Abstract
In 1932 the renowned Horace Lamb, while addressing the British Association for the Advancement of Science, reportedly said, "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former, I am rather optimistic". The quote perfectly describes our understanding of turbulence and our attempts to control it.Turbulence appears as a phenomenon characterizing the flow of fluids. Since fluid models are often used in physics, turbulence frustratingly appears in many different areas. Thus, it is no surprise that it also manifests in the plasma contained in fusion machines. These machines attempt to mimic processes occurring in stars, meaning that if successful, they would produce vast amounts of energy to sustain our technologically evolving world.The main obstacle to achieving this goal is turbulence, which enhances the transport of energy and ma ...
In 1932 the renowned Horace Lamb, while addressing the British Association for the Advancement of Science, reportedly said, "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former, I am rather optimistic". The quote perfectly describes our understanding of turbulence and our attempts to control it.Turbulence appears as a phenomenon characterizing the flow of fluids. Since fluid models are often used in physics, turbulence frustratingly appears in many different areas. Thus, it is no surprise that it also manifests in the plasma contained in fusion machines. These machines attempt to mimic processes occurring in stars, meaning that if successful, they would produce vast amounts of energy to sustain our technologically evolving world.The main obstacle to achieving this goal is turbulence, which enhances the transport of energy and mass inside fusion machines, destabilizing the plasma and disrupting machine operation. The primary types of magnetic fusion devices used are the tokamak and the stellarator, which are also the focus of this thesis. These are remarkable machines since they contain plasma heated to hundreds of millions of degrees at their core, while at their edge, the temperature must remain low enough to avoid melting their metal walls. This suggests a steep temperature gradient inside these machines, which, combined with the twisting of the magnetic field needed for containing the plasma, results in a variety of disruptive phenomena.Turbulence, as already stated, is one of these phenomena, and to make matters more challenging, it appears for various reasons and at different scales. Early magnetic fusion devices suffered from magnetohydrodynamic (MHD) mode-driven turbulence, but as they evolved, turbulence due to micro-instabilities on the spatial scale of the Larmor radius became the primary problem. These instabilities gave rise to complex phenomena leading to anomalous transport properties in the fusion machines. One of the physical mechanisms proposed to influence the transport properties of fusion machines is a self-organization process related to high-value avalanching events in heat flux that increase transport levels. Therefore, Self-Organized Criticality (SOC) and its appearance and effect in the physical system of magnetic fusion device plasmas are crucial to explore.The scope of this work will be the study of turbulence produced by micro-instabilities, specifically the so-called drift wave turbulence, and its effect on radial heat flux transport in tokamaks and stellarators that suffer from this issue. Additionally, the research will examine the existence and impact of self-organized criticality (SOC) in these physical systems.Reducing the cost of designing and optimizing fusion experiments has made it clear that large-scale computer simulations are needed. Due to the variety of length and time scales in fusion devices, such numerical experiments are challenging. Thus, reducing the computational cost by adopting specific assumptions according to the type of turbulence under study is necessary. In the study of micro-turbulence, the main approach is the gyrokinetic theory (GK). The equations describing the gyrokinetic approach in plasma studies are used in simulations and have been implemented by various numerical codes specifically for the magnetic geometry of tokamaks and stellarators. The code used throughout this work is GENE, developed at IPP Garching by the team of Prof. Dr. Frank Jenko, which has a large and worldwide user community.In Chapter 1 of this thesis, a brief introduction to the main theoretical concepts of magnetic fusion machines and the instabilities under study is presented. Chapter 2 outlines the key points of gyrokinetic theory (GK), along with a short presentation of the GENE code and its implementation of the gyrokinetic equations. Then, the statistical methods used in the analysis of turbulent data, as well as the methods used in the study of Self-Organized Criticality (SOC), are explained in Chapter 3, concluding the theoretical introduction to the subjects studied.The main turbulent mechanism simulated and examined in this thesis is a drift wave type of instability known as the ion temperature gradient (ITG) instability, with electrons considered adiabatic. The temperature gradient provides free energy to these modes and enhances instability, while at the same time, a competing mode known as zonal flow absorbs part of the energy of the unstable modes. Under certain conditions, this physical system self-regulates and exhibits self-organization characteristics. Gyrokinetic simulations are categorized based on the portion of the magnetic field simulated: they are either local, where the gyrokinetic equations are solved in a flux tube geometry, or global, where a complete radial description of the simulated area is adopted, allowing for the variation of physical quantities along the radial direction.In Chapter 4, we examine the characteristics of ITG turbulence and attempt to detect the existence of self-organization and the conditions needed for its appearance in local gyrokinetic simulations. A similar analysis is performed for global simulations in Chapter 5, with simulations being either gradient-driven, having prescribed temperature and density radial profiles, or flux-driven, where a localized heat source is adopted, allowing the temperature profile to evolve following heating. Turbulent fluctuations of heat flux are examined statistically for both types of global simulations, and the characteristics of SOC are researched. Finally, in Chapter 6, the stellarator machine is studied using a realistic quasi-isodynamic magnetic field geometry through local simulations of ITG mode-driven turbulence, and spectral analysis is attempted to examine its transport properties. The study summarizes its results in Chapter 7, providing insights into the subject of describing turbulence characteristics in magnetic fusion devices while attempting to quantify the existence of SOC and its impact on transport in these complex physical systems.
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