Towards integrated control of tokamak plasmas: physics-based control of neoclassical tearing modes in the TCV tokamak

Neoclassical tearing modes (NTMs), magnetic islands located at rational $q$ surfaces, are an important class of resistive magnetohydrodynamics (MHD) instabilities in tokamak plasmas, with $q$ the safety factor. NTMs are one of the main constraints of the achievable plasma pressure by increasing the local radial transport and NTMs can lead to plasma disruptions. It is therefore crucial to understand the physics of NTMs and ensure their reliable control.

This thesis explores the physics and control of NTMs, by means of dedicated experiments in the TCV tokamak and interpretative simulations with the modified Rutherford equation (MRE), a model widely used in interpreting island width evolutions. Triggerless NTMs originating from unstable tearing modes (TMs, stability index $\Delta'>0$ ) and saturating under the effects of the perturbed bootstrap current are the main focus of this thesis.

In TCV, triggerless NTMs are reproducibly observed in low-density discharges with strong near-axis electron cyclotron current drive (ECCD), providing an excellent opportunity of studying these modes. Instead of direct computations of $\Delta'$ , a model for $\Delta'$ is developed based on extensive experiments and interpretative simulations. This model facilitates the clarification of the complete evolution of triggerless NTMs, from onset as TMs to saturation as NTMs. Our $\Delta'$ model also explains an unexpected density dependence of the onset of NTMs, where NTMs only occur with a certain range of density that broadens with increasing near-axis ECCD power and with lower plasma current. The density range is found to result from the density and plasma current dependence of the stability of ohmic plasmas and the density dependence of ECCD efficiency.

Given its high localization and flexibility, off-axis ECH/ECCD will be used for NTM control in future tokamaks. Comprehensive experimental and numerical studies of the dynamics of NTMs are carried out in this thesis, concerning both the stabilization of existing NTMs and the prevention of NTMs by means of preemptive off-axis ECCD. It is shown and predicted that the prevention of NTMs is much more efficient than NTM stabilization in terms of EC power. Interpretative simulations of the complex set of experiments constrain well the coefficients in the MRE and quantify NTM evolutions. The prevention effects from off-axis ECCD are found to result from local ECH/ECCD instead of a change of $\Delta'$ .

A key element of a reliable real-time (RT) control of NTMs is the alignment of EC beams with the target mode location. A small sinusoidal sweeping of the deposition location of EC beams around the target location proves to be effective for both NTM stabilization and prevention, making it a promising technique. Integrated control of NTMs, plasma pressure and model-estimated $q$ profiles is demonstrated on TCV, including advanced plasma state reconstruction, monitoring, supervision and actuator management. A RT-capable MRE module, based on our validated MRE, is developed for the first time and tested by extensive offline simulations for TCV and AUG. It provides a more intelligent physics-based NTM controller, aware of the EC power it requires to stabilize or prevent a given NTM. The information from the RT-MRE is also valuable for RT actuator allocations and decision-making in view of the overall integrated control, in particular for future long-pulse tokamaks like ITER and DEMO.

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

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

Federico Alberto Alfredo Felici

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.

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

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

Federico Alberto Alfredo Felici

EPFL2011

Edge Localized Mode Control in TCV

Jonathan Rossel

EPFL2012