Analysis of global hydromagnetic instabilities driven by strongly sheared toroidal flows in tokamak plasmas

Recent numerical calculations have shown that while strong toroidal rotation can increase the external kink limit of tokamak plasmas, the associated rotation shear can drive a Kelvin-Helmholtz like global instability in the plasma, if the rotation frequency exceeds a threshold value (Chapman et al 2011 Plasma Phys. Control. Fusion 53 125002; Chapman et al 2012 Nucl. Fusion 52 042005). On the basis of a large aspect ratio toroidal expansion of the magnetohydrodynamic stability equations, the present paper investigates analytically various properties of this instability in tokamak plasmas with sonic toroidal flows and low magnetic shear in the core region. We also compare the analytical results with numerical code calculations. Many characteristic features and parameter dependences of the instability can be understood from the analytical theory, such as an eigenmode structure peaking at the position of largest rotation shear, and insensitivity of the growth rate to the plasma beta and to the precise value of the safety factor in the region of low magnetic shear. From an algebraic expression for the growth rate, valid asymptotically at large rotation frequencies, the drop in the dynamic pressure associated with the flow in the plasma can be identified as a major driving mechanism of the instability. For modes with (dominant) poloidal mode number m > 1, and rotating equilibria with isothermal magnetic surfaces, another driving mechanism of the instability is related to the centrifugally induced density variation along the magnetic field lines.

Electron Cyclotron Heating and Suprathermal Electron Dynamics in the TCV Tokamak

Silvano Gnesin

This thesis is concerned with the physics of suprathermal electrons in thermonuclear, magnetically confined plasmas. Under a variety of conditions, in laboratory as well as space plasmas, the electron velocity distribution function is not in thermodynamic equilibrium owing to internal or external drives. Accordingly, the distribution function departs from the equilibrium Maxwellian, and in particular generally develops a high-energy tail. In tokamak plasmas, this occurs especially as a result of injection of high-power electromagnetic waves, used for heating and current drive, as well as a result of internal magnetohydrodynamic (MHD) instabilities. The physics of these phenomena is intimately tied to the properties and dynamics of this suprathermal electron population. This motivates the development of instrumental apparatus to measure its properties as well as of numerical codes to simulate their dynamics. Both aspects are reflected in this thesis work, which features advanced instrumental development and experimental measurements as well as numerical modeling. The instrumental development consisted of the complete design of a spectroscopic and tomographic system of four multi-detector hard X-ray (HXR) cameras for the TCV tokamak. The goal is to measure bremsstrahlung emission from suprathermal electrons with energies in the 10-300 keV range, with the ultimate aim of providing the first full tomographic reconstruction at these energies in a noncircular plasma. In particular, suprathermal electrons are generated in TCV by a high-power electron cyclotron heating (ECH) system and are also observed in the presence of MHD events, such as sawtooth oscillations and disruptive instabilities. This diagnostic employs state-of-the-art solid-state detectors and is optimized for the tight space requirements of the TCV ports. It features a novel collimator concept that combines compactness and flexibility as well as full digital acquisition of the photon pulses, greatly enhancing its potential for full spectral analysis in high-fluency scenarios. Additional flexibility is afforded by the possibility to rotate the orientation of two of the cameras, permitting the crucial comparison of radiation emitted perpendicular and parallel to the primary magnetic field. The design of the HXR system was optimized through an extensive iterative simulation process with the aid of tomographic reconstruction codes as well as quasilinear Fokker-Planck modeling of ECH-driven TCV plasmas. In parallel, the selection of the detectors for this system was performed through comprehensive laboratory testing of several candidate detectors available on the market. While the design was completed in the course of the thesis work, commissioning of the system has only commenced recently with one of the four cameras installed on TCV. The first preliminary results, discussed in the last part of this thesis, include basic parameter scans of ECH wave-plasma interaction and the investigation of the dynamic response of suprathermal electrons to modulated ECH. In addition, the cameras possess the novel ability to discriminate against very high-energy γ-ray radiation that cannot be collimated and must thus be excluded from spatial distribution analysis. A basic study of the conditions for γ-ray suppression was conducted in preparation for future experiments. The Fokker-Planck modeling tool used in this diagnostic development was acquired through a collaboration with CEA-Cadarache, initially with the primary motivation of studying the simultaneous plasma heating by 2nd and 3rd harmonic electron cyclotron waves that is uniquely possible on TCV. This motivated a dedicated study, both theoretical and experimental, of one particular instance of this combined heating, which became a second primary subject of this thesis work. The particular scenario studied here is one in which a single ECH frequency is resonant at both harmonics in the same plasma. The primary objective of this study was to determine whether a synergy effect existed, permitting an enhancement of the intrinsically weak 3rd harmonic absorption by the suprathermal electrons generated at the 2nd harmonic resonance. An associated question was whether this effect, if it existed, was experimentally measurable or was in fact observed in TCV. The simulations performed in the course of this study indeed predict the existence of such a synergy, although the answer to the second question was ultimately negative, at least within the current technical limitations. This study has proven nevertheless highly valuable in providing new insight into the complex velocity-space dynamics that govern ECH wave-particle interaction and suprathermal electron dynamics.

