Turbulence at the boundary of toroidal plasmas with open and closed magnetic flux surfaces
Lausanne, EPFL, 2015.
DOI : 10.5075/epfl-thesis-6734.
The control and confinement of fusion plasmas are currently limited by a lack of understanding of the physical mechanisms behind the evolution of the turbulent transport experienced by particles and energy. In-situ investigations of plasma turbulence in fusion experiments is strongly hampered by the high temperatures and densities. Basic plasma physics devices represent an alternative solution to perform turbulence studies with the possibility of rigorously validating numerical codes. One of these experiments is TORPEX, in which a comprehensive characterization of plasma turbulence has been conducted in the presence of open helical magnetic field lines in toroidal geometry. These reproduce the main features of the scrape-off layer (SOL), which is the open flux surface region at the edge of magnetically confined fusion plasmas. The SOL has a key role in the balance of the dynamics that determine the overall plasma confinement. The first achievement of this thesis work is a technical upgrade of TORPEX that consists in the installation of a copper toroidal conductor inside the TORPEX vacuum vessel. A poloidal magnetic field is produced by a current flowing inside the conductor, introducing a rotational transform. This allows studying plasma turbulence in magnetic geometries of increasing complexity, starting with the simplest configuration of quasi-concentric flux surfaces. The initial exploration of the main plasma properties, including plasma production mechanisms and particle confinement time, is followed by a detailed spectral characterization of the measured electrostatic quasi-coherent fluctuations. Measurements of the toroidal and poloidal mode numbers reveal field-aligned modes. These present a poloidal localization indicating a clear ballooning feature that is in agreement with the results of a linear fluid code. The first experimental measurements of plasma blobs in the presence of a single-null X-point are performed. Blobs radially propagating outwards across the X-point are conditionally sampled, which allows us to track and analyze in detail the corresponding dynamics. The ExB drifts induced by the background potential gradients and the fluctuating potential dipole are both responsible for the measured blob acceleration in the X-point region. The contribution of the potential dipole is explained on the basis of an analytical model, in which the variation of the magnetic field intensity close to the X-point plays a key role. This results in a blob speed scaling that is in good agreement with the measured values.
Suprathermal ion transport in turbulent magnetized plasmas
Lausanne, EPFL, 2015.
DOI : 10.5075/epfl-thesis-6527.
Suprathermal ions, which have an energy greater than the quasi-Maxwellian background plasma temperature, are present in many laboratory and astrophysical plasmas. In fusion devices, they are generated by the fusion reactions and auxiliary heating. Controlling their transport is essential for the success of future fusion devices that could provide a clean, safe and abundant source of electric power to our society. In space, suprathermal ions include energetic solar particles and cosmic rays. The understanding of the acceleration and transport mechanisms of these particles is still incomplete. Basic plasma devices allow detailed measurements that are not accessible in astrophysical and fusion plasmas, due to the difficulty to access the former and the high temperatures of the latter. The basic toroidal device TORPEX offers an easy access for diagnostics, well characterized plasma scenarios and validated numerical simulations of its turbulence dynamics, making it the ideal platform for the investigation of suprathermal ion transport. This Thesis presents three-dimensional measurements of a suprathermal ion beam injected in turbulent TORPEX plasmas. The combination of uniquely resolved measurements and first-principle numerical simulations reveals the general non-diffusive nature of the suprathermal ion transport. A precise characterization of their transport regime shows that, depending on their energies, suprathermal ions can experience either a superdiffusive transport or a subdiffusive transport in the same background turbulence. The transport character is determined by the interaction of the suprathermal ion orbits with the turbulent plasma structures, which in turn depends on the ratio between the ion energy and the background plasma temperature. Time-resolved measurements reveal a clear difference in the intermittency of suprathermal ions time-traces depending on the transport regime they experience. Conditionally averaged measurements uncover the influence of field elongated turbulent structures, referred to as blobs, on the suprathermal ion beam. A theoretical model extending the Brownian motion to include non-Gaussian (Lévy) statistics and long-range temporal correlation is developed. This model successfully describes the evolution of the radial particle density from the numerical simulations and provides information on the microscopic processes underlying the non-diffusive transport of suprathermal ions.
