Electron Cyclotron Heating and Suprathermal Electron Dynamics in the TCV Tokamak

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.

Suprathermal electron studies in Tokamak plasmas by means of diagnostic measurements and modeling

Josef Kamleitner

To achieve reactor-relevant conditions in a tokamak plasma, auxiliary heating systems are required and can be realized by waves injected in the plasma that heat ions or electrons under certain conditions. Electron cyclotron resonant heating (ECRH) is a very flexible and robust technique featuring localized power deposition and current drive (CD) capabilities. Its fundamental principles such as damping on the cyclotron resonance are well understood and the application of ECRH is a proven and established tool; electron cyclotron current drive (ECCD) is regularly used to develop advanced scenarios and control magnetohydrodynamics (MHD) instabilities in the plasma by tailoring the current profile. There remain important open questions, such as the phase space dynamics, the observed radial broadening of the suprathermal electron distribution function (e.d.f.) and discrepancies in predicted and experimental CD efficiency. These are addressed in this thesis. One of its main goals is indeed to improve the understanding of wave-particle interaction in plasmas and current drive mechanisms. This was accomplished by combined experimental and numerical studies, strongly based on the conjunction of hard X-ray (HXR) bremsstrahlung measurements and Fokker-Planck modeling, characterizing the suprathermal electron population. The hard X-ray tomographic spectrometer (HXRS) diagnostic was purposely developed to perform these studies, in particular by investigating spatial HXR emission asymmetries in the co- and counter-current directions and within the poloidal plane. The system uses cadmium-telluride (CdTe) detectors and digital acquisition to store the complete time history of incoming photon pulses. An extensive study of digital pulse processing algorithms was performed and its consequent application allows the HXRS to handle high count rates in a noisy tokamak environment. Numerous other numerical tools were developed in the course of this thesis, among others to improve the time resolution by conditional averaging and to obtain local information with the general tomographic inversion (GTI) package. The interfaces of the comparatively new LUKE code and well-established CQL3D Fokker-Planck (F-P) code to the tokamak à configuration variable (TCV) data were refurbished and a detailed benchmarking of these two codes was performed for the first time. Indeed, the theory-predicted toroidal and poloidal emission asymmetries could be consistently verified by experiment and modeling in many cases, including scans of a variety of plasma and wave parameters. The effects of supra-thermal electron diffusion and radio frequency (RF) wave scattering, both resulting in a radial broadening of the HXR emission, were separated by a poloidal deposition location angle scan. Furthermore, previous results on anomalous diffusion and CD efficiency were reproduced with increased confidence arising from enhanced diagnostic specifications. The plasma response to electron cyclotron (EC) absorption and the role of quasi-linear effects were investigated using the coherent averaging capabilities of the HXRS. Several MHD instabilities can occur in the plasma center and better understanding of these modes and events is indispensable for their mitigation in order to prevent their negative effects on confinement and stability. Sawtooth crashes are such a major instability and localized at the q=1 surface. They can be described as the evolution of an internal m=1 kink mode leading to [...]

EPFL2015

Model-based optimization of magnetic control in the TCV tokamak: design and experiments

