Hierarchical Model Predictive Control in Fusion Reactors

Nuclear fusion still has to pass several milestones on its way to successful energy production, one of them being successful plasma stabilization. The present article presents an innovative control implementation related to plasma control for the generation of electricity with magnetically confined plasma. The implementation has been carried out over a specific device of tokamak type, called Tokamak it Configuration Variable (TCV). This novel hybrid control design allows for real time implementation of an optimal model predictive control over a large scale complex system with small time constant. At each closed loop iteration, the full model is first controlled by a straightforward controller, then the output values are used for model reduction so that finally the discretized control system is optimized only for the variables of interest. In the case of the TCV, this novel hybrid model predictive control enhances the power availability on the actuators and extends the pulse duration. Thus, this control strategy will help to achieve fusion energy stated goal of "ignition", where nuclear fusion generates as much energy as it is needed to start the reaction.

A Variable Structure Control Scheme Proposal for the Tokamak a Configuration Variable

Himank Anand, Yanis Andrebe, Patrick Blanchard, Yann Camenen, Francesco Carpanese, Oulfa Chellaï, Stefano Coda, Joan Decker, Basil Duval, Ambrogio Fasoli, Federico Alberto Alfredo Felici, Ivo Furno, Cristian Galperti, Timothy Goodman, Jonathan Graves, Jean-Philippe Hogge, Jan Horacek, Zhouji Huang, Rémy Jacquier, Josef Kamleitner, Alexander Karpushov, Mengdi Kong, Benoît Labit, Hoang Bao Le, Xavier Llobet, Claudio Marini, Yves Martin, Roberto Maurizio, Antoine Pierre Emmanuel Alexis Merle, Jean-Marc Moret, Federico Nespoli, Alessandro Pau, Laurie Porte, Holger Reimerdes, Paolo Ricci, Fabio Riva, Olivier Sauter, Christian Schlatter, Francesco Sciortino, Umar Sheikh, Joyeeta Sinha, Anna Teplukhina, Duccio Testa, Christian Gabriel Theiler, Minh Quang Tran, Cedric Kar-Wai Tsui, Kevin Henricus Annemarie Verhaegh, Nicola Vianello, Wouter Vijvers, Henri Weisen, Marco Wischmeier

Fusion power is the most significant prospects in the long-term future of energy in the sense that it composes a potentially clean, cheap, and unlimited power source that would substitute the widespread traditional nonrenewable energies, reducing the geographical dependence on their sources as well as avoiding collateral environmental impacts. Although the nuclear fusion research started in the earlier part of 20th century and the fusion reactors have been developed since the 1950s, the fusion reaction processes achieved have not yet obtained net power, since the generated plasma requires more energy to achieve and remain in necessary particular pressure and temperature conditions than the produced profitable energy. For this purpose, the plasma has to be confined inside a vacuum vessel, as it is the case of the Tokamak reactor, which consists of a device that generates magnetic fields within a toroidal chamber, being one of the most promising solutions nowadays. However, the Tokamak reactors still have several issues such as the presence of plasma instabilities that provokes a decay of the fusion reaction and, consequently, a reduction in the pulse duration. In this sense, since long pulse reactions are the key to produce net power, the use of robust and fast controllers arises as a useful tool to deal with the unpredictability and the small time constant of the plasma behavior. In this context, this article focuses on the application of robust control laws to improve the controllability of the plasma current, a crucial parameter during the plasma heating and confinement processes. In particular, a variable structure control scheme based on sliding surfaces, namely, a sliding mode controller (SMC) is presented and applied to the plasma current control problem. In order to test the validity and goodness of the proposed controller, its behavior is compared to that of the traditional PID schemes applied in these systems, using the RZIp model for the Tokamak a Configuration Variable (TCV) reactor. The obtained results are very promising, leading to consider this controller as a strong candidate to enhance the performance of the PID-based controllers usually employed in this kind of systems.