The role of the sheath in magnetized plasma turbulence and flows
Lausanne, EPFL, 2013.
DOI : 10.5075/epfl-thesis-5985.
Controlled nuclear fusion could provide our society with a clean, safe, and virtually inexhaustible source of electric power production. The tokamak has proven to be capable of producing large amounts of fusion reactions by confining magnetically the fusion fuel at sufficiently high density and temperature, thus in the plasma state. Because of turbulence, however, high temperature plasma reaches the outermost region of the tokamak, the Scrape-Off Layer (SOL), which features open magnetic field lines that channel particles and heat into a dedicated region of the vacuum vessel. The plasma dynamics in the SOL is crucial in determining the performance of tokamak devices, and constitutes one of the greatest uncertainties in the success of the fusion program. In the last few years, the development of numerical codes based on reduced fluid models has provided a tool to study turbulence in open field line configurations. In particular, the GBS (Global Braginskii Solver) code has been developed at CRPP and is used to perform global, three-dimensional, full-n, flux-driven simulations of plasma turbulence in open field lines. Reaching predictive capabilities is an outstanding challenge that involves a proper treatment of the plasma-wall interactions at the end of the field lines, to well describe the particle and energy losses. This involves the study of plasma sheaths, namely the layers forming at the interface between plasmas and solid surfaces, where the drift and quasineutrality approximations break down. This is an investigation of general interest, as sheaths are present in all laboratory plasmas. This thesis presents progress in the understanding of plasma sheaths and their coupling with the turbulence in the main plasma. A kinetic code is developed to study the magnetized plasma-wall transition region and derive a complete set of analytical boundary conditions that supply the sheath physics to fluid codes. These boundary conditions are implemented in the GBS code and simulations of SOL turbulence are carried out to investigate the importance of the sheath in determining the equilibrium electric fields, intrinsic toroidal rotation, and SOL width, in different limited configurations. For each study carried out in this thesis, simple analytical models are developed to interpret the simulation results and reveal the fundamental mechanisms underlying the system dynamics. The electrostatic potential appears to be determined by a combined effect of sheath physics and electron adiabaticity. Intrinsic flows are driven by the sheath, while turbulence provides the mechanism for radial momentum transport. The position of the limiter can modify the turbulence properties in the SOL, thus playing an important role in setting the SOL width.
Basic Investigation of Turbulent Structures and Blobs of Relevance for Magnetic Fusion Plasmas
Lausanne, EPFL, 2011.
DOI : 10.5075/epfl-thesis-5228.
Similarly to neutral fluids, plasmas often exhibit turbulent behavior. Turbulence in plasmas is usually more complex than in neutral fluids due to long range interactions via electric and magnetic fields, and kinetic effects. It gives rise to many interesting phenomena such as self-generated magnetic fields (dynamos), zonal-flows, transport barriers, or particle pinches. Plasma turbulence plays a crucial role for the success of nuclear fusion as a potentially clean, safe, and long-term source for electric power production. Turbulent processes in the edge and scrape-off layer (SOL) of magnetic fusion plasmas determine, to a large extent, the overall confinement properties. They also influence the life time of plasma facing components, impurity production and influx, main chamber recycling, tritium retention, and helium ash removal. Edge turbulence is often dominated by blobs or filaments, magnetic-field-aligned plasma structures observed in the edge of virtually all magnetized plasmas. This thesis investigates basic aspects of edge turbulence and blobs in simple magnetized toroidal TORPEX plasmas. TORPEX includes important ingredients of SOL physics, such as pressure gradients, "∇B" and curvature of the magnetic field, together with open field lines. A relatively simple magnetic geometry, full diagnostics access and the possibility of controlled parameter scans allow isolating and studying instabilities and turbulence effects that occur in more complicated forms in fusion and astrophysical plasmas. Using a number of optimized probe diagnostic methods, the mechanisms for the generation of blobs from ideal interchange waves and for their subsequent propagation are elucidated. A blob velocity scaling law is introduced that takes into account several damping effects of blob cross-field velocity. This scaling law is in good agreement both with blob simulations and experiments on TORPEX. Studies on blob parallel dynamics shed light on blob induced parallel currents and the transport of parallel momentum. Based on this understanding of blob motion, several tools to influence blobs and turbulence as a whole are developed. A methodology for plasma turbulence code validation is established. Using a large set of observables, the agreement between experiments and both 2D and global 3D two-fluid simulations is quantified.
