Refine
Year of publication
Document Type
- Doctoral Thesis (13)
Language
- English (13)
Has Fulltext
- yes (13)
Is part of the Bibliography
- no (13)
Keywords
- Stellarator (13) (remove)
Institute
- Institut für Physik (13)
In course of the recent results from Wendelstein 7-X, stellarators are on the brink for assessing their maturity as a fusion reactor. To this end, stellarator specific transport regimes need detailed exploration both with appropriate systematic experimental investigations and models. A way to enhance the efficiency of this process is seen in an systematic evaluation of existing experimental data. We propose appropriate tools developed in information theory for examining large datasets. Information entropy calculations, that have proven to assist the systematic assessment of datasets in many other scientific fields, are used for novelty detection.
Potentially, as a first use-case of this holistic process, this thesis attempts to link and to develop approaches to examine the stellarator specific core-electron-root-confinement (CERC) regime. The specific interest for CERC emerges from the behavior of the radial electric field. While ion-root conditions exhibit negative radial electric fields, CERC’s positive field in the very core of fusion grade plasmas adds an outward thermodynamic force to high-Z impurities and could add to potential actuators to control impurity influx as to be examined for full-metal wall operation in large stellarators. Recently, this feature received revived intent for reactor scale stellarators.
Also, in this work, parameter regions close to the transition from ion-root to CERC are
examined. At lower rotational transform (a characteristic feature of the magnetic field confining fusion grade plasmas), transitions were detected when the plasma current evolved. As in smaller stellarators, it is concluded that low-order rationals and magnetic islands are related to the transitions. This is widely supported by extensive MHD simulations which finally provide indications for the role of zonal flow oscillations. As one of the outcomes, gyrokinetic instabilities are seen interacting for the first time with the neoclassical mechanisms in experiments.
In order to cope with the vast number of highly sampled spatio-temporal plasma data, new
techniques for novelty detection are required. Fundamental prerequisites for the detailed
physics investigations were the feasibility study of entropy-based data analysis techniques, and their adaptation to detect previously unrevealed transition mechanisms. These tools were applied to multivariate bulk plasma emissivity data, which allowed the exploration of large parameter spaces and provided insights in the spatio-temporal dynamics of CERC transitions.
In this manner, this research highlights the feasibility of information flow measure analysis in fusion studies. Applications of different entropy-based complexity measures are explored and this work sheds light on the capabilities, added value and limitations of these techniques. This investigation presents the integration of information flow measures to gain deeper understanding of plasma transport phenomena, by providing an approach to fast systematic data mining suited for real-time analysis. This work paves the way for further development and implementation of information-theoretic methods for plasma data analysis.
In summary, this research highlights the gained insight on CERC transitions, while showcasing the feasibility, added values and limitations of information flow measure analysis for fusion studies, to induce theory based analysis revealing new insights in fundamental, stellarator-specific transport mechanisms.
This work investigates turbulence in the core plasma of the optimised stellarator
Wendelstein 7-X. It focuses on experimental characterisation and
evaluation of the electrostatic micro-instabilities, which drive turbulent fluctuations,
and the saturation of turbulence by zonal flows. Expectations for
Wendelstein 7-X are formulated by reviewing theoretical work and with
the help of gyrokinetic simulations. The experimental analysis centres on
line-integrated density fluctuation measurements with the phase contrast
imagining diagnostic in electron cyclotron heated hydrogen discharges. An
absolute amplitude calibration was implemented, and a method for reliable
determination of dominant phase velocities in wavenumber-frequency
spectra of density fluctuations has been developed. Line-averaged density
fluctuation levels are observed to vary between magnetic configurations.
The wavenumber spectra exhibit a dual cascade structure, indicating fully
developed turbulence. The dominant instability driving turbulent density
fluctuations on transport relevant scales is identified as ion-temperaturegradient-
driven modes, which are mainly localised in the edge region of the
confined plasma. Despite the line-integrated nature of the measurement, the
localisation of density fluctuations is shown by comparing their dominant
phase velocity with the radial profile of the E × B rotation velocity due to
the ambipolar neoclassical electric field. Nonlinear gyrokinetic simulations
and a simplified plasma rotation model within a synthetic diagnostic confirm
the localisation. Oscillations of the dominant phase velocity indicate
the existence of zonal flows as a saturation mechanism of ion-temperaturegradient-
driven turbulence. A direct effect on turbulent density fluctuation
amplitudes and radial transport is observed.
This thesis describes how the data of the Langmuir probes in the Wendelstein 7-X (W7X) Test Divertor Unit (TDU) were evaluated, checked for consistency with other diagnostics and used to analyse plasma detachment.
Langmuir probes are an electronic diagnostic, and were among the first to be used in plasma physics to determine particle fluxes, potentials, temperatures and densities.