2019

Étude du transport d'énergie thermique dans les plasmas du tokamak à configuration variable au moyen de chauffage électronique cyclotronique

Yann Camenen

The development of controlled thermonuclear fusion, a quasi-unlimited energy source suitable for large scale electricity production, is one of the main goals of plasma physics research. Among the directions explored to date, the use of toroidal devices called tokamaks to create and confine hot plasmas using strong magnetic fields is particularly promising. The energy used to heat the plasma must remain well confined in order to achieve plasma temperatures higher than one hundred millon degrees for a sufficiently long period to obtain numerous fusion reactions. In the frame of efficient electricity production, maximising the energy confinement is also essential to achieve the required temperature with the lowest heating power. In tokamak plasmas, energy losses are mainly due to radiation and radial energy transport from the plasma core to the edge. A significant fraction of plasma physics research is therefore dedicated to the study of radial transport in tokamaks and the exploration of new operation regimes characterised by a low transport level. The development and optimisation of diagnostics used to observe plasmas is also part of this work. This thesis work, performed on the Tokamak à Configuration Variable (TCV) in Lausanne, covers the implementation and exploitation of a multi-channel soft X-ray detector with high spatial and temporal resolution, together with the development of the tomographic inversion routines used for data analysis. The detector, comprised of two superposed wire chambers, has been tested and calibrated using an X-ray source and then installed onto the tokamak. The position of the detector was chosen such as to observe the whole plasma cross-section with maximum spatial resolution leading to high quality tomographic inversions. A mobile absorber holder was installed between the plasma and the wire chambers. The energy range of the soft X-ray emission observed by the detector was thus chosen by selecting the appropriate absorber. These various features have made possible the use of the detector for numerous studies and in particular for the spatial and temporal characterisation of the plasma internal transport barrier formation. Plasma shaping abilities covering a wide range of plasma elongations and triangularities, including negative values, are one of the strengths of the TCV tokamak. For instance, plasmas with elongated cross-sections offer higher energy confinement as well as higher plasma current and pressure limits. However, the increase of the plasma vertical instability growth rate with elongation makes the vertical control of elongated plasmas difficult, in particular if the plasma current profile is too peaked. As the current profile is usually peaked for low plasma currents, current profile broadening is required there to achieve high elongation. During this thesis, a current profile broadening method based on temperature profile modification by localised EC heating has been studied in detail. The mechanism of this method has been documented and the optimal conditions for the EC power deposition determined. Using these conditions, the TCV operational space has been extended towards higher elongation at low current. The highest elongation obtained at low current has been increased by over 25% permitting the exploration of the plasma transport properties in this regime. The flexibility of the TCV EC heating system has also been used to investigate radial electron heat transport in L-mode plasmas. For the first time, the normalised temperature gradient has been varied by a factor of four and its influence on electron heat transport has been separated from that of the electron temperature. Electron heat transport increases strongly with the normalised temperature gradient, for values between 6 and 10, and then becomes independent of this parameter. In addition, electron heat transport increases with increasing electron temperature, decreasing density and increasing effective charge. The electron heat transport dependence on these three parameters can be cast as a single dependence on the plasma collisionality. TCV shaping abilities have then been used to test the influence of plasma triangularity. The main variations of the level of electron heat transport are described by a decrease of the electron heat diffusivity towards negative triangularity and high collisionality. At constant collisionality, electron heat transport is two times lower at a negative triangularity of –0.4 than at a positive triangularity of +0.4. Concerning micro-instabilities, gyro-fluid and gyro-kinetic simulations indicate that TEM and ITG instabilities are at play in these plasmas. The good qualitative agreement between the observed experimental dependencies and the predictions of simulations suggests strongly that the TEM instabilities are involved in the transport of electron heat. The experimental study provides dependable scaling of the electron heat transport on plasma parameters that can now be used to test the prediction of transport simulations. New elements such as the saturation of electron heat transport at high values of the normalised temperature gradient and the decrease of electron heat transport towards negative triangularities have been demonstrated.

