Plasma rotation and momentum transport studies in the TCV tokamak based on charge exchange spectroscopy measurements

Thermonuclear controlled fusion research is a highly active branch of plasma physics. The main goal is the production of energy from the fusion reaction of hydrogen isotope nuclei, the same reaction that powers stars. The most promising present approach are Tokamaks, toroidal devices where high temperature plasmas are confined by means of magnetic fields. This thesis is devoted to a detailed and systematic study of plasma rotation nthe Tokamak à Configuration Variable (TCV), at the Centre de Recherches en Physique des Plasmas (CRPP) in Lausanne Switzerland. In a tokamak, confinement is limited by particle and energy transport from the hot core to the cold edge and by macroscopic perturbations of magnetic equilibrium. Recently, plasma rotation has been demonstrated to beneficially affect both confinement and stability, explaining the great recent interest in plasma rotation studies Relatively little is understood about plasma rotation physics and, in particular, the so called "intrinsic" rotation that will constitute the main component of plasma rotation in next generation machines. That is why a great theoretical and experimental effort is being deployed in studying intrinsic rotation and this work is part of this context. In TCV, plasma rotation is measured by the Charge eXchange Recombination Spectroscopy diagnostic (CXRS). The spectroscopic signal comes from the perpendicular observation of a low power Diagnostic Neutral Beam Injector (DNBI), which applies a negligible torque to the plasma. Hence, the DNBI/CXRS pair is an effective tool for the experimental study of intrinsic tokamak plasma rotation. During this work, the pre existing toroidal observation view was complemented with two new systems, permitting the measurement of toroidal rotation, on inboard plasma radius, and poloidal rotation in the plasma periphery. The implementation of an automated wavelength calibration procedure, based on reference Neon spectra, permitted the first viable (toroidal and poloidal) rotation measurements of TCV, with uncertainties down to 1km/s. Using upgraded light collection optics and fiber optic transmission lines, simultaneous measurement of core and edge plasma was achieved, with a doubling of of the radial resolution of the toroidal rotation measurements. The measurable range of plasma parameters was also extended to higher densities by the installation of back illuminated CCD detectors. In the present configuration (CXRS09), the diagnostic is capable of routinely measuring toroidal and poloidal plasma rotations with a radial resolution of ≲ 1 cm and a sample frequency of 10 ÷ 20 Hz, for plasma densities of 0.8 ≲ ne,av ≲ 8 × 1019 m-3. The basic scenario of Ohmically heated discharges in limiter L-mode configuration was initially addressed. A large core toroidal rotation up to uφ ≈ 50 km/s in the counter current direction is measured, reversing nearly exactly upon reversal of plasma current Ip. The toroidal rotation profile may be schematically divided into a core, a peripheral and an intermediate region. For qe ≈ 3 (magnetic safety factor at the plasma edge) the core region velocity is relatively flat or slightly "bulged" in the co current direction inside the sawtooth inversion radius. In the peripheral region, the toroidal rotation is small with a monotonic intermediate region. The central rotation appears to be limited to approximately its value at the sawtooth inversion radius. Poloidal rotation uθ ≲ 3 km/s, measured in Ohmic discharges, is only weakly dependent on plasma parameters but reverses with reversed magnetic field, with values and direction coherent with neoclassical predictions. Combining uφ and uθ measurements, the profile of the radial electric field Er was estimated through the radial force balance equation. Er down to 8 kVm (inward directed) is found in the plasma bulk, and close to zero at the plasma edge. A spontaneous reversal of the toroidal rotation profile is observed when the average density exceeds ne,av ≈ 4 × 1019 m-3 at low qe ≈ 3, with the plasma now rotating in the co current direction. The transition between the co and counter rotation regimes is studied dynamically using ne and Ip ramps and with the application of Electro Cyclotron Heating (ECH). The rotation reversal is weakly sensitive to impurity concentration and positive plasma triangularity appears to be a key ingredient. Whilst a physical explanation has not been identified yet, dynamic uφ reversal observations indicate that it results from a changed balance of radial non-diffusive fluxes of toroidal momentum. The study was extended to the divertor magnetic configuration in which the plasma column rotates in the co current direction at low ne, and uφ reverses at high ne opposite from the limited configuration. The rotation profile may again be divided into three regions, although the rotation at the plasma periphery does not always remain close to zero but evolves with the plasma parameters. In particular, independently on the core rotation regime, peripheral uφ decreases with ne and Ip and is strongly sensitive to the ion B→ × ∇B direction, suggesting a link with parallel fluxes in the Scrape-Off Layer (SOL). Combined measurements of of CXRS and Mach probe indicate that in the plasma edge toroidal rotation matches the toroidal component of SOL flows. From the analysis of toroidal rotation in stationary and transient phases, a characterization of the momentum transport is presented. The resulting radial momentum diffusivity, of the order of Χφ ∼ 0.1 – 0.3 m2/s, exceeds by 2 orders of magnitude the neoclassical estimation. A remarkable result is the existence of a "residual stress" component, which sustains a substantial stationary rotation gradient for null background rotation. Conversely, the analysis suggests a minor role for the convective (pinch) component, that is preliminarily confirmed by gyro-kinetic simulations including turbulent Coriolis convective pinch. Neoclassical predictions are in quantitative and qualitative disagreement with the experimental observations. The effect of the sawtooth instability on the core rotation was addressed in a specific experimental scenario where the inter crash evolution of the core uφ could be measured. The measurement required the development of a fast CXRS acquisition scheme based on a trigger constructed in real time from a Soft X-ray measurement. At the sawtooth crash the plasma core undergoes a strong acceleration in the co current direction (∆uφ ≈ 9 km/s in the experimental scenario), possibly related to a strong transient toroidal electric field. The systematic and varied observations reported in this work extend the experimental knowledge of bulk plasma rotation in low confinement regimes. In particular, the rotation reversal phenomena constitute an important test for momentum transport models of tokamak plasmas.

