Self-consistent simulation of multi-component plasma turbulence and neutral dynamics in the tokamak boundary

The interaction between neutral particles and the plasma plays a key role in determining the dynamics of the tokamak boundary that, in turn, significantly impact the overall performance of the device. Leveraging the work in Wersal and Ricci [Nucl. Fusion 55, 123014 (2015)], the present thesis describes the development and implementation in the GBS code of a mass-conserving multi-component self-consistent model to simulate the interplay between neutrals and plasma in the tokamak boundary. The simulation results are shown to be a useful tool to disentangle the physics at play in the tokamak boundary, and in particular for the interpretation of gas puff imaging (GPI).Developed in the last decade, the GBS code [Ricci et al, Plasma Phys. Control. Fusion 54, 124047 (2012)] allows for self-consistent three-dimensional numerical simulations of the turbulent plasma and neutral dynamics in the tokamak boundary. In GBS, a set of Braginskii equations in the drift limit describes the plasma time evolution, and the neutrals are modelled by solving a kinetic equation using the method of characteristics. While GBS enables simulations in arbitrary magnetic configurations, here we focus on limited plasmas. We first describe the geometrical operators and proper boundary conditions to ensure that mass conservation is satisfied. In comparison to the previous non-mass-conserving model of GBS, the mass-conserving simulations capture more accurately the sharp transition of the plasma and neutral quantities between the edge and scrape-off layer regions. In addition, we show that mass conserving simulations allow for reliable quantitative studies of particle fluxes in the tokamak boundary.A multi-component model of the neutral-plasma interaction is then developed by extending the single-component model to the description of a deuterium plasma that includes electrons, D+ ions, D atoms, D2 molecules and D2+ ions. The molecular dynamics is introduced through a set of drift-reduced Braginskii equations for the D2+ species and considering a kinetic equation for D2 molecules, in addition to the kinetic equation for D atoms, thus resulting in a coupled system of kinetic equations for the atomic and molecular neutral distribution functions. The first multi-component GBS simulations show that, in the sheath-limited regime under consideration, most of the D2 molecules cross the last closed flux surface (LCFS) and are dissociated or ionized in the edge region, thus giving rise to sources of D atoms inside the LCFS. This leads to an inward radial shift of the peak of the plasma source due to ionization of D atoms with respect to the single-component simulations.The multi-component model is applied to the simulation of GPI diagnostics, where the presence of a molecular gas puff is simulated self-consistently with the plasma and neutral dynamics of the tokamak boundary. The injected molecules interact with the boundary plasma, resulting in the emission of light in the D alpha wavelength that can be measured to infer the turbulent properties of the plasma. The simulated mechanisms underlying the light emission, which include the excitation of D atoms and dissociation of both D2 and D2+, provide a reliable tool for the interpretation of GPI experimental measurements. The impact of neutral fluctuations on the D alpha emission rate is investigated, as well as the correlation between the D alpha emission and the plasma and neutral quantities.