EPFL2006

Extremely Shaped Plasmas to Improve the Tokamak Concept

Francesco Piras

Energy is essential for human existence and our future depends on plentiful and accessible sources of energy. The world population is fast growing and the average energy used per capita increases. One of the greatest challenges for human beings is that of meeting the growing demand for energy in a responsible, equitable and sustainable way. The possibility to obtain energy by "fusing" light atoms addresses these needs. Nuclear fusion reactions are clean, safe and the amount of fuel present on Earth (hydrogen isotopes) is practically inexhaustible and well distributed. Nuclear fusion is a natural process that occurs in all active stars like our Sun. Since the first demonstration of a deuterium fusion reaction (Rutherford 1933), researchers worldwide have tried to replicate this process on Earth by building a thermonuclear fusion reactor. Nevertheless, the challenge posed by the construction of a nuclear fusion reactor is greater than the one presented earlier by the development of a fission reactor. During the IAEA Conference in Geneva in the early 1958, L.A.Artsimovich declared: "Plasma physics is very difficult. Worldwide collaboration is needed for progress" and E.Teller, at the same conference: "Fusion technology is very complex. It is almost impossible to build a fusion reactor in this century". They were right. The extremely high temperature and density necessary to fuse hydrogen isotopes makes it difficult indeed to create a successful fusion reactor. Even though the physics of the fusion reaction appears clear, we are still facing problems on the road towards bulding the "box" that can efficiently confine the hot gas in the state of plasma. The best results so far have been obtained confining a plasma with strong magnetic fields in a toroidal configuration ("tokamak"). The Centre de Recherches en Physique des Plasmas in Switzerland actively studies this promising configuration towards the development of a nuclear fusion reactor. The experimental activity of the Tokamak à Configuration Variable (TCV) mainly focuses on the research of optimized plasma shapes capable of improving the global performance and solve the technological challenges of a tokamak reactor. Several theoretical and experimental results show the importance of the plasma shape in tokamaks. The maximum value of β (an indicator of the confinement efficiency) is for example related to the ratio between the height and the width of the plasma. The plasma shape can also affect the power necessary to access improved confinement regimes, as well as the plasma stability. This thesis reports on a contribution towards the optimization of the tokamak plasma shape. In particular, it describes the theoretical and experimental studies carried out in the TCV tokamak on two innovative plasma shapes: the doublet shaped plasma and the snowflake divertor. Doublet shaped plasmas have been studied in the past by the General Atomics group. Since then, the development of new plasma diagnostics and the discovery of new confinement regimes have given new reasons for interest in this unusual configuration. TCV is the only tokamak worldwide theoretically able to establish and control this configuration. This thesis illustrates new motivations for creating doublet plasmas. The vertical stability of the configuration is studied using a rigid model and the results are compared with those obtained with the KINX MHD stability code. The best strategy for controlling a doublet on TCV is also investigated, and a possible setup of the TCV control system is suggested for the doublet configuration. Analyzing the possible scenarios for doublet creation, the most promising scenario consists of the creation of two independent plasmas, which are subsequently merged to establish a doublet. For this reason, particular attention needs to be devoted to the problem of the plasma start-up. In this thesis, a general analysis of the TCV ohmic and assisted with ECH plasma start-up is presented, and recent attempts to create a doublet plasma are reported. Since the magnetic field reconstruction at the breakdown time is important to better diagnose these plasmas, the entire magnetic system of TCV has been calibrated with an original technique, also described in the manuscript. The last part of this thesis is devoted to the snowflake divertor configuration. This innovative plasma shape has been proposed and theoretically studied by Dr. D.D.Ryutov from the Lawrence Livermore National Laboratory. In Ryutov's articles, this configuration was proposed to alleviate the problems of the plasma-wall interaction and possibly affect the plasma edge stability. The TCV tokamak was the first to report the creation and control of a snowflake configuration, and the candidate was the principal investigator of this work. These results are accordingly discussed in this thesis. Details are provided in particular on the strategy used to establish the configuration. An edge-localized mode (ELM) H-mode regime, supported by electron cyclotron heating, has been successfully established in a snowflake. This regime exhibits 2 to 3 times lower ELM frequency but only a 20%-30% increase in normalized ELM energy (ΔWELM/WP ) compared to an identically-shaped, conventional, single-null, diverted H-mode. Enhanced stability of mid- to high-toroidal-mode-number ideal modes is consistent with the different snowflake ELM phenomenology. Finally, the capability of the snowflake to redistribute the edge power on the additional strike points has been confirmed experimentally and is also reported in this thesis.