W7X is a large, advanced stellarator, magnetic confinement fusion experiment, operated at the Max-Planck-Institut for Plasma Physics(IPP) in Greifswald, Germany.
Its TDU is an uncooled graphite component, shaped and positioned to intercept the convective heat load of the plasma.
Detachment describes a desirable operation state of strongly reduced loads on this component.
The evaluation of Langmuir probe data relies heavily on models of the sheath, formed at the interface between plasma and a solid surface, to infer plasma parameters from the directly measured quantities.
Multiple such models are analysed, generalised, and adapted to our use case.
A detailed comparison is made to determine the most suitable model, as this choice strongly affects the predicted parameters.
Special attention is paid to uncertainties on the parameters, which are determined using a Bayesian framework.
From the inferred parameters, heat and particle fluxes are calculated.
These are also indirectly measured by two other, camera-based diagnostic systems.
Observations are compared to test the validity of assumptions and calculations in the evaluation of all three diagnostics by checking their results for consistency.
The first comparison, with the infrared emission camera system, shows good agreement with theoretical predictions and reported measurements of the sheath transmission factor, for which we derive and measure a value in W7X.
Parameter dependencies in the quality of this agreement hint at remaining issues.
The second comparison, with the Hydrogen alpha photon flux camera system, shows significant discrepancy with expectations.
These are argued to originate from systematic differences in the measurement locations, which are quantified and related to the magnetic topology.
Langmuir probe observations of individual discharges are analysed to discuss conditions under which detachment occurs, transition into that state and fluctuations observed prior to and during it.
A spatial parametrisation of the data is developed and used to facilitate this.
These observations contribute to the larger aim of understanding particle balance control and fusion plasma edge processes.
In this work, studies with respect to the exhaust problem were performed
in the stellarator experiment Wendelstein 7-X with different target concepts and different magnetic field geometries. Different infrared cameras were used to study the heat flux from the plasma onto the PFC. In the first publication, the limiter set-up was used with a simpler magnetic topology in the plasma edge. The radial fall-off of the parallel heat flux for inboard limiters in W7-X shows, similar to inboard limiters in tokamaks, two different radial fall-off lengths, a short (narrow) one, characterizing the near-SOL, and a long (broad) characterizing the far-SOL. For the far-SOL, the heating power and connection length have been identified as the main scaling parameters, while for the near-SOL, the electron temperature close to the LCFS has been identified as the main scaling parameter. The two fall-off lengths differ by a factor 10, and the found scalings for both regimes differ from known models and experimental scalings in tokamaks. A turbulent-driven feature was discussed in the publication as a possible explanation for the behavior of the fall-off length in W7-X.
The gained information and data have been further used to support many
other publications, covering the symmetry of the heat loads, the
energy balance of the machine, and seeding experiments.
The heat exhaust in W7-X with an island divertor was studied in the second
and third publication. Definitions of parameters such as peaking factor and
wetted area were applied for the heterogeneous heat flux pattern on the
W7-X divertor. It was shown that the island divertor concept is capable
of spreading out the heat efficiently, resulting in large wetted areas of up to 1.5 m2. The reached values for the wetted area are comparable to the ones of the larger tokamak JET but with a much smaller ratio of wetted
area to the area of the last closed flux surface. Furthermore, a positive
scaling of the wetted area with the power in the SOL was observed. This
scaling is beneficial for future reactors but needs further investigation of the involved transport processes. The peaking factor (discussed in the second publication) describes how concentrated the heat load is within the region of the strike line. It was shown that this factor is decreasing for increasing densities without affecting the wetted area. The present work paves the way for further analysis of the transport processes of the heat flux towards the island divertor of Wendelstein 7-X.
Experience in the construction of optimized stellarators shows the coil system is a significant challenge. The precision necessary allow the generation of accurate flux surfaces in recent experiments affected both cost and schedule negatively. Moreover, recent experiments at Wendelstein 7-X have shown that small field corrections were necessary for the operation of specific desired magnetic configurations. Therefore, robust magnetic configurations in terms of coil geometry and assembly tolerances have a high potential to facilitate swifter and less expensive construction of future, optimized stellarators. We present a new coil optimization technique that is designed to seek out coil configurations that are resilient against 3D coil displacements. This stochastic version of stellarator coil optimization uses the sampling average approach to incorporate an iterative perturbation analysis into the optimization routine. The result is a robust magnetic configuration that simultaneously reproduces the target magnetic field more accurately and leads to a better fusion performing coil configuration.
With this thesis, studies which form the bedrock for the long term goal of first wall heat load control and optimization for the advanced stellarator Wendelstein 7-X are developed, described and put into context. It is laid out how reconstruction of features of the edge magnetic field from plasma facing component heat loads is an important first step and can successfully be achieved by artificial neural networks. A detailed study of plasma facing component heat load distribution, potential overloads and overload mitigation possibilities is made in first order approximation of the impact of the main plasma dynamic effects.
