Inline ECE measurements for NTM control on ASDEX Upgrade

The successful use of a tokamak for generating fusion power requires an active control of magnetic instabilities, such as neoclassical tearing modes (NTMs). Commonly, the NTM location is determined using electron cyclotron emission (ECE) and this is used to apply electron cyclotron heating (ECH) on the NTM location. In this paper, an inline ECE set-up at ASDEX Upgrade is presented in which ECE is measured and ECH is applied via the same path. First results are presented and a means to interpret the measurement data is given. Amplitude and phase with respect to a reference magnetic signal are calculated. Based on the amplitude and phase, the time of mode crossing is determined and shown to compare well with real-time estimates of the mode crossing time. The ECH launcher and [formula]; flux surface geometries at ASDEX Upgrade, which are optimized for current drive by a beam path that is tangential to the flux surface near deposition, make it difficult to identify the mode crossing without inline ECE launcher movement. Therefore, NTM control based on inline ECE requires launcher movement to determine and maintain a reliable estimate of the NTM location.</p

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

Strategies for Optimal Control of the Current and Rotation Profiles in the DIII-D Tokamak

The tokamak is currently the most promising device for realizing commercially-viable fusion energy production. The device uses magnetic fields to confine a circulating ring of hydrogen in the plasma state, i.e. a cloud of hydrogen ions and electrons. When sufficiently heated the hydrogen ions can overcome the electrostatic forces and fuse together, providing an overwhelmingly abundant energy source. However, 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, two key control issues are studied intensely, namely the optimization and control of the plasma current profile and control of the plasma rotation (or flow).In order to maximize performance, it is preferable that tokamaks achieve advanced scenarios (AT) characterized by good plasma confinement, improved magnetohydrodynamic stability, and a largely non-inductively driven plasma current. A key element to the development of AT scenarios is the optimization of the spatial distribution of the current profile. Also, research has shown that the plasma rotation can stabilize the tokamak plasma against degradations in the desired MHD equilibrium.In this thesis, new model-based control approaches for the current profile and rotation profile are developed to allow experimental exploration of advanced tokamak scenarios. Methods for separate control of both the current profile and rotation are developed. The advanced model-based control methods presented in this thesis have contributed to theory of tokamak profile control and in some cases they have been successfully validated experimentally in the DIII-D tokamak

Plasma Shape and Current Density Profile Control in Advanced Tokamak Operating Scenarios

The need for new sources of energy is expected to become a critical problem within the next few decades. Nuclear fusion has sufficient energy density to potentially supply the world population with its increasing energy demands. The tokamak is a magnetic confinement device used to achieve controlled fusion reactions. Experimental fusion technology has now reached a level where tokamaks are able to produce about as much energy as is expended in heating the fusion fuel. The next step towards the realization of a nuclear fusion tokamak power plant is ITER, which will be capable of exploring advanced tokamak (AT) modes, characterized by a high fusion gain and plasma stability. The extreme requirements of the advanced modes motivates researchers to improve the modeling of the plasma response as well as the design of feedback controllers. This dissertation focuses on several magnetic and kinetic control problems, including the plasma current, position and shape control, and data-driven and first-principles-driven modeling and control of plasma current density profile and the normalized plasma pressure ratio βN.The plasma is confined within the vacuum vessel by an external electromagnetic field, produced primarily by toroidal and poloidal field coils. The outermost closed plasma surface or plasma boundary is referred to as the shape of the plasma. A central characteristic of AT plasma regimes is an extreme elongated shape. The equilibrium among the electromagnetic forces acting on an elongated plasma is unstable. Moreover, the tokamak performance is improved if the plasma is located in close proximity to the torus wall, which guarantees an efficient use of available volume. As a consequence, feedback control of the plasma position and shape is necessary. In this dissertation, an H∞-based, multi-input-multi-output (MIMO) controller for the National Spherical Torus Experiment (NSTX) is developed, which is used to control the plasma position, shape, and X-point position.Setting up a suitable toroidal current profile is related to both the stability and performance of the plasma. The requirements of ITER motivate the research on plasma current profile control. Currently, physics-based control-oriented modeling techniques of the current profile evolution can be separated into two major classes: data-driven and first-principles-driven. In this dissertation, a two-timescale linear dynamic data-driven model of the rotational transform profile and βN is identified based on experimental data from the DIII-D tokamak. A mixed-sensitivity H∞ controller is developed and tested during DIII-D high-confinement (H-mode) experiments by using the heating and current drive (H&CD) systems to regulate the plasma rotational transform profile and βN around particular target values close to the reference state used for system identification. The preliminary experimental results show good progress towards routine current profile control in DIII-D. As an alternative, a nonlinear dynamic first-principles-driven model is obtained by converting the physics-based model that describes the current profile evolution in H-mode DIII-D discharges into a form suitable for control design. The obtained control-oriented model is validated by comparing the model prediction to experimental data. An H∞ control design problem is formulated to synthesize a stabilizing feedback controller, with the goal of developing a closed-loop controller to drive the current profile in DIII-D to a desirable target evolution. Simulations show that the controller is capable of regulating the system around the target rotational transform profile in the presence of disturbances. When compared to a previously designed data-driven model-based controller, the proposed first-principles-driven model-based controller shows potential for improving the control performance

