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

Model predictive control of resistive wall mode for ITER

Active feedback stabilization of the dominant resistive wall mode (RWM) for an ITER H-mode scenario at high plasma pressure using infinite-horizon model predictive control (MPC) is presented. The MPC approach is closely-related to linear-quadratic-Gaussian (LQG) control, improving the performance in the vicinity of constraints. The control-oriented model for MPC is obtained with model reduction from a high-dimensional model produced by CarMa code. Due to the limited time for on-line optimization, a suitable MPC formulation considering only input (coil voltage) constraints is chosen, and the primal fast gradient method is used for solving the associated quadratic programming problem. The performance is evaluated in simulation in comparison to LQG control. Sensitivity to noise, robustness to changes of unstable RWM dynamics, and size of the domain of attraction of the initial conditions of the unstable modes are examined.Comment: Original manuscript as submitted to Fusion Engineering and Desig

Investigation of intrinsic errors fields in MAST-U device (Oxford, UK)

In magnetic fusion devices, undesired non-axisymmetric magnetic field perturbations, typically called error fields, have been observed to have a detrimental effect on plasma stability and confinement. These spurious perturbations can arise from many sources, namely misalignment introduced in the construction of the device, imperfections in the manufacture of the field coils, 3D structures in the wall surrounding the plasma, current feeds and the presence of ferromagnetic materials near the plasma surface. Error fields with toroidal mode number n = 1 can destabilize magnetic islands in otherwise tearing-stable plasmas, as the m=2, n=1 mode (being m the poloidal mode number), leading to plasma termination. Moreover, error fields can inhibit the exploration of some operational regimes, such as at low density and at high-pressure, and within a plasma scenario, they can be also responsible of fast ion losses, rotation braking, thus causing plasma performance degradation. The main strategies that can be adopted to reduce n=1 error fields are: a careful alignment of the divertor, poloidal field coils, i.e. applying coil shift and tilt, when assembling a fusion device, and the installation of error field correction coils capable of inducing a magnetic field pattern which counteract the error field source. In this Thesis work, a database of 90 discharges performed in the MAST-U device, upgrade of the previous MAST tokamak, located at the Culham Centre for Fusion Energy, Oxfordshire, England, has been analyzed to achieve the following objectives: i) identify the n=1 error field and ii) investigate the dependence of the m=2, n=1 mode onset, i.e. the locked mode, with plasma density. During the assembly of MAST-U, to minimize the n=1 intrinsic error field due to the coil manufacturing, a careful alignment of the magnetic field coils has been applied. To assess the presence of a residual error field, the compass scan method has been executed. This method consists in triggering a locked mode by applying a n=1 probing error field with different phases and relies on an accurate detection of the locked mode onset. In this Thesis work, a robust and reliable tool able to detect such a triggering mechanism has been developed which allows to reach the objectives above mentioned. Thanks to its portability, such a tool can be also exploited for real-time applications, such as disruption avoidance, as proposed in the next MAST-U campaign.In magnetic fusion devices, undesired non-axisymmetric magnetic field perturbations, typically called error fields, have been observed to have a detrimental effect on plasma stability and confinement. These spurious perturbations can arise from many sources, namely misalignment introduced in the construction of the device, imperfections in the manufacture of the field coils, 3D structures in the wall surrounding the plasma, current feeds and the presence of ferromagnetic materials near the plasma surface. Error fields with toroidal mode number n = 1 can destabilize magnetic islands in otherwise tearing-stable plasmas, as the m=2, n=1 mode (being m the poloidal mode number), leading to plasma termination. Moreover, error fields can inhibit the exploration of some operational regimes, such as at low density and at high-pressure, and within a plasma scenario, they can be also responsible of fast ion losses, rotation braking, thus causing plasma performance degradation. The main strategies that can be adopted to reduce n=1 error fields are: a careful alignment of the divertor, poloidal field coils, i.e. applying coil shift and tilt, when assembling a fusion device, and the installation of error field correction coils capable of inducing a magnetic field pattern which counteract the error field source. In this Thesis work, a database of 90 discharges performed in the MAST-U device, upgrade of the previous MAST tokamak, located at the Culham Centre for Fusion Energy, Oxfordshire, England, has been analyzed to achieve the following objectives: i) identify the n=1 error field and ii) investigate the dependence of the m=2, n=1 mode onset, i.e. the locked mode, with plasma density. During the assembly of MAST-U, to minimize the n=1 intrinsic error field due to the coil manufacturing, a careful alignment of the magnetic field coils has been applied. To assess the presence of a residual error field, the compass scan method has been executed. This method consists in triggering a locked mode by applying a n=1 probing error field with different phases and relies on an accurate detection of the locked mode onset. In this Thesis work, a robust and reliable tool able to detect such a triggering mechanism has been developed which allows to reach the objectives above mentioned. Thanks to its portability, such a tool can be also exploited for real-time applications, such as disruption avoidance, as proposed in the next MAST-U campaign