Federico Pesamosca

Thermonuclear controlled fusion is a promising answer to the current energy and climate issues, providing a safe carbon-free source of energy which is virtually inexhaustible. In magnetic confinement thermonuclear fusion based on tokamak reactors, hydrogen fuel in the state of plasma is confined using a system of external and self-generated magnetic fields. This thesis contributes to the development of magnetic confinement fusion research by applying techniques derived from control engineering to designing magnetic controllers for tokamak plasmas. Specifically, a new design for feedback control of plasma shape and position in the TCV tokamak is provided, and its efficacy is studied in dedicated simulations and experiments.Elongated plasmas lead to improved plasma performance in tokamaks, which is key to sustaining fusion conditions in reactors. The required magnetic field for shaping the plasma column however results in an unstable equilibrium that makes feedback control of the vertical plasma position mandatory. Active stabilization of the axisymmetric plasma vertical instability is a standard feature of elongated tokamaks and will be a fundamental feature in the ITER magnetic control system, since a loss of vertical control and the subsequent plasma disruption can lead to unacceptable heat loads on the plasma facing components.The TCV tokamak is the ideal benchmark for investigating the effect of plasma shaping on tokamak physics and performance, with its system of 16 independently powered poloidal field coils and a vessel with an elongated cross section. Shape and position control are coupled problems in TCV as they share the same poloidal field coils as actuators, requiring a multivariable approach to designing magnetic controllers.In this thesis, controller design for TCV is based on a model for the coupled plasma-vessel-coils electromagnetic dynamics: the RZIp model. In this axisymmetric model, the plasma current distribution is fixed but is free to move radially and vertically in the poloidal plane of a toroidal reference frame. An extension to this model is suggested, relaxing the assumption of rigid displacement in the radial direction to include plasma shape deformation and leading to a semi-rigid RZIp model which better fits numerical equilibria.An improvement to the existing algorithm for shape and position control in TCV is then proposed. In this new approach, tuning of the plasma position controller, in charge of vertical stabilization, can be performed independently of the shape controller, which itself acts on a stable system. Static decoupling is achieved and the shape controller is designed on the basis of an improved model for the plasma deformation, which includes the plasma contribution to the static magnetic flux perturbation. Simulations in closed loop with the RZIp model are provided to evaluate several optimized schemes.Finally, the vertical controller is optimized including the plasma dynamics as part of the controller design. Structured H-infinity, extending classical H-infinity to fixed-structure control systems, is applied to obtain a controller using all available coils for position control, and in particular a coil combination optimized for vertical stabilization. Closed-loop performance improvement is demonstrated in dedicated TCV experiments, confirming the simulation results and paving the way for the routine integration of the optimized position and shape controller in TCV discharges.

EPFL2021

Experimental analysis of suprathermal electrons generated by electron cyclotron waves in tokamak plasmas

Dahye Choi

This thesis focuses on the physics of suprathermal electrons generated by electron cyclotron (EC) waves in tokamak plasmas, which play an important role in the physics of current drive and energetic particle-driven instabilities. The suprathermal electron dynamics and their effect on the plasma stability have been experimentally studied utilizing high power EC waves, in the TCV tokamak of the Swiss Plasma Center at EPFL, Switzerland. A hard X-ray diagnostic, which measures the bremsstrahlung radiation of the suprathermal electrons in radial and energy spaces, has been mainly used for the analysis, and the measurement has been compared to an estimation made by Fokker-Planck modeling coupled with a hard X-ray synthetic diagnostic. In order to study the response of the suprathermal electrons to ECCD, ECCD modulation discharges have been developed. The time evolution of the hard X-ray profiles has been measured using coherent averaging techniques in order to observe the creation and relaxation of suprathermal electrons. Time-dependent Fokker-Planck modeling coupled with the hard X-ray synthetic diagnostic has been used to compare the experimental and simulation results, with various suprathermal electron transport models. A dependency of the radial transport of suprathermal electrons on the EC wave power has been demonstrated and a possibility of EC wave scattering has been addressed. The effect of the suprathermal electron population on the plasma stability has been studied, and in particular the destabilization and dynamics of the electron fishbone mode. The response of hard X-ray profiles to the internal kink mode has been observed directly by the hard X-ray diagnostic for the first time, at the frequency of the mode. The experimental evidence and a solution of a linear fishbone dispersion relation coupled to the Fokker-Planck modeling demonstrate the role of suprathermal electrons in destabilizing the fishbone mode and in particular the interaction of trapped electrons with the mode. This work provides the framework for a comprehensive understanding of the physics of suprathermal electrons related to ECCD, and explains how ECCD-generated suprathermal electrons behave in real and velocity spaces, and how they interact with and are redistributed by the MHD mode.

EPFL2020