Fast Imaging of Turbulent Plasmas in the TORPEX Device
Lausanne, EPFL, 2011.
DOI : 10.5075/epfl-thesis-5073.
This thesis addresses the issue of turbulence generated modes and intermittent structures using a fast visible imaging system on TORPEX. The plasma radiation mechanisms and experimental setup of the imaging system are discussed together with an optimized tomographic reconstruction method. In TORPEX typical plasmas, radiative ionization is the dominant radiation mechanism. The photon flux emitted by hydrogen plasmas is a linear function of √Te and ne for Te ≥ 4eV. A Photron Ultima APX-RS fast visible camera was used to acquire the light emission of TORPEX plasmas. The camera equipped with the image intensifier is able to image TORPEX plasmas up to 200 kframes/s of framing rate and down to 1µs of exposure time, which results in clear images of plasma structures. The time-resolved poloidal emissivity of TORPEX plasma emission is tomographically reconstructed from tangentially viewed images using a pixel method and singular value decomposition approach. The spatial resolution in the reconstructed emissivity profiles, is 2cm. The plasma emissivity and ion saturation current profiles are compared using the conditional average sampling (CAS) technique and statistical analysis of fluctuations. The CAS is performed to visualize the mode structures and to estimate their sizes. The resulting fast imaging of the plasma, non-perturbative and high spatio-temporal resolution diagnostics, can visualize small scale turbulent plasma structures, well beyond the typical spatial resolution of probe arrays. A two-dimensional gas puff (2D-GPI) imaging system, including a 2D movable gas puff nozzle and a fast framing camera, has been developed in the TORPEX device. Direct local measurements from a large number of probes, distributed across the plasma column, are used to establish a correlation between the plasma parameters and the locally measured visible light emission. GPI and ion saturation current signals are well correlated, with correlation coefficients higher than 0.75. Fourier analysis of the GPI and internal probes show that the GPI can detect the dominant interchange mode. Quasi-coherent interchange modes and intermittent, turbulence generated blobs can be detected and studied using fast visible imaging in TORPEX. For an increasing vertical magnetic field, the principal interchange mode is damped and a sharp transition occurs between low-k and high-k harmonics. The scaling of the radial width of different interchange harmonics with respect to the vertical wave-number (kz) shows good agreement between the experimental and theoretical radial-width-kz scaling in TORPEX plasmas. The gradient-removal mechanism, describing the level of turbulent fluctuations, was tested using experimental data from the visible camera. The saturation level of the interchange instabilities predicted by the gradient-removal mechanism is in reasonable agreement with the experimental measurements. Tomographically inverted data from the fast camera were used to study the propagation of intermittent blobs. The experimental speed-versus-size scaling of blobs in the camera data is in good agreement with theoretical predictions. This thesis confirms the possibility of using fast imaging to estimate saturation level of fluctuations associated with ideal interchange instability and to reconstruct the blob speed-size scaling law in tokamak plasmas non-perturbatively. This can be used to non-perturbatively estimate the transport levels in the SOL of fusion devices.
