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

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.

Pedestal Characteristics and MHD Stability of H-Mode Plasmas in TCV

Andreas Pitzschke

The tokamak à configuration variable (TCV) is unique in its ability to create a variety of plasma shapes and to heat the electron population in high density regimes using microwave power at the third harmonic of the electron cyclotron frequency. In the frame of this thesis, the impact of plasma shaping and heating on the properties of the edge transport barrier (ETB) in the high confinement mode (H-mode) was studied. This mode of operation is foreseen as one of the reference scenarios for ITER, the International Tokamak Experimental Reactor, which is being built to demonstrate the feasibility of thermonuclear fusion using magnetic confinement. A feature of H-mode regime operation are edge localized modes (ELMs), instabilities driven by the steep pressure gradients that form in the plasma edge region due to a transport barrier. During an ELM event, energy and particles are expelled from the plasma in a short burst. This will cause serious problems with respect to the heat load on plasma facing components in a tokamak of the size of ITER. Understanding of the phenomena associated with ELMs is thus required and dedicated investigations of their theory and experimental observations are carried out in many laboratories worldwide. This thesis presents several experimental and numerical investigations of tokamak behavior for configurations where the plasma edge plays an important role. From the experimental viewpoint, studies of transport barriers are challenging, as plasma parameters change strongly within a narrow spatial region. As part of the work presented here, the TCV Thomson scattering system was upgraded to meet the requirements for diagnosing electron temperature and density with high spatial resolution in the region of internal and external transport barriers. Simultaneously, the data analysis was significantly improved to cope with statistical uncertainties and alleviate eventual systematic errors. For measurements of the time evolution of density and temperature profile during the ELM cycle, the low repetition rate of the lasers used for Thomson scattering is a limiting. Although the system on TCV comprises 3 laser units that may be triggered in sequence with time separations down to 1 ms, time evolution over longer periods can only be reconstructed from repetitive events. In this context, an adjustment of the laser trigger to improve the synchronization with the ELM event is an advantage. A method was developed and implemented to generate a synchronizing trigger sequence, by a real-time monitoring of the D-alpha emission, which provides a marker for the ELM event. Recently, a "snowflake" (SF) divertor configuration, proposed as a possible solution to reduce the plasma-wall interaction by changing the divertor's poloidal magnetic field topology, was generated, for the first time, in TCV. A numerical code (KINX), based on a magnetohydrodynamic model (ideal MHD), was used to investigate the stability limits of this configuration under H-mode conditions and compare them with a similar standard single-null equilibrium. In a series of experiments, improved energy confinement was found and explained by improved stability of the edge region in the SF configuration. The influence of the pedestal structure in ELMy H-mode plasmas on the energy confinement and on ELM energy losses was investigated. The different ELM regimes found in TCV were analyzed, in particular the transition between type-III to type-I ELMs. The operational boundary of each ELM regime was characterized and verified by ideal MHD stability simulations for the ETB region. Recent studies on the scaling of the pedestal width with normalized poloidal pressure were confirmed. Using the capabilities of TCV, the influence of plasma shaping on pedestal parameters and MHD stability limits was investigated. In the past, models were developed to describe the onset of type-I ELMs, which are associated with modes in the ETB region arising from a coupling of pressure- and current-driven instabilities (coupled kink-ballooning modes). Experimental studies were performed to trace the temporal evolution of pedestal parameters characterizing the ETB during an ELM cycle. The results of these experiments were analyzed using information from MHD stability calculations. It is concluded that these models are capable of predicting limits as necessary conditions for ELM activity, but are not sufficient to fully explain ELM triggering.

EPFL2011

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

Edge Localized Mode Control in TCV

Jonathan Rossel

The Tokamak concept, based on magnetic confinement of a hydrogen plasma, is one of today's most promising paths to energy production by nuclear fusion. The experimental scenarios leading to the largest fusion rate are based on a high confinement plasma regime, the H-mode, in which the energy and particle confinement are enhanced by a transport barrier located at the plasma edge and forming a pedestal in the plasma pressure profile. In standard axisymmetric magnetic configurations, stationary H-mode regimes suffer from instabilities of the plasma edge, the so-called edge localized modes (ELMs), leading to potentially damaging repetitive ejections of heat and particles toward the plasma facing components. In ITER, a Tokamak currently being built to demonstrate net power production from fusion, type I ELMs are expected to occur during high performance discharges. It is expected that the power flux released by these ELMs will cause an intolerable erosion and heat load on the plasma facing components. The control of ELMs, in terms of frequency and energy loss, is therefore of primary importance in the field of magnetic fusion and is subject to an intense research effort worldwide. This thesis, in line with this effort, focuses on two particular ELM control methods: local continuous or modulated heating of the plasma edge, and application of resonant magnetic perturbations (RMP). In this thesis, the effects of plasma edge heating on the ELM cycle have been investigated by applying electron cyclotron resonant heating (ECRH) to the edge of an H-mode plasma featuring type I ELMs in the Tokamak à Configuration Variable (TCV). As the power deposition location is shifted gradually toward the plasma pressure pedestal, an increase of the ELM frequency by a factor 2 and a decrease of the energy loss per ELM by the same factor are observed, even though the power absorption efficiency is reduced. This unexpected and, as yet, unexplained phenomenon, observed for the first time, runs contrary to the intrinsic type I ELM power dependence and provides a new approach for ELM mitigation. The effects of heating power modulation on the ELM cycle have also been experimentally investigated. It showed that power modulation synchronized in real-time with the ELM cycle is able to pace the ELMs with low deviation from a given frequency. Experimental results also clearly indicate that the ELM frequency purely remains a function of the heating power averaged over the ELM cycle, so that power modulation itself is not able to drive the ELM frequency and only has a stabilization effect. These results are in qualitative agreement with a simple 0D finite confinement time integrator model of the ELM cycle. RMP consists in applying a magnetic field perpendicular to the plasma magnetohydrodynamic equilibrium flux surfaces with a spatial variation tuned to align with the equilibrium magnetic field lines. If each coil of an RMP coil system (i.e. a set of toroidally and poloidally distributed coils) is powered with an independent power supply, the coil current distribution can be tuned to optimize the RMP space spectrum. In the course of this thesis, a multi-mode Lagrange method, with no assumption on the coil geometry or spatial distribution, has been developed to determine this optimum, in the limit of the vacuum magnetic field approximation. This method appears to be an efficient way to minimize the parasitic spatial modes of the magnetic perturbation, and the coil current requirements, while imposing the amplitude and phase of a set of target modes. A figure of merit measuring the quality of a perturbation spectrum with respect to RMP independently of the considered coil system or plasma equilibrium is also proposed. To facilitate the application of the Lagrange method, a spectral characterization of the coil system, based on a generalized discrete Fourier transform applied in current space, is performed to determine how spectral degeneracy and side-bands creation limit the number of simultaneously controllable target modes. Finally, this thesis sets the foundations of experimental research in the particular subject of RMP at CRPP by proposing a physics-based design for a multi-purpose saddle coil system (SCS) for TCV, a coil system located and powered such as to create a helical magnetic perturbation. Using independent power supplies, the toroidal periodicity of this perturbation is tunable, allowing simultaneously ELM control, error field correction and vertical control. Other experimental applications, like resistive wall mode and rotation control, are also in view. In this thesis, the adequacy of two SCS designs, an in-vessel one and an ex-vessel one, is assessed with respect to the desired experimental applications. The current requirements and the system performances are also characterized. The conducting vessel wall is accounted for in a model used to determine the coupled response functions of the SCS, the screening of the magnetic perturbation by the wall, the induced voltages and currents during a plasma disruption and the maximal magnetic forces exerted on the SCS. A scaling of the SCS parameters with the number of coil turns is presented and the issue of coil heating and cooling is discussed.

EPFL2012

Pedestal Characteristics and MHD Stability of H-Mode Plasmas in TCV

Andreas Pitzschke

EPFL2011

Electron Cyclotron Heating and Suprathermal Electron Dynamics in the TCV Tokamak

Silvano Gnesin

EPFL2011

Edge Localized Mode Control in TCV

Jonathan Rossel

EPFL2012