A Far-Infrared Polarimeter Diagnostic for the Measurement of the Poloidal Magnetic Field in the TCV Tokamak

Information about the poloidal field inside the plasma and about the current density profile is essential for the understanding of the behavior of tokamak plasmas. The poloidal field outside the plasma edge is easily measured by a set of magnetic coils, whereas measurements of the magnetic field distribution inside the plasma requires dedicated and often complex diagnostic systems. One of the methods is polarimetry using beams of electromagnetic waves traversing the plasma. It makes use of the fact that the magnetic field modifies the refractive index of the plasma and as a consequence affects the state of polarization of the passing waves. Specifically, Faraday rotation refers to the case of a linearly polarized wave propagating parallel to a magnetic field. In this case, the rotation of the polarization vector is proportional to the product of electron density and parallel magnetic field component. This thesis is devoted to the design of a specific polarimeter system and its implementation on the TCV tokamak. The conceptual design took into account the particular requirements of the TCV experiments and its experimental program with particular interest in measurements of current density profiles in low-density, EC-heated plasmas. Aiming at optimum performance of the polarimeter in this parameter range, the FIR laser wavelength of 432.5 µm was chosen. Since TCV is already equipped with an interferometer (at 214 µm) for measurements of the line-integrated density along 14 chords, the polarimeter was built as a separate instrument. The number of 10 spatial channels to cover the plasma diameter was found as a compromise between desired spatial resolution, access constraints and cost. The measurement of the Faraday rotation angle is based on a method suggested by Dodel and Kunz [1], which uses optical beams with rotating linear polarization. In this case, the Faraday rotation angle is retrieved from a phase measurement comparing the modulated signals from the probe detectors with that from a reference detector and to first order is insensitive to amplitude variations of the signals. Waveguide detectors based on Schottky barrier diodes are used as detectors for their sensitivity and large electrical bandwidth. Signal processing and analysis is performed in two branches : a) using specifically built analog electronic phase detectors followed by slow (250 kHz) ADCs b) using fast (5 MHz) ADCs and numeric signal processing on a mainframe computer. The thesis covers the description of the design and the various components of the polarimeter, presents initial tests and an evaluation of its performance based on simulations using real plasma configurations of TCV. The analysis of specific tests with the system installed on TCV revealed the presence of perturbations leading to parasitic contributions to the measured phase angles. The results of first measurements of the Faraday rotation angle for different plasma conditions on TCV are presented. Comparing the measured Faraday rotation angles with the results of calculations showed qualitative agreement, in particular the effects of an increase in electron density and of the reversal of the current direction were clearly seen. The system is also capable to detect a radial displacement of the magnetic axis of the plasma, as was demonstrated by comparing measurements from two specific plasma configurations. However, the absolute values still show significant deviations from the expected ones based on calculations. The discrepancies increase with increasing Faraday angle and depend on the direction of the plasma current. At high electron densities beam refraction becomes a problem and may lead to significant errors in the measurements and eventually to complete loss of the signal in several channels. In its present status, the polarimeter cannot yet provide results that are suitable to reconstruct the poloidal field or the current density profile of the plasma. Tentative explanations for this problem are given, but further specific tests are necessary to confirm them. Even in its present state, the polarimeter may be used to detect transient relative changes in the profiles of electron density and current. This was demonstrated by a series of experiments in plasmas with sawtooth activity. Comparing the signals from the polarimeter with those from other multi-chord diagnostics (interferometer and soft X-ray detectors) clearly revealed correlations but also specific differences. These experimental studies showed that the Far-Infrared Polarimetry still requires further improvements, but has potential to become a valuable diagnostic capable of directly measuring the current density profile in the TCV tokamak.