Electron Cyclotron Heating and Suprathermal Electron Dynamics in the TCV Tokamak

Silvano Gnesin

This thesis is concerned with the physics of suprathermal electrons in thermonuclear, magnetically confined plasmas. Under a variety of conditions, in laboratory as well as space plasmas, the electron velocity distribution function is not in thermodynamic equilibrium owing to internal or external drives. Accordingly, the distribution function departs from the equilibrium Maxwellian, and in particular generally develops a high-energy tail. In tokamak plasmas, this occurs especially as a result of injection of high-power electromagnetic waves, used for heating and current drive, as well as a result of internal magnetohydrodynamic (MHD) instabilities. The physics of these phenomena is intimately tied to the properties and dynamics of this suprathermal electron population. This motivates the development of instrumental apparatus to measure its properties as well as of numerical codes to simulate their dynamics. Both aspects are reflected in this thesis work, which features advanced instrumental development and experimental measurements as well as numerical modeling. The instrumental development consisted of the complete design of a spectroscopic and tomographic system of four multi-detector hard X-ray (HXR) cameras for the TCV tokamak. The goal is to measure bremsstrahlung emission from suprathermal electrons with energies in the 10-300 keV range, with the ultimate aim of providing the first full tomographic reconstruction at these energies in a noncircular plasma. In particular, suprathermal electrons are generated in TCV by a high-power electron cyclotron heating (ECH) system and are also observed in the presence of MHD events, such as sawtooth oscillations and disruptive instabilities. This diagnostic employs state-of-the-art solid-state detectors and is optimized for the tight space requirements of the TCV ports. It features a novel collimator concept that combines compactness and flexibility as well as full digital acquisition of the photon pulses, greatly enhancing its potential for full spectral analysis in high-fluency scenarios. Additional flexibility is afforded by the possibility to rotate the orientation of two of the cameras, permitting the crucial comparison of radiation emitted perpendicular and parallel to the primary magnetic field. The design of the HXR system was optimized through an extensive iterative simulation process with the aid of tomographic reconstruction codes as well as quasilinear Fokker-Planck modeling of ECH-driven TCV plasmas. In parallel, the selection of the detectors for this system was performed through comprehensive laboratory testing of several candidate detectors available on the market. While the design was completed in the course of the thesis work, commissioning of the system has only commenced recently with one of the four cameras installed on TCV. The first preliminary results, discussed in the last part of this thesis, include basic parameter scans of ECH wave-plasma interaction and the investigation of the dynamic response of suprathermal electrons to modulated ECH. In addition, the cameras possess the novel ability to discriminate against very high-energy γ-ray radiation that cannot be collimated and must thus be excluded from spatial distribution analysis. A basic study of the conditions for γ-ray suppression was conducted in preparation for future experiments. The Fokker-Planck modeling tool used in this diagnostic development was acquired through a collaboration with CEA-Cadarache, initially with the primary motivation of studying the simultaneous plasma heating by 2nd and 3rd harmonic electron cyclotron waves that is uniquely possible on TCV. This motivated a dedicated study, both theoretical and experimental, of one particular instance of this combined heating, which became a second primary subject of this thesis work. The particular scenario studied here is one in which a single ECH frequency is resonant at both harmonics in the same plasma. The primary objective of this study was to determine whether a synergy effect existed, permitting an enhancement of the intrinsically weak 3rd harmonic absorption by the suprathermal electrons generated at the 2nd harmonic resonance. An associated question was whether this effect, if it existed, was experimentally measurable or was in fact observed in TCV. The simulations performed in the course of this study indeed predict the existence of such a synergy, although the answer to the second question was ultimately negative, at least within the current technical limitations. This study has proven nevertheless highly valuable in providing new insight into the complex velocity-space dynamics that govern ECH wave-particle interaction and suprathermal electron dynamics.

EPFL2011

Neutral atom dynamics and plasma turbulence in the tokamak periphery

Christoph Wersal

Understanding the physical mechanisms at play in the interaction between turbulent plasma and neutral particles is a crucial issue that we approach in this Thesis by using a first-principles self-consistent model of the tokamak periphery implemented in the GBS code. While the plasma is modeled by the drift-reduced two-fluid Braginskii equations, a kinetic model for the neutrals is developed, valid in short and in long mean free path scenarios. The model includes ionization, charge-exchange, recombination, and elastic collisional processes. The neutral kinetic equation is solved by using the method of characteristics. We identify the key elements determining the interaction between neutrals and the turbulent plasma focusing on a tokamak with a toroidal rail limiter on the high-field side equatorial midplane. For this purpose, we simulate the dynamics of the plasma and the neutrals in a domain that includes both the confined edge region and the scrape-off layer (SOL). It turns out that, in the considered plasma conditions, neither the fluctuations of the neutral moments, nor the friction between neutrals and the plasma impact the time-averaged plasma profiles significantly. Thanks to this study, we derive a simple model for the neutral-plasma interaction, which is helpful to identify and understand the principal physical processes at play in the tokamak periphery. By studying the dynamics of the neutral-plasma interplay along the magnetic field lines in the SOL, we derive a refined two-point model from the drift-reduced Braginskii equations that balances the parallel and perpendicular transport of plasma and heat, and takes into account the plasma-neutral interaction. The model estimates the electron temperature drop along a field line, from a region far from the limiter to the limiter plates. The refined two-point model is shown to be in very good agreement with the simulation results. Finally, we self-consistently simulate a diagnostic neutral gas puff, which is often used experimentally as a tool to learn about the turbulence properties in the tokamak periphery. In particular, we investigate the impact of neutral density fluctuations on the D-Î± light emission, finding that at a radial distance from the gas puff smaller than the neutral mean free path, neutral density fluctuations are anti-correlated with plasma density, electron temperature, and D-Î± fluctuations, while at distances from the gas puff larger than the neutral mean free path, a non-local shadowing effect influences the neutrals, and the D-Î± fluctuations are correlated with the neutral density fluctuations.