Interaction of supra-thermal ions with turbulence in a magnetized toroidal plasma
Lausanne, EPFL, 2009.
DOI : 10.5075/epfl-thesis-4543.
This thesis addresses the interaction of a supra-thermal ion beam with turbulence in the simple magnetized toroidal plasma of TORPEX. The first part of the thesis deals with the ohmic assisted discharges on TORPEX. The aim of these discharges is the investigation of the open to closed magnetic field line transition. The relevant magnetic diagnostics were developed. Ohmic assisted discharges with a maximum plasma current up to 1kA are routinely obtained. The equilibrium conditions on the vacuum magnetic field configuration were investigated. In the second part of the thesis, the design of the fast ion source and detector are discussed. The accelerating electric field needed for the fast ion source was optimized. The fast ion source was constructed and commissioned. To detect the fast ions a specially designed gridded energy analyzer was used. The electron energy distribution function was obtained to demonstrate the efficiency of the detector. The experiments with the fast ion beam were conducted in different plasma regions of TORPEX. In the third part of the thesis numerical simulations are used to interpret the measured fast ion beam behavior. It is shown that a simple single particle equation of motion explains the beam behavior in the experiments in the absence of plasma. To explain the fast ion beam experiments with the plasma a turbulent electric field must be used. The model that takes into account this turbulent electrical field qualitatively explains the shape of the fast ion current density profile in the different plasma regions of TORPEX. The vertically elongated fast ion current density profiles are explained by a spread in the fast ion velocity distribution. The theoretically predicted radial fast ion beam spreading due to the turbulent electric field was observed in the experiment.
Electrostatic instabilities and turbulence in a toroidal magnetized plasma
Lausanne, EPFL, 2007.
DOI : 10.5075/epfl-thesis-3849.
This Thesis aims at characterizing the linear properties of electrostatic drift instabilities arising in a toroidal plasma and the mechanisms leading to their development into turbulence. The experiments are performed on the TORoidal Plasma EXperiment (TORPEX) at CRPP-EPFL, Lausanne. The first part of the Thesis focuses on the identification of the nature of the instabilities observed in TORPEX, using a set of electrostatic probes, designed and built for this purpose. The global features of fluctuations, analyzed for different values of control parameters such as the magnetic field, the neutral gas pressure and the injected microwave power, are qualitatively similar in different experimental scenarios. The maximum of fluctuations is observed on the low field side, where the pressure gradient and the gradient of the magnetic field are co-linear, indicating that the curvature of the magnetic field lines has an important role in the destabilization of the waves. The power spectrum is dominated by electrostatic fluctuations with frequencies much lower than the ion cyclotron frequency. Taking advantage of the extended diagnostics coverage, the spectral properties of fluctuations are measured over the whole poloidal cross-section. Both drift and interchange instabilities develop and propagate on TORPEX, with the stability of both being affected by the curvature of the magnetic field. It is shown that modes of different nature are driven at separate locations over the plasma cross-section and that the wavenumber and frequency spectra, narrow at the location where the instabilities are generated, broaden during convection, suggesting an increase in the degree of turbulence. The transition from coherent to turbulent spectral features and the role of nonlinear coupling between modes in the development of turbulence are treated in the second part of this work. It is found that nonlinear mode-mode coupling is responsible for the redistribution of spectral energy from the dominant instabilities to other spectral components and that this mechanism is independent of the nature of the instabilities. Nonlinear interactions between the mode and its nonlinearly generated harmonics are responsible for the filling of the spectral regions between harmonics. Later in the development along the convection path, the unstable mode transfers energy to spectral components with significantly larger frequencies. This transfer of energy can be interpreted in the investigated plasma scenarios as a forward cascade in wavenumbers, with transfer of energy from large to small scales.
Plasma production and transport in a simple magnetised toroidal plasma
Lausanne, EPFL, 2007.