This dissertation focusses on the numerical modelling of resonant destabilization of Alfvén eigenmodes by fast ions in fusion plasmas. It especially addresses non-linear simulations of stellarator plasmas in which particle collisions are retained. It is shown that collisions are required for a realistic description of Alfvén waves in plasmas relevant to nuclear fusion.
We start by carefully verifying the implementation of the collision operators into the electromagnetic version of the gyro-kinetic delta-f particle-in-cell code EUTERPE. After these initial benchmarks are completed successfully, the code is in a position to be applied to realistic tokamak and stellarator scenarios.
Since every collision operator needs to fulfil conservation laws, a momentum-conserving version of the pitch-angle scattering operator is implemented. This is in particular important for neoclassical transport simulations aimed at computing flux-surface variations of the electrostatic potential in stellarators.
Using the simplified CKA-EUTERPE model (employing a fixed-mode-structure approximation), we perform non-linear simulations in tokamaks and stellarators. We show that the non-linear dynamics of fast-ion-driven Alfvén eigenmodes is significantly influenced by collisions. They have the potential to enhance the saturation level and to affect the frequency chirping of the modes.
It is thus concluded that collisions play an essential role in determining Alfvén-eigenmode-induced fast-ion transport - an important issue for future fusion devices. In order to address this issue the CKA-EUTERPE model is extended to evolve multiple modes at the same time. First results of this multi-mode version (which enhances the level of realism of the simulations) are shown in the Appendix of the thesis.
The confinement of energy has always been a challenge in magnetic confinement fusion devices. Due to their toroidal shape there exist regions of high and low magnetic field, so that the particles are divided into two classes - trapped ones that are periodically reflected in regions of high magnetic field with a characteristic frequency, and passing particles, whose parallel velocity is high enough that they largely follow a magnetic field line around the torus without being reflected. The radial drift that a particle experiences due to the field inhomogeneity depends strongly on its position, and the net drift therefore depends on the path taken by the particle. While the radial drift is close to zero for passing particles, trapped particles experience a finite radial net drift and are therefore lost in classical stellarators. These losses are described by the so-called neoclassical transport theory. Recent optimised stellarator geometries, however, in which the trapped particles precess around the torus poloidally and do not experience any net drift, promise to reduce the neoclassical transport down to the level of tokamaks. In these optimised stellarators, the neoclassical transport becomes small enough so that turbulent transport may limit the confinement instead. The turbulence is driven by small-scale-instabilities, which tap the free energy of density or temperature gradients in the plasma. Some of these instabilities are driven by the trapped particles and therefore depend strongly on the magnetic geometry, so the question arises how the optimisation affects the stability. In this thesis, collisionless electrostatic microinstabilities are studied both analytically and numerically. Magnetic configurations where the action integral of trapped-particle bounce motion, J, only depends on the radial position in the plasma and where its maximum is in the plasma centre, so-called maximum-J configurations, are of special interest. This condition can be achieved approximately in quasi-isodynamic stellarators, for example Wendelstein 7-X. In such configurations the precessional drift of the trapped particles is in the opposite direction from the direction of propagation of drift waves. Instabilities that are driven by the trapped particles usually rely on a resonance between these two frequencies. Here it is shown analytically by analysing the electrostatic energy transfer between the particles and the instability that, thanks to the absence of the resonance, a particle species draws energy from the mode if the frequency of the mode is well below the charateristic bounce frequency. Due to the low electron mass and the fast bounce motion, electrons are almost always found to be stabilising. Most of the trapped-particle instabilities are therefore predicted to be absent in maximum- J configurations in large parts of parameter space. Analytical theory thus predicts enhanced linear stability of trapped-particle modes in quasi-isodynamic stellarators compared with tokamaks. Moreover, since the electrons are expected to be stabilising, or at least less destabilising, for all instabilities whose frequency lies below the trapped-electron bounce frequency, other modes might benefit from the enhanced stability as well. In reality, however, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with another, non-quasiisodynamic stellarator, the National Compact Stellarator Experiment (NCSX) and a typical tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, several microinstabilities, driven by the density as well as both ion and electron temperature gradients, are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilising when the electrostatic energy transfer is analysed. In contrast, if only the ions are treated kinetically but the electrons are taken to be in thermodynamic equilibrium, no such stabilising effect is observed. These results suggest that imperfectly optimised stellarators can retain most of the stabilising properties predicted for perfect maximum-J configurations. Quasi-isodynamic stellarators, in addition to having reduced neoclassical transport, might therefore also show reduced turbulent transport, at least in certain regions of parameter space.