EPFL2011

Ideal MHD stability of tokamak plasmas with moderate and low aspect ratio

The need of durable and abundant energy sources for future ages stimulates the studies of thermonuclear energy sources, based on hot plasma confinement by magnetic fields. The most developed concept of hot plasma trap is the tokamak, where the plasma confinement is obtained by a combination of external magnetic fields with the magnetic field of the current flowing in the plasma torus. The stability of the tokamak plasma is the main subject of the present work. The hot plasma is approximated by the model of the ideal magnetohydrodynamics (ideal MHD) as a superconductive liquid. Being relatively simple, this model describes basic plasma stability properties and establishes necessary stability conditions. The analytical ideal MHD theory is well developed, but some assumptions, required for analytical treatment may not be valid for the plasmas of modern tokamaks and for future tokamak-based reactors. To circumvent this numerical codes have been created. These codes are free from such limitations, but they are not as convenient in use as analytical formulae. In the present work the validity of the analytical approach for the conditions of tokamaks like TCV and MAST is examined in comparison with numerical code predictions by studying the dependence of the ideal MHD stability on plasma toroidicity and shape parameters. The experimental study of the plasma dependence on triangularity, carried out on the TCV tokamak, is consistent with the results of the numerical calculations. A new formula, describing the ideal MHD stability dependence on plasma toroidicity and shape parameters is proposed for use in modern tokamaks and future reactors. This formula could be used instead of analytical expansions, which are not valid in such conditions. The ideal MHD stability of highly elongated TCV plasmas has been studied using numerical codes and the optimum plasma shape, which allows higher plasma performance, was found. Experimental data on the high elongation plasmas in TCV are consistent with the numerical predictions. Advanced tokamak plasma configurations, which provide better plasma properties, are amongst the main goals of the TCV tokamak research activity. The ideal MHD stability analysis of such plasmas, using numerical codes, can be useful for optimization of plasma parameters, and designing new experiments with improved plasma performance. Reversed shear plasmas with internal transport barrier were analyzed and the influence of the plasma pressure and current profiles on the ideal MHD stability of these plasmas was examined in detail. By fine tuning of the electron cyclotron heating and current drive system of TCV it was found that it might be possible to improve the plasma performance in reversed shear plasmas, by creating the optimal current and pressure profiles.

EPFL2005

Model-based optimization of magnetic control in the TCV tokamak: design and experiments

Federico Pesamosca

Thermonuclear controlled fusion is a promising answer to the current energy and climate issues, providing a safe carbon-free source of energy which is virtually inexhaustible. In magnetic confinement thermonuclear fusion based on tokamak reactors, hydrogen fuel in the state of plasma is confined using a system of external and self-generated magnetic fields. This thesis contributes to the development of magnetic confinement fusion research by applying techniques derived from control engineering to designing magnetic controllers for tokamak plasmas. Specifically, a new design for feedback control of plasma shape and position in the TCV tokamak is provided, and its efficacy is studied in dedicated simulations and experiments.Elongated plasmas lead to improved plasma performance in tokamaks, which is key to sustaining fusion conditions in reactors. The required magnetic field for shaping the plasma column however results in an unstable equilibrium that makes feedback control of the vertical plasma position mandatory. Active stabilization of the axisymmetric plasma vertical instability is a standard feature of elongated tokamaks and will be a fundamental feature in the ITER magnetic control system, since a loss of vertical control and the subsequent plasma disruption can lead to unacceptable heat loads on the plasma facing components.The TCV tokamak is the ideal benchmark for investigating the effect of plasma shaping on tokamak physics and performance, with its system of 16 independently powered poloidal field coils and a vessel with an elongated cross section. Shape and position control are coupled problems in TCV as they share the same poloidal field coils as actuators, requiring a multivariable approach to designing magnetic controllers.In this thesis, controller design for TCV is based on a model for the coupled plasma-vessel-coils electromagnetic dynamics: the RZIp model. In this axisymmetric model, the plasma current distribution is fixed but is free to move radially and vertically in the poloidal plane of a toroidal reference frame. An extension to this model is suggested, relaxing the assumption of rigid displacement in the radial direction to include plasma shape deformation and leading to a semi-rigid RZIp model which better fits numerical equilibria.An improvement to the existing algorithm for shape and position control in TCV is then proposed. In this new approach, tuning of the plasma position controller, in charge of vertical stabilization, can be performed independently of the shape controller, which itself acts on a stable system. Static decoupling is achieved and the shape controller is designed on the basis of an improved model for the plasma deformation, which includes the plasma contribution to the static magnetic flux perturbation. Simulations in closed loop with the RZIp model are provided to evaluate several optimized schemes.Finally, the vertical controller is optimized including the plasma dynamics as part of the controller design. Structured H-infinity, extending classical H-infinity to fixed-structure control systems, is applied to obtain a controller using all available coils for position control, and in particular a coil combination optimized for vertical stabilization. Closed-loop performance improvement is demonstrated in dedicated TCV experiments, confirming the simulation results and paving the way for the routine integration of the optimized position and shape controller in TCV discharges.

EPFL2021