Edge Localized Mode Control in TCV

The Tokamak concept, based on magnetic confinement of a hydrogen plasma, is one of today's most promising paths to energy production by nuclear fusion. The experimental scenarios leading to the largest fusion rate are based on a high confinement plasma regime, the H-mode, in which the energy and particle confinement are enhanced by a transport barrier located at the plasma edge and forming a pedestal in the plasma pressure profile. In standard axisymmetric magnetic configurations, stationary H-mode regimes suffer from instabilities of the plasma edge, the so-called edge localized modes (ELMs), leading to potentially damaging repetitive ejections of heat and particles toward the plasma facing components. In ITER, a Tokamak currently being built to demonstrate net power production from fusion, type I ELMs are expected to occur during high performance discharges. It is expected that the power flux released by these ELMs will cause an intolerable erosion and heat load on the plasma facing components. The control of ELMs, in terms of frequency and energy loss, is therefore of primary importance in the field of magnetic fusion and is subject to an intense research effort worldwide. This thesis, in line with this effort, focuses on two particular ELM control methods: local continuous or modulated heating of the plasma edge, and application of resonant magnetic perturbations (RMP). In this thesis, the effects of plasma edge heating on the ELM cycle have been investigated by applying electron cyclotron resonant heating (ECRH) to the edge of an H-mode plasma featuring type I ELMs in the Tokamak a Configuration Variable (TCV). As the power deposition location is shifted gradually toward the plasma pressure pedestal, an increase of the ELM frequency by a factor 2 and a decrease of the energy loss per ELM by the same factor are observed, even though the power absorption efficiency is reduced. This unexpected and, as yet, unexplained phenomenon, observed for the first time, runs contrary to the intrinsic type I ELM power dependence and provides a new approach for ELM mitigation. The effects of heating power modulation on the ELM cycle have also been experimentally investigated. It showed that power modulation synchronized in real-time with the ELM cycle is able to pace the ELMs with low deviation from a given frequency. Experimental results also clearly indicate that the ELM frequency purely remains a function of the heating power averaged over the ELM cycle, so that power modulation itself is not able to drive the ELM frequency and only has a stabilization effect. These results are in qualitative agreement with a simple 0D finite confinement time integrator model of the ELM cycle. RMP consists in applying a magnetic field perpendicular to the plasma magnetohydrodynamic equilibrium flux surfaces with a spatial variation tuned to align with the equilibrium magnetic field lines. If each coil of an RMP coil system (i.e. a set of toroidally and poloidally distributed coils) is powered with an independent power supply, the coil current distribution can be tuned to optimize the RMP space spectrum. In the course of this thesis, a multi-mode Lagrange method, with no assumption on the coil geometry or spatial distribution, has been developed to determine this optimum, in the limit of the vacuum magnetic field approximation. This method appears to be an efficient way to minimize the parasitic spatial modes of the magnetic perturbation, and the coil current requirements, while imposing the amplitude and phase of a set of target modes. A figure of merit measuring the quality of a perturbation spectrum with respect to RMP independently of the considered coil system or plasma equilibrium is also proposed. To facilitate the application of the Lagrange method, a spectral characterization of the coil system, based on a generalized discrete Fourier transform applied in current space, is performed to determine how spectral degeneracy and side-bands creation limit the number of simultaneously controllable target modes. Finally, this thesis sets the foundations of experimental research in the particular subject of RMP at CRPP by proposing a physics-based design for a multi-purpose saddle coil system (SCS) for TCV, a coil system located and powered such as to create a helical magnetic perturbation. Using independent power supplies, the toroidal periodicity of this perturbation is tunable, allowing simultaneously ELM control, error field correction and vertical control. Other experimental applications, like resistive wall mode and rotation control, are also in view. In this thesis, the adequacy of two SCS designs, an in-vessel one and an ex-vessel one, is assessed with respect to the desired experimental applications. The current requirements and the system performances are also characterized. The conducting vessel wall is accounted for in a model used to determine the coupled response functions of the SCS, the screening of the magnetic perturbation by the wall, the induced voltages and currents during a plasma disruption and the maximal magnetic forces exerted on the SCS. A scaling of the SCS parameters with the number of coil turns is presented and the issue of coil heating and cooling is discussed.