Self-consistent interaction of fast particles and ICRF waves in 3D applications of fusion plasma devices

Tokamaks and stellarators are the most promising reactor concepts using the magnetic confinement to contain the plasma fuel. Reactors capable of sustaining deuterium-tritium (D-T) fusion reactions requires the confinement of a very high temperature plasma (above 100 millions kelvin). In addition to external heating methods, the slowing down of alpha particles (helium-4 nuclei) born from D-T fusion reactions on the background plasma represents a significant source of plasma heating. The good confinement of fast particles is therefore one of the most important aspect of magnetic fusion devices. Furthermore, long plasma operation in future fusion reactors requires the control of inherent plasma instabilities. These instabilities are particularly dangerous in tokamaks because of the large plasma current necessary to establish the confining magnetic field. In this thesis we use the numerical code package SCENIC to study the application of Ion Cyclotron Range of Frequency (ICRF) waves to tokamak and stellarator devices. This numerical tool was built to self-consistently solve, in three dimensional configurations, the plasma magnetohydrodynamic (MHD) equilibrium, the ICRF wave propagation and the resonant ion distribution function. SCENIC is used to interpret how the sawtooth instability can be controlled in tokamaks by appropriate application of ICRF waves. This control method was successfully tested in the JET tokamak and it is foreseen to be applied in the future ITER tokamak. Such plasma degrading instabilities are not, however, expected in stellarators because they operate with no plasma current. The recently started stellarator Wendelstein 7-X (W7-X) must however prove experimentally that fast particles particles can be confined in an optimised quasi-isodynamic magnetic configuration. An efficient auxiliary source of fast ions is required in W7-X since it is not designed to procude alpha particles via D-T fusion reactions. In this thesis, we address the possibility of generating a significant fast ion population with ICRF waves in W7-X. SCENIC simulations are employed in order to identify relevant fast ion loss channels that may still exist in the W7-X quasi-omnigenous equilibrium. These simulations show that ICRF minority heating may not be suitable for producing fast ions in W7-X plasmas. It is found that a high energy tail is more likely to be developed if a three-ion species scheme is applied.

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

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.