Heavy impurity transport in the presence of 3D MHD ideal perturbations

Heavy impurity accumulation poses a problem for the operation of tokamaks featuring tungsten plasma facing components. Early termination of the plasma due to tungsten accumulation is often observed following long living 3D MHD perturbations. Such scenarios areoften observed in present tokamaks like JET and ASDEX-U, and may be of concern for futuremachines like ITER and the European DEMO. Finding a way of designing high performancescenarios while preventing tungsten accumulation is therefore crucial. This thesis aims atunderstanding and modelling heavy impurity transport in tokamak plasmas in the presenceof long living 3D MHD ideal perturbations. In the first part of the thesis, we develop thetheoretical framework to treat the problem, building on stellarator theory for the main ions,while including the effect of strong toroidal rotation that is only present in tokamaks. Theorderings of the background ion species and the heavy impurity species are developed indetail. The background ions are subsonic which allows for the calculation of their flows usingthe stellarator 1/Îœ collisional regime, while the heavy impurities flow supersonically whichrequires the inclusion of centrifugal effects for the impurity description. An expression forthe neoclassical heavy impurity flux is obtained which helps identify the contrasting physicsinvolved. In the second part of the thesis, we present the development of the numerical toolsused to model the problem according to the theoretical framework presented. The usage ofthe VMEC code to obtain suitable 3D MHD equilibria is explained. Also, the development ofnew codes for calculating the background ion and heat flux flow of the ions, and the impurityflow from such magnetic equilbria is described. The heavy impurities are followed in thisbackground plasma using the VENUS-LEVIS code. This code describes the guiding-centermovement of the heavy impurities, accounting for the centrifugal and Coriolis drifts, as wellas for the correct effect of friction and thermal forces exerted by the background ions onthe impurities through a newly implemented collision operator. Finally, the numerical toolsdeveloped in this thesis are used to model the impact of long living 1/1 internal kink modeson heavy impurity transport. Heavy impurity accumulation is observed to occur rapidly inthe presence of a 1/1 internal kink mode, contrary to what is observed in axisymmetry, inwhich off-axis accumulation occurs due to the strong rotation. These cases agree well witha JET pulse where tungsten accumulates following rapid growth of a continuous 1/1 mode.In the weakly 3D phase of the pulse, off-axis accumulation of tungsten is observed, whilstin the strong 3D phase of the pulse, strong tungsten on-axis accumulation is observed. Thetheoretical developments allow us to break down all the relevant physics effects. It is seen thatsuch on-axis accumulation is due to the synergetic effect of the 1/1 mode, the strong toroidalrotation and the NTV ambipolar electric field.

Edge Localized Mode Control in TCV

Jonathan Rossel

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 à 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.

EPFL2012

Poloidal CX visible light plasma rotation diagnostics in TCV

Claudio Marini

Controlled thermonuclear fusion is the main goal of plasma physics. At the Swiss Plasma Center, the Tokamak `a Configuration Variable (TCV) constitutes the main experiment on fusion research, where high temperature plasmas are confined by means of magnetic fields. The confinement of plasma energy and particles is limited by transport arising from the gradients between the hot-dense plasma core and the cold-rarefied plasma edge. Due to the tokamak topology, plasma can rotate in the toroidal and poloidal directions. Plasma rotation has a strong influence on confinement and stability, which makes its understanding a priority. There are many discrepancies between the theoretical rotation description and experiments, which stimulated research in the field. In this context this work provided experimental results of unprecedented accuracy, where plasma impurity parameters are measured with the charge exchange recombination spectroscopy (CXRS) diagnostic. CXRS exploits the CX signal induced by a diagnostic neutral beam injector (DNBI), permitting localised measurements of impurity rotation, density and temperature. During this work, the CXRS diagnostic was extended with the development of a new high resolution system, termed CXRS-EDGE, devoted to the study of edge profiles. The accuracy improvements with respect to the legacy systems were obtained through an high throughput lens spectrometer and numerical aperture matching optics, resulting in rotation uncertainties

EPFL2017

Heavy Impurity Confinement in Hybrid Operation Scenario Plasmas with a Rotating 1/1 Continuous Mode

Wilfred Anthony Cooper, Jonathan Graves, David Pfefferlé, Madhusudan Raghunathan

In future tokamaks like ITER with tungsten walls, it is imperative to control tungsten accumulation in the core of operational plasmas, especially since tungsten accumulation can lead to radiative collapse and disruption. We investigate the behaviour of tungsten trace impurities in a JET-like hybrid-scenario with both axisymmetric and saturated 1/1 ideal helical-core in the presence of strong plasma rotation. For this purpose, we obtain the equilibria from VMEC and use VENUS-LEVIS, a guiding-centre orbit-following code, to follow heavy impurity particles. In this work, VENUS-LEVIS has been modified to account for strong plasma flows with associated neoclassical effects arising from such flows. We find that the combination of helical core and plasma rotation augments the standard neoclassical inward pinch compared to axisymmetry, and leads to a strong inward pinch of impurities towards the magnetic axis despite the strong outward diffusion provided by the centrifugal force, as frequently observed in experiments.

IOP Science2017

Edge Localized Mode Control in TCV

Jonathan Rossel

EPFL2012