Publications associées à Instabilité

Studying the effect of non-adiabatic passing electron dynamics on microturbulence self-interaction in fusion plasmas using gyrokinetic simulations

Microturbulence driven by plasma instabilities is in most cases the dominant cause of heat and particle loss from the core of magnetic confinement fusion devices and therefore presents a major challenge in achieving burning plasma conditions. The role of passing electron dynamics in turbulent transport driven by ion-scale microinstabilities, in particular Ion Temperature Gradient (ITG) and Trapped Electron Mode (TEM) instabilities, has been given relatively little attention. In first approximation, these particles, which are highly mobile along the confining magnetic field, are assumed to respond adiabatically to the low frequency ion-scale modes. However, near mode rational surfaces (MRSs), the non-adiabatic response of passing electrons becomes important and can no longer be neglected. This non-adiabatic electron response actually has a destabilising effect and leads to generation of fine-structures located at the MRSs of each eigenmode. This thesis focuses on the effects of non-adiabatic response of passing electrons in tokamak core turbulence. One such effect of non-adiabatic passing electrons that is of particular interest to this work is the self-interaction mechanism. It is essentially a process by which a microinstability eigenmode that is extended along the direction parallel to the magnetic field interacts non-linearly with itself, in turn generating E x B zonal flows. Unlike the usual picture of zonal flow drive in which microinstability eigenmodes coherently amplify the flow via modulational instabilities, the self-interaction drive of zonal flows from these eigenmodes are uncorrelated with each other. In the case of ITG driven turbulence, using novel statistical diagnostic methods, it is shown that the associated shearing rate of the fluctuating zonal flows therefore reduces as more toroidal modes are resolved in the simulation. In simulations accounting for the full toroidal domain, such an increase in the density of toroidal modes corresponds in fact to an increase in the system size, leading to a finite system size effect that is distinct from the other better known system size effects such as profile shearing or finite radial extend of the unstable region. The study of non-adiabatic passing electron dynamics is pursued further to include more reactor relevant conditions such as collisions and background shear flow. It is found that, with increasing collisionality, electrons behave more adiabatic-like, especially the trapped electrons away from MRSs, thereby leading to a decrease in the growth rate of ITG eigenmodes. Furthermore, the shortened electron mean free path in presence of collisions leads to a radial broadening of the fine-structures at the MRS of corresponding eigenmodes. In nonlinear simulations, the turbulent flux levels decrease with increasing collisionality, as a result of the reduced drive from the less unstable ITG eigenmodes. The radial width of the fine structures at MRSs is found to reduce with increasing collisionality as a result of reduced nonlinear modification of the eigenmodes in turbulence simulations. A study of the effect of collisions on the self-interaction mechanism reveals that for physically relevant values of collisionality, the effect of self-interaction is still significant. A preliminary study of the effect of background E x B flow shear shows that the fine-structures associated with the non-adiabatic passing electron response persist even with finite background flow.

EPFL2020

Open flows, such as wakes, jets, separation bubbles, mixing layers, boundary layers, etc., develop in domains where fluid particles are continuously advected downstream. They are encountered in a wide variety of situations, ranging from nature to technology. Such configurations are characterised by the development of strong instabilities resulting in observable unsteady dynamics. They can be categorised as oscillators which present intrinsic dynamics through self-sustained oscillations, or as amplifiers, which exhibit a strong sensitivity to external disturbances through extrinsic dynamics. Over the years, different linear and nonlinear approaches have been adopted to describe the dynamics of oscillators and amplifiers. However, a simplified physical description that accurately accounts for the nonlinear saturation of instabilities in oscillators as well as that of the response to disturbances in stable amplifier flows is still missing. In this thesis, this question is addressed by introducing a self-consistent semi-linear model. The model is formally constructed by a set of equations where the mean flow is coupled to a linear perturbation equation through the Reynolds stress. The full nonlinear fluctuating motion is thus approximated by a linear equation. The nonlinear dynamics of oscillators is studied in the cylinder wake, where the most unstable eigenmode of finite amplitude is coupled to the instantaneous mean flow for different oscillation amplitudes. This family of solutions provides an instantaneous mean flow evolution as a function of an equivalent slow time. A transient physical picture is formalised, wherein a harmonic perturbation grows and changes the amplitude, frequency, growth-rate and structure due to the modification of the instantaneous mean flow by the Reynolds stress forcing. Eventually this perturbation saturates when the flow is marginally stable. In contrast to standard linear stability analysis around the mean flow, the iterative solution of the model provides a priori an accurate prediction of the instantaneous amplitude, frequency and growth rate, as well as the flow fields, without resorting to any input from numerical or experimental data. Regarding noise amplifiers, the nonlinear saturation of the large linear amplification to external disturbances is studied in the framework of the receptivity analysis of the backward facing step flow. The self-consistent model is first introduced for harmonic forcing and later generalised to stochastic forcing by reformulating it conveniently in frequency domain. The results show an accurate prediction of the response energy as well as the flow fields. Hence, a similar picture is revealed, wherein the Reynolds stress dominates the saturation process. Despite