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

Advanced Tools for Three-Dimensional Modeling and Control of Thermonuclear Fusion Devices

This thesis represents the summary of the research activities carried out during a three-years Ph.D. project. The work is divided into two parts, with the common feature of investigating the physical properties related to stability and control of Magneto-Hydro-Dynamic modes in fusion relevant plasmas. One of the aims of the work is to better understand the interaction between such plasmas and a wide range of 3-dimensional electro-magnetic boundary conditions. This part of the research has been carried out on the RFX-mod device, where advanced control strategies have been developed thanks to its state-of-the-art magnetic feedback system. A variety of interlaced problems have been addressed, starting with the improvement of the vacuum magnetic field spectrum through actuator-sensor decoupling, compensation of broken or deactivated coils with simple and real-time applicable strategies and multi-modal Resistive Wall Mode control with varying coil number and geometry. This has allowed to develop relevant control optimization techniques and knowledge for both the Reversed Field Pinch and Tokamak configurations. The former is an excellent playground for RWM studies, given the instability spectrum that is naturally developing. For the latter configuration instead, RWM stability is considered to be one major milestone to be achieved along the road to a commercial fusion reactor. The second part of the work is dedicated to this issue, and deals with the stability properties of Advanced Tokamak scenarios, with reference to the JT-60SA experiment in particular. Studies to understand RWM physics in high beta plasmas, where fluid rotation profiles and hot ions populations from Neutral Beams can play an important role, have been carried out with the MARS-F/K linear MHD codes. If detailed physics such as kinetic effects is coupled to a simplified description of the passive/active structures on one side, on the other hand a simplified plasma can be coupled to a complex 3-D model of the structures to assess realistic active control capabilities of a given system. Different tools are used and described for studying RWM damping physics, and to five a proof-of-principle for feedback control of such instabilities in Advanced Tokamak plasmas operating beyond the no-wall pressure limit

MODELING OF MHD INSTABILITIES IN EXISTING AND FUTURE FUSION DEVICES IN VIEW OF CONTROL

In questo lavoro viene presentata una versione migliorata del codice CarMa, chiamato CarMa-D, per lo studio di Resistive Wall Modes (RWMs) nei reattori a fusione termonucleare. Tale codice \ue8 in grado di rappresentare accuratamente le strutture conduttrici tridimensionali della macchina, e considerare simultaneamente nel modello gli effetti dovuti alla dinamica del plasma, alla toroidal rotation e agli effetti drift-cinetici. CarMa-D \ue8 il risultato dell\u2019accoppiamento dei codici CARIDDI, per lo studio delle correnti indotte nelle strutture conduttrici, e MARS-K per analisi di stabilit\ue0 MHD nel plasma. Punto di forza della strategia di accoppiamento alla base di CarMa-D \ue8 che non si basa sulle ipotesi semplificative su cui si basa la versione statica di CarMa, ovvero non vengono trascurati la massa del plasma, toroidal rotation e l\u2019effetto del damping cinetico. In questo modo la risposta del plasma a perturbazioni esterne dipende dall\u2019andamento temporale della perturbazione stessa: questo andamento viene approssimato per mezzo di funzioni razionali di Pad\ue9 a coefficienti matriciali. Il passo successivo \ue8 dato dalla combinazione della risposta di plasma approssimata con l\u2019equazione delle correnti indotte nelle strutture passive, per ottenere un modello matematico desctitto come un sistema di equazioni differenziali lineari formalmente uguale alla versione statica di CarMa, ma con un numero maggiori di gradi di libert\ue0 per tener conto della dinamica di plasma. La nuova versione del codice supera le principali limitazioni del modello originale, in particolare: (i) considerando la massa del plasma \ue8 possibile modellare modi con dinamiche molto veloci, come l\u2019external-kink ideale, (ii) il modello \ue8 in grado di tener conto rigorosamente di toroidal rotation e damping cinetico. Questi vantaggi rendono CarMa-D uno strumento potente, in grado di studiare fenomeni macroscopici in cui sia la dinamica del plasma, che gli effetti 3-D delle strutture, sono marcati. Inoltre, il modello matematico risultate \ue8 stato generalizzato per tener conto della simulazione pi\uf9 armoniche toroidali simultaneamente (multi-modal CarMa-D). Il codice \ue8 stato poi testato con successo su un equilibrio di riferimento dato da un plasma a sezione circolare, e successivamente per lo studio di stabilit\ue0 per i modi n = 1 e n = 2 su JT-60SA, Scenario 5. Infine, si \ue8 dimostrato come il modello matematico di CarMa-D possa essere scritto in una formulazione state-space, in vista di un successivo impiego nella progettazione di un controllo in retoazione per la stabilizzazione attiva dei RWMs