EPFL2017

Collisions in Global Gyrokinetic Simulations of Tokamak Plasmas using the Delta-f Particle-In-Cell Approach

Thibaut Vernay

The present work takes place within the general context of research related to the development of nuclear fusion energy. More specifically, this thesis is mainly a numerical and physical contribution to the understanding of turbulence and associated transport phenomena occuring in tokamak plasmas, the most advanced and promising form of magnetically confined plasmas. The complexity of tokamak plasma phenomena and related physical models, either fluid or kinetic, requires the development of numerical codes to perform simulations of the plasma behaviour under given conditions defined by the magnetic geometry as well as density and temperature profiles. The studies presented in this work are based on electrostatic kinetic simulations, taking advantage of a reduced kinetic model (the gyrokinetic model) which is particularly suitable for studying turbulent transport in magnetically confined plasmas, in effect solving an approximate form of the Vlasov equation for the distribution function of each species (electrons, ions) along with a reduced form of the Poisson equation providing the self-consistent electric fields. The main tool of this work, the gyrokinetic ORB5 code making use of numerical particles according to the Particle-In-Cell (PIC) method, has been upgraded during this thesis with different linearized collision operators related to both ions and electrons. The BIRDIE code, enabling to study collisional effects on the evolution of Langmuir waves in an unmagnetized plasma, has been written in order to serve as a test-bed for the collision operators ultimately implemented in ORB5. Some essential algorithms related to collisional simulations have been jointly implemented, such as the two-weight scheme which is extensively described in this work. The collision operators in ORB5 have been further carefully tested through neoclassical simu- lations and benchmarked against other codes, providing reliable levels of collisional transport. Together with different procedures controlling the numerical noise, the collision operators have then been applied to the study of collisional turbulent transport in two different regimes, the Ion-Temperature-Gradient (ITG) regime and the Trapped-Electron-Mode (TEM) regime re- quiring a trapped electron kinetic response. Although not dominant in core tokamak plasmas, collisional effects nevertheless lead to interesting modifications in the turbulence behaviour which are not captured by the often considered collisionless gyrokinetic models. The so-called coarse-graining procedure, a noise-control algorithm which is suitable for collisional gyrokinetic simulations with particles, is shown to enable carrying out relevant simulations over many col- lision times. Consequently, reliable conclusions regarding turbulent transport in the presence of collisions could be drawn in this thesis. Namely, the turbulent transport in the ITG regime is found to be enhanced by ion collisions through interactions with so-called zonal flows as- sociated to axisymmetric modes, while it is reduced by electron collisions in the TEM regime through electron detrapping processes. The zonal flow dynamics in collisionless and collisional ITG turbulence simulations is studied, emphasizing the limitation of the zonal flow level due to Kelvin-Helmoltz-type instabilities. Additionally, some purely collisionless issues related to tokamak physics are discussed, such as the finite plasma size effects in TEM-dominated regime which are found to be important in non-linear simulations but unimportant in linear simu- lations. The role of zonal flows in temperature-gradient-driven TEM turbulence saturation is confirmed to be weak, in agreement with previous studies. Finally, a realistic global gy- rokinetic simulation, accounting for a proper TCV tokamak magnetic equilibrium and related experimental profiles, has been successfully carried out thus demonstrating the relevance of the ORB5 code for predictions related to physics of real tokamaks. A good agreement with GAM experimental measurements is indeed obtained.

EPFL2013