There is a wide variety of Alfvén waves in tokamak and stellarator plasmas. While most of them are damped, some of the global eigenmodes can be driven unstable when they interact with energetic particles. By coupling the MHD code CKA with the gyrokinetic code EUTERPE, a hybrid kinetic-MHD model is created to describe this wave–particle interaction in stellarator geometry. In this thesis, the CKA-EUTERPE code package is presented. This numerical tool can be used for linear perturbative stability analysis of Alfvén waves in the presence of energetic particles. The equations for the hybrid model are based on the gyrokinetic equations. The fast particles are described with linearized gyrokinetic equations. The reduced MHD equations are derived by taking velocity moments of the gyrokinetic equations. An equation for describing the Alfvén waves is derived by combining the reduced MHD equations. The Alfvén wave equation can retain kinetic corrections. Considering the energy transfer between the particles and the waves, the stability of the waves can be calculated. Numerically, the Alfvén waves are calculated using the CKA code. The equations are solved as an eigenvalue problem to determine the frequency spectrum and the mode structure of the waves. The results of the MHD model are in good agreement with other sophisticated MHD codes. CKA results are shown for a JET and a W7-AS example. The linear version of the EUTERPE code is used to study the motion of energetic particles in the wavefield with fixed spatial structure, and harmonic oscillations in time. In EUTERPE, the gyrokinetic equations are discretized with a PIC scheme using the delta-f method, and both full orbit width and finite Larmor radius effects are included. The code is modified to be able to use the wavefield calculated externally by CKA. Different slowing-down distribution functions are also implemented. The work done by the electric field on the particles is measured to calculate the energy transfer between the particles and the wave and from that the growth rate is determined. The advantage of this approach is that the full magnetic geometry is retained without any limiting assumptions on guiding center orbits. Extensive benchmarks have been performed to test the new CKA-EUTERPE code. Three tokamak benchmarks are presented, where the stability of TAE modes are studied as a function of fast particle energy, or in one case as a function of the fast particle charge. The benchmarks show good agreement with other codes. Stellarator calculations were performed for Wendelstein 7-AS and the results demonstrate that the finite orbit width effects tend to be strongly stabilizing.
The WEGA stellarator is used to confine low temperature, overdense (densities exceeding the cut-off density of the heating wave) plasmas by magnetic fields in the range of B=50-500 mT. Microwave heating systems are used to ignite gas discharges using hydrogen, helium, neon or argon as working gases. The produced plasmas have been analyzed using Langmuir and emissive probes, a single-channel interferometer and ultra-high resolution Doppler spectroscopy. For a typical argon discharge in the low field operation, B=56 mT, the maximum electron density is n_e~10^18m^{-3} with temperatures in the range of T=4-12 eV. The plasma parameters are determined by using Langmuir probes and are cross-checked with interferometry. It is demonstrated within this work that the joint use of emissive probes and ultra-high resolution Doppler spectroscopy allows a precise measurement of the radial electric field. Here the floating potential measurements using emissive probes have been compared to measurements of the poloidal rotation of the plasma which is also linked to the radial electric field. In order to alter the plasma parameters a biasing probe setup has been used during this work. The focus of this work is on demonstrating the ability to modify the existing radial electric field in a plasma by using the biasing probe. This technique is in principle not new, as it has been around for decades. Looking at details, it turns out that describing low field operation WEGA argon plasmas in connection with biasing is not covered by the present set of theoretical approaches and experimental cognition. This work will commence with a basic approach and first establishes the diagnostic tools in a well-known discharge. Then the perturbation caused by the biasing probe is assessed. Following the characterization of the unperturbed plasmas, plasma states altered by the operation of the energized biasing probe will be characterized. It is demonstrated that modifying the existing radial electric field can be achieved and reliably diagnosed using spectroscopy and probe measurements. In order to verify the different approaches for determining the radial electric field the diagnostics are cross-checked against another whenever possible. During biasing the plasma two different stable plasma states have been found. Stable here refers to the state existing much longer than the confinement time for WEGA. The presence of a calorimetric limiter placed in the scrape-off layer has an impact on the type of the plasma state. The two observed plasma states differ in plasma parameter profiles, such as density, temperature, electric field and confined energy. The results are compared to two simple models. One model relies on the relevant atomic processes and a second one is based on neoclassical theory. Both models can be used to derive the particle and power flux from the plasma. The losses predicted by the atomic models can be tested using bolometry. It can be shown that both models agree well in the description of the particle balance of the electrons for large regions of the plasma. By comparing the models the neoclassical heat flux turns out to be small compared to the energy fluxes caused by atomic processes. For the reference discharge taking the energy flux due to the atomic processes and balancing it by the input microwave power is satisfying the energy balance, without the need for transport. For the biased discharges it turns out that neoclassical transport can be neglected as well, but the additional biasing power has to be taken into account. A simple model for the biasing power is motivated and tested. An agreement in the energy balance can be reached in this way as far as the models are applicable. The models also allow drawing conclusions on the amount of absorbed microwave power.