Physics-model-based Optimization and Feedback Control of the Current Profile Dynamics in Fusion Tokamak Reactors

As the demand for energy continues to increase, the need to develop alternative energy sources to complement (and one day replace) conventional fossil fuels is becoming increasingly important. One such energy source is nuclear fusion, which has the potential to provide a clean source of energy and possesses an abundant fuel supply. However, due to the technological difficulty in creating the conditions necessary for controlled fusion to occur, nuclear fusion is not yet commercially viable. The tokamak is a device that utilizes magnetic fields to confine the reactants, which are in the plasma state, and it is one of the most promising devices capable of achieving controlled fusion. The ITER tokamak project is the next phase of tokamak development and will be the first tokamak reactor to explore the burning plasma (one with a significant amount of fusion reactions) operating regime.In order for ITER to meet its demanding goals, extensive research has been conducted to develop advanced tokamak operating scenarios characterized by a high fusion gain, good plasma confinement, magnetohydrodynamic stability, and a significant fraction of noninductively driven plasma current to maximize the plasma performance and potentially enable steady-state operation. As the dynamics of the tokamak plasma magnetic and kinetic states are highly coupled, distributed, nonlinear systems that exhibit many instabilities, it is extremely difficult to robustly achieve advanced operating scenarios. Therefore, active control of the plasma dynamics has significant potential to improve the ability to access advanced operating regimes. One of the key plasma properties investigated in the development of advanced scenarios is the plasma current profile because of its intimate relationship to plasma energy/particle transport and to plasma stability limits that are approached by increasing the plasma pressure. The plasma density and temperature profiles are also important parameters due to their close relationship to the amount of generated fusion power, to the total plasma stored energy, and to the amount of noninductive current drive. In tokamaks, the current and electron temperature profiles are coupled through resistive diffusion, noninductive current drive, and plasma energy/particle transport. As a result, integrated algorithms for current profile and electron temperature profile control will be necessary to maintain plasma stability, optimize plasma performance, and respond to changing power demand in ITER, and eventually a commercial, power producing tokamak reactor.In this work, model-based feedforward and feedback algorithms are developed to control the plasma current profile and thermal state dynamics with the goal of improving the ability to achieve robust tokamak operation. A first-principles-driven (FPD), physics-based approach is employed to develop models of the plasma response to the available actuators, which provides the freedom to handle the trade-off between the physics accuracy and the tractability for control design of the models. A numerical optimization algorithm to synthesize feedforward trajectories for the tokamak actuators that steer the plasma through the tokamak operating space to achieve a predefined target scenario (characterized by a desired current profile and total stored energy), subject to the plasma dynamics (described by the developed physics-based model), actuator constraints, and plasma state constraints, is developed. Additionally, robust feedback control algorithms for current profile, combined current profile + total stored energy, and simultaneous current profile + electron temperature profile control are synthesized for various tokamaks by embedding a FPD model into the control design process.Examples of the performance of the controllers in simulations (DIII-D, ITER, and TCV tokamaks) and DIII-D experiments are presented to illustrate the potential and versatility of the employed control methodology. The DIII-D experimental tests demonstrate the potential physics-model-based profile control has to provide a systematic approach for the development and robust sustainment of advanced scenarios. The ITER simulations demonstrate the ability to drive the current profile to a stationary target while simultaneously modulating the amount of fusion power that is generated. Finally, the TCV simulations demonstrate the ability to drive the current and electron temperature profiles to a self consistent target, as well as to maintain the current profile in a stationary condition while simultaneously modulating the electron temperature profile between equilibrium points

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