DOI : 10.5075/epfl-thesis-3765.
This Thesis addresses questions related to transport phenomena and the plasma production mechanisms by injection of microwaves in the electron-cyclotron frequency range in the simple magnetised toroidal plasma TORPEX. The second subject is investigated in detail in Part II. The mechanisms of the interaction between the injected microwaves and the plasma are identified. The experimental results highlight the different roles played by the electron-cyclotron and upper-hybrid plasma resonances in the absoprtion of the microwave power by the plasma. The effects of the plasma-wave interaction on the electron distribution function are investigated, confirming that the high-energy electrons that are able to ionise the neutral gas mainly come from interactions at the upper-hybrid resonance. Based on the experimental results, an expression is derived for the particle source term, which can be used in numerical codes simulating the plasma dynamics on TORPEX. The plasma production mechanisms are then related to the properties of the time-averaged plasma profiles. A set of control parameters, including the injected microwave power and the vertical magnetic field, are identified. These allow one to vary in a systematic way the plasma profiles, as needed for a detailed study of plasma instabilities and related transport. The study of particle and heat transport is undertaken in Part III. A number of experimental and analysis techniques, including a method based on the combination of "conditional-average sampling" and "boxcar-averaging", are applied to identify and quantify specific contributions to the total fluxes. The two-dimensional temporal behaviour of density, electron temperature and plasma potential is simultaneously reconstructed, thus contributing significantly to the characterisation of transport mechanisms at play in TORPEX plasmas. Two clearly distinct mechanisms are mainly responsible for the transport across the magnetic field. They are respectively associated to unstable low-frequency electrostatic modes, identified as drift waves and interchange modes, and to intermittent high-density plasma structures (or blobs). It is shown that the blobs originate from the intermittent radial expansion of the unstable modes in a region of strongly sheared E × B flow.
Turbulence in basic toroidal plasmas
Lausanne, EPFL, 2007.
DOI : 10.5075/epfl-thesis-3672.
This thesis work contributes to the improvement of the experimental assessment of turbulence in fusion-relevant toroidal plasmas via the construction and dedicated exploitation of the TORPEX basic toroidal plasma experiment. Several contributions to the construction phase of TORPEX between November 2001 and March 2003 are presented, including design studies of the magnetic-field configurations and the concept and realization of the IT system. For the studies of fluctuations and turbulence, a toroidal magnetic field complemented by a small vertical component is used in rf-driven discharges. An analytical model of the particle confinement mechanism in this topology is developed and experimentally verified. The basic plasma properties are characterized as a function of the available control parameters, namely the toroidal and vertical magnetic field, the injected microwave power, and the neutral gas type and pressure. The fluctuations and turbulence in TORPEX are investigated via the specifically developed plasma-imaging probe HEXTIP, which employs a hexagonal disposition of 86 Langmuir probes, covering the entire poloidal cross section. Established one- and two-point Fourier-space analysis techniques are generalized to be suitable for such a 2D diagnostic. A novel real-space analysis method for fluctuating spatiotemporal structures is developed based on a pattern-recognition approach combined with a massive statistical analysis of measurements of many realizations of turbulent structures, permitting to assess the probabilistic properties of the turbulent fluctuations directly with convincing detail and statistical accuracy. The combined force of the generalized Fourier-space and the probabilistic real-space analysis techniques, applied automatically to a wide variety of discharges, is used to characterize the fluctuations in the TORPEX plasma in detail. Structures are observed to occur mostly on the low-field side, in patterns expected for drift-interchange type instabilities. The magnitude of the fluctuations is generally comparable to the time-average density level and the areas occupied by the structures extend over a significant fraction of the poloidal cross-section. The development of a 3D fluid simulation code, ESELTPX, is initiated in the framework of this thesis, aiming at performing global nonlinear simulations of TORPEX plasma discharges for detailed experiment-theory comparison. The present state of the project is summarized and future development strategies are outlined.