EPFL2011

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

A Fast Ion Loss Detector for the TCV Tokamak

Lorenzo Stipani

A Fast Ion Loss Detector (FILD) was designed, assembled, installed and commissioned for TCV. This is a radially positionable, scintillator based detector that provides information on the 2D fast-ion velocity space lost at the probe's location. The collected particles are collimated inside the probe head and impinge upon a plate coated with a scintillator material that emits light. The photon flux is relayed to two acquisition systems: a sCMOS camera for high spatial resolution measurements of the emission locations in the scintillator, and fast photo-multipliers that allow time-correlation studies of fast-ion losses with high-frequency electromagnetic fluctuations. From its position with respect to the confined plasma and the fast-ion sources on TCV, FILD probes a small portion of the lost fast-ion phase space with high velocity-space and temporal resolution. Therefore, it naturally complements other available diagnostics such as neutral particle analysers, spectroscopy techniques for light emission from energetic particles following CX reactions, or neutron counters, which feature a broader, but less resolved, spatial coverage of fast-ion dynamics.The TCV-FILD design introduces some novelties for exploring new ranges of operation that may be adopted in similar systems for other Tokamaks, such as ITER. Two entrance slits can collect particles that circulate in co- and cntr-plasma current directions. This will be particularly useful when the second NBH system, injecting in the opposite toroidal direction, with particle energies that can excite strong Alfvénic modes, will be operated on TCV. A controlled pneumatic linear actuator radially positions the detector to expose the slits to the particle flux up to 9mm inward of the vessel wall. A plug-in design was conceived to facilitate diagnostic installation. The diagnostic was installed and commissioned during TCV experiments in 2020. The sensitivity of the detector to the local magnetic field line direction was investigated. The direction of the plasma current was found to select which of the two slits may be traversed by lost particles. The operational limits in discharges with NBH with total delivered energies up to 1MJ were assessed with the help of sensors monitoring the temperature of the probe head and cameras detecting visible light emissions resulting from the graphite shield heating by particle fluxes. Using FILD, fast-ion losses were detected for the first time on TCV in plasma discharges exhibiting strong MHD modes. Ejections of energetic ions were found correlated in time with Sawtooth crashes, as a sequence of individual events, and in strong phase coherence, as a continuous loss in time, with magnetic perturbations of a saturated and toroidally rotating magnetic island of a NTM. These observations, in addition to providing initial results on the relevant physics phenomena, stimulating further experiments and comparisons with theory, demonstrate the ability of TCV-FILD to provide valuable information in plasma discharges of interest for fast-ion studies. These measurements and additional information from other TCV diagnostics may now be combined to reconstruct, with tomographic inversion techniques, more of the fast-ion phase space. This will be used to identify the conditions for the excitation/suppression of magnetic instabilities, develop methods for their real-time control with heating and/or shaping actuators and investigate their dependencies on plasma parameters.

EPFL2021