs. The results are encouraging for MPC to be a useful tool for future MCF operation.
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| 6. |
- Stefanikova, Estera, 1987-
(author)
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Pedestal structure and stability in JET-ILW and comparison with JET-C
- 2020
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Doctoral thesis (other academic/artistic)abstract
- Controlled thermonuclear fusion offers a promising concept for safe and sustainable production of electrical energy. However, there are still many issues to be investigated on the way to a commercial fusion reactor. An important point for detailed studies is connected to wall materials surrounding hot thermonuclear plasma. The JET tokamak (the largest fusion experiment in the world) in the United Kingdom has completed a major upgrade in 2011 in which the materials of the vessel surrounding the fusion fuel have been changed from a carbon-fibre-composite (or JET-C wall) to Beryllium and Tungsten. These new materials are the same as those that will be used in a next step fusion device International Thermonuclear Experimental Reactor ITER (hence the name ITER-like wall or JET-ILW), designed to demonstrate the feasibility of fusion reactor based on the tokamak concept. One of the goals of JET with the ILW is to act as a test bed for ITER technologies and for ITER operating scenarios.The overall purpose of the thesis work is to characterise the effect of the ILW on the structure and stability of edge plasma phenomenon called the pedestal, a steep pressure gradient associated with the H-mode, an operational regime with improved confinement. The aim is to contribute to the understanding of the difference in the pedestal performance between JET-C and JET-ILW.The work is focused on experimental characterisation of the pedestal structure in deuterium discharges by analysing the experimental data (radial profiles of electron temperature and density measured in H-mode plasmas) from Thomson scattering diagnostics at JET and on investigating the differences in pedestal stability between JET-ILW and JET-C plasmas in terms of the pedestal modelling. The pedestal structure is determined using a modified hyperbolic tangent fit to the experimental Thomson scattering profiles. The modelling is performed with the pedestal predictive code Europed, based on the EPED model commonly used to predict the pedestal height in JET.The experimental analysis has shown several differences in the pedestal structure of comparable JET-ILW and JET-C discharges. One of the key differences introduced in this work is the pedestal relative shift (a separation between the middle of the pedestals of the electron density and temperature) that plays a major role in the difference in the pedestal performance between JET-C and JET-ILW. The work shows that the relative shift can vary significantly from pulse to pulse and that, on average, JET-C plasmas have lower relative shift than JET-ILW plasmas. The pedestal relative shift tends to increase with increase in the gas fuelling and the heating power. Furthermore, the increase in the relative shift has been empirically correlated with the degradation of the experimental normalized pressure gradient αexp.To understand the differences in the JET-C and JET-ILW pedestal stability, parameters that affect the pedestal stability and that tend to vary between comparable JET-C and JET-ILW discharges have been identified. These parameters are the pedestal relative shift, pedestal density neped, effective charge number Zeff, pedestal pressure width wpe, and normalized pressure βN. The modelling performed with the predictive Europed code has shown that these five parameters are sufficient to explain the difference in the pedestal performance between JET-C and JET-ILW.Furthermore, the modelling has shown that the relative shift and neped play a major role in affecting the critical normalized pressure gradient αcrit (normalized pressure gradient expected by the model comparable to αexp), while the relative shift, wpe and Zeff have a major impact on the pedestal pressure height. Finally, a possible mechanism that has led to the degradation of the pedestal pressure from JET-C to JET-ILW is proposed.
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| 7. |
- Olofsson, Erik, 1982-
(author)
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Closed-loop control and identification of resistive shell magnetohydrodynamics for the reversed-field pinch
- 2010
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Licentiate thesis (other academic/artistic)abstract
- It is demonstrated that control software updates for the magnetic confinement fusion experiment EXTRAP T2R can enable novel studies of plasma physics. Specifically, it is shown that the boundary radial magnetic field in T2R can be maintained at finite levels by feedback. System identification methods to measure in situ magnetohydrodynamic stability are developed and applied with encouraging results. Subsequently, results from closed-loop identification are used for retooling the T2R regulator. The track of research here pursued could possibly be relevant for future thermonuclear fusion reactors.
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