Tokamak Edge Plasma Turbulence Interaction with Magnetic X-Point in 3D Global Simulations

Turbulence in the edge plasma of a tokamak is a key actor in the determination of the confinement properties. The divertor configuration seems to be beneficial for confinement, suggesting an effect on turbulence of the particular magnetic geometry introduced by the X-point. Simulations with the 3D fluid turbulence code TOKAM3X are performed here to evaluate the impact of a diverted configuration on turbulence in the edge plasma, in an isothermal framework. The presence of the X-point is found, locally, to affect both the shape of turbulent structures and the amplitude of fluctuations, in qualitative agreement with recent experimental observations. In particular, a quiescent region is found in the divertor scrape-off layer (SOL), close to the separatrix. Globally, a mild transport barrier spontaneously forms in the closed flux surfaces region near the separatrix, differently from simulations in limiter configuration. The effect of turbulence-driven Reynolds stress on the formation of the barrier is found to be weak by dedicated simulations, while turbulence damping around the X-point seems to globally reduce turbulent transport on the whole flux surface. The magnetic shear is thus pointed out as a possible element that contributes to the formation of edge transport barriers.

Mirko Wensing

Thermonuclear fusion of light atoms is the primary energy source of stars, such as our Sun, that led to the emergence of life on Earth. However, its economic exploitation as a virtually unlimited and clean energy source is yet to be developed. One of the most promising designs for a nuclear fusion reactor is the tokamak, a toroidal device that uses strong magnetic fields to contain matter so it may be heated to fusion-relevant temperatures of

\sim 10^8\;^\circ

C. A substantial fraction of the heating power, required to maintain fusion-relevant plasma conditions, is transported across magnetic flux surfaces and channeled through a thin region of open magnetic field lines that surround the confined zone, the scrape-off layer, towards the plasma wall interface at the divertor targets. If left unmitigated, anticipated target heat fluxes in current reactor designs exceed the material limit and raise the need for an accurate predictive model of heat transport and power dissipation in the plasma edge to achieve a viable reactor configuration. This doctoral thesis is devoted to further understanding of divertor power exhaust, a key challenge on the way towards fusion energy, and contributes to the validation of such a predictive model, the SOLPS-ITER code. This work employs stringent comparisons between simulation results and experiments on the TCV tokamak to validate this model, where possible, and/or indicate remaining problems. This thesis presents the first scrape-off layer simulations that fully account for drifts, currents, carbon impurities and kinetic neutrals, for the TCV tokamak, and thereby provides unprecedented insight into drift-driven transport and plasma-neutral interaction within its divertor. In an initial stage, the SOLPS-ITER code was used to predict the effectiveness of divertor gas baffles to guide the first baffled TCV campaign. The experimental assessment in 2019 confirmed the essential simulation predictions. Drift simulations identify the diamagnetic current as the dominant cross-field contribution to the divertor charge balance. The resulting characteristics of target current profiles are tested and confirmed in TCV measurements. It is demonstrated, for the first time, that such electric currents give rise to a potential well below the magnetic X-point for the unfavorable magnetic field direction for H-mode access in highly resistive, i.e. low temperature, divertors. The simulation result is supported by reduced analytic models that highlight the underlying physics. The prediction is tested and confirmed in TCV experiments following novel diagnostic capabilities. The presence of such a potential well is shown to substantially reshape the divertor transport in detached divertor conditions. The simulations identify the

E\times B

-drift as the dominant radial transport channel for particles, heat and momentum in the divertor. A stringent comparison of simulation results to a wide set of edge-relevant diagnostics yields typically excellent qualitative agreement, but quantitative differences remain: the simulations conclude a colder and denser divertor plasma state with an overestimated neutral pressure. The identified shortcomings in this approach will contribute to further development towards a predictive divertor model of present day, and future fusion devices.

EPFL2021

Measurement of edge electrostatic turbulence in the TCV tokamak plasma boundary

Jan Horacek

Almost since the first density profile measurements were made in the scrape-off layer (SOL) of the early tokamaks, it has been recognized that the rate of particle transport perpendicular to magnetic surfaces exceeds that expected on the basis of classical collisional diffusion by as much as three orders of magnitude. Plasma turbulence has rightfully been claimed as the origin of such large discrepancies, much as it has for enhanced (over classical or neoclassical) transport rates observed in the confined plasma. But in the SOL, the "bursty" or "blobby" nature of the measured density fluctuations is of a much higher amplitude than that found in the core, making large-scale, convective fluid turbulence a strong candidate mechanism. This thesis will demonstrate quantitatively and unequivocally, for the first time, that such interchange motions are indeed the driver for the edge density and particle flux fluctuations observed on the Tokamak a Configuration Variable (TCV). Since the principle driver of this turbulence is a curved magnetic field, with gradient direction matching that of the local edge plasma pressure profile, together with a region of open magnetic field lines, the interchange mechanism identified here is very likely to be the very same process at the root of transport in all tokamak SOLs. In showing that the measured turbulence driven cross-field particle flux in TCV is quantitatively consistent with interchange physics, a path is opened by which the anomalous transport rates might be estimated in a predictive way for larger tokamaks, like the ITER device, which are yet to be built but for which concerns are now being raised that such transport might lead to excessive plasma-wall interactions. Using a fast reciprocating Langmuir probe, fluctuation measurements have been made in the TCV low-field-side SOL across a wide range of ohmic discharges comprising variations in plasma shape and configuration (limiter and divertor), plasma current, confinement mode (L and H), plasma density, toroidal magnetic field direction and plasma fuel species (deuterium and helium). Statistical analysis of the time series is used to demonstrate a remarkable degree of similarity across the database and to show that the radial dependence of the probability distribution functions (PDFs) of flux and density fluctuations can be well approximated by the known Gamma and Lognormal analytic PDFs, characterized in terms only of the relative fluctuation levels. In the vicinity of the SOL-main chamber interface, where particles interact with the walls, the density fluctuations exhibit clear evidence of self-similarity over two orders of magnitude in frequency and a PDF which is universal in shape. The observed constancy of the correlation between density and poloidal field fluctuations in turn implies a universal PDF for the radial particle flux which moreover is found to scale almost linearly with the local mean density. Careful comparison of one particular case inside the experimental database with the results of 2D fluid turbulence simulations of the TCV SOL using the ESEL code developed at the Risø National Laboratory, Denmark has shown a remarkable level of agreement between theory and experiment when the simulation output time series is analyzed in exactly the same way as that applied to the tokamak data. Quantitative agreement between model and experiment has been found for radial profiles of mean values, fluctuation levels, PDF shapes, timescales and power spectra of both density and turbulent driven flux throughout the main SOL and even partially inside the separatrix. Automatically, this level of agreement also implies that the code output conforms quite closely to the Gamma and Lognormal distributions. Parallel SOL flow data have also been gathered simultaneously with the turbulence measurements. An extensive database of radial Mach flow profiles has been assembled, most notably including a direct comparison of the density dependence of the flow dynamics in carefully matched discharges with forward and reversed toroidal field. These constitute the first measurements of their kind in TCV and reveal the presence of very strong flows, up to Mach numbers of ∼ 0.6. The magnitude and direction of the measured flows is found to be surprisingly well described by neoclassical return parallel flows (Pfirsch-Schlüter) compensating the poloidal ExB and diamagnetic drifts. Combining the forward and reversed field data uncovers a slight, field independent offset thought to originate from the excess transport, driven by the interchange motions, in the outboard midplane vicinity. The flow and fluctuation data have been combined to test the possible link between flow generation and turbulence first demonstrated from similar data on JET. No such correlations have been found on TCV throughout most of the SOL, supporting the finding that the neoclassical component can account for the majority of the measured parallel flow.

EPFL2006

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.

EPFL2006

Mirko Wensing