Real-Time Control of Tokamak Plasmas: from Control of Physics to Physics-Based Control

Stable, high-performance operation of a tokamak requires several plasma control problems to be handled simultaneously. Moreover, the complex physics which governs the tokamak plasma evolution must be studied and understood to make correct choices in controller design. In this thesis, the two subjects have been merged, using control solutions as experimental tool for physics studies, and using physics knowledge for developing new advanced control solutions. The TCV tokamak at CRPP-EPFL is ideally placed to explore issues at the interface between plasma physics and plasma control, by combining a state-of-the-art digital real-time control system with a flexible and powerful set of actuators, in particular the electron cyclotron heating and current drive system (ECRH/ECCD). This unique experimental platform has been used to develop and test new control strategies for three important and reactor-relevant tokamak plasma physics instabilities, including the sawtooth, the edge localized mode (ELM) and the neoclassical tearing mode (NTM). These control strategies offer new possibilities for fusion plasma control and at the same time facilitate studies of the physics of the instabilities with greater precision and detail in a controlled environment. The period of the sawtooth crash, a periodic MHD instability in the core of a tokamak plasma, can be varied by localized deposition of ECRH/ECCD near the q = 1 surface, where q is the safety factor. Exploiting this known physical phenomenon, a sawtooth pacing controller was developed which is able to precisely control the time of appearance of the next sawtooth crash. It was also shown that each individual sawtooth period can be controlled in real-time. A similar scheme is applied to H-mode plasmas with type-I ELMs, where it is shown that pacing regularizes the ELM period. The regular, reproducible and therefore predictable sawtooth crashes obtained by the sawtooth pacing controller have been used to study the relationship between sawteeth and NTMs. It is known that post-crash MHD activity can provide the "seed" island for an NTM, which then grows under its neoclassical bootstrap drive. Experiments are shown which demonstrate that the seeding of 3/2 NTMs by long sawtooth crashes can be avoided by preemptive, crash-synchronized EC power injection pulses at the q = 3/2 rational surface location. NTM stabilization experiments in which the ECRH deposition location is moved in real-time with steerable mirrors have shown effective stabilization of both 3/2 and 2/1 NTMs, and have precisely localized the deposition location that is most effective. Studies of current-profile driven destabilization of tearing modes in TCV plasmas with significant amounts of ECCD show a great sensitivity to details of the current profile, but failed to identify a stationary region in the parameter space in which NTMs are always destabilized. This suggests that transient effects intrinsically play a role. Next to instability control, the simultaneous control of magnetic and kinetic plasma profiles is another key requirement for advanced tokamak operation. While control of kinetic plasma profiles around an operating point can be handled using standard linear control techniques, the strongly nonlinear physics of the coupled profiles complicates the problem significantly. Even more, since internal magnetic quantities are difficult to measure with sufficient spatial and temporal resolution —even after years of diagnostic development— routine control of tokamak plasma profiles remains a daunting and extremely challenging task. In this thesis, a model-based approach is used in which physics understanding of plasma current and energy transport is embedded in the control solution. To this aim, a new lightweight transport code has been derived focusing on simplicity and speed of simulation, which is compatible with the demands for real-time control. This code has been named RAPTOR (RApid Plasma Transport simulatOR). In a first-of-its-kind application, the partial differential equation for current diffusion is solved in real-time during a plasma shot in the TCV control system using RAPTOR. This concept is known in control terms as a state observer, and it is applied experimentally to the tokamak current density profile problem for the first time. The real-time simulation gives a physics-model-based estimate of key plasma quantities, to be controlled or monitored in real-time by different control systems. Any available diagnostics can be naturally included into the real-time simulation providing additional constraints and removing measurement uncertainties. The real-time simulation approach holds the advantage that knowledge of the plasma profiles is no longer restricted to those points in space and time where they are measured by a diagnostic, but that an estimate for any quantity can be computed at any time. This includes estimates of otherwise unmeasurable quantities such as the loop voltage profile or the bootstrap current distribution. In a first closed-loop experiment, an estimate of the internal inductance resulting from the real-time simulation is feedback controlled, independently from the plasma central temperature, by an appropriate mix of co- and counter- ECCD. As a tokamak plasma evolves from one state to another during plasma ramp-up or ramp-down, the profile trajectories must stay within a prescribed operational envelope delimited by physics instabilities and engineering constraints. Determining the appropriate actuator command sequence to navigate this operational space has traditionally been a trial-and-error procedure based on experience of tokamak physics operators. A computational technique is developed based on the RAPTOR code which can calculate these trajectories based on the profile transport physics model, by solving an open-loop optimal control problem. The solution of this problem is greatly aided by the fact that the code returns the plasma state trajectory sensitivities to input trajectory parameters, a functionality which is unique to RAPTOR. This information can also be used to construct linearized models around the optimal trajectory, and to determine the active constraint, which can be used for time-varying closed-loop controller design. This physics-model-based approach has shown excellent results and holds great potential for application in other tokamaks worldwide as well as in future devices

Free-Boundary Simulations of ITER Advanced Scenarios

The successful operation of ITER advanced scenarios is likely to be a major step forward in the development of controlled fusion as a power production source. ITER advanced scenarios raise specific challenges that are not encountered in presently-operated tokamaks. In this thesis, it is argued that ITER advanced operation may benefit from optimal control techniques. Optimal control ensures high performance operation while guaranteeing tokamak integrity. The application of optimal control techniques for ITER operation is assessed and it is concluded that robust optimisation is appropriate for ITER operation of advanced sce- narios. Real-time optimisation schemes are discussed and it is concluded that the necessary conditions of optimality tracking approach may potentially be appropriate for ITER operation, thus offering a viable closed-loop optimal control approach. Simulations of ITER advanced operation are necessary in order to assess the present ITER design and uncover the main difficulties that may be encountered during advanced operation. The DINA-CH&CRONOS full tokamak simulator is used to simulate the operation of the ITER hybrid and steady-state scenarios. It is concluded that the present ITER design is appropriate for performing a hybrid scenario pulse lasting more than 1000s, with a flat-top plasma current of 12MA, and a fusion gain of Q ∼= 8. Similarly, a steady-state scenario without internal transport barrier, with a flat-top plasma current of 10MA, and with a fusion gain of Q ∼= 5 can be realised using the present ITER design. The sensitivity of the advanced scenarios with respect to transport models and physical assumption is assessed using CRONOS. It is concluded that the hybrid scenario and the steady- state scenario are highly sensitive to the L-H transition timing, to the value of the confinement enhancement factor, to the heating and current drive scenario during ramp-up, and, to a lesser extent, to the density peaking and pedestal pressure

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

Toroidal simulations of nonlinear thresholds and saturations of classical and neoclassical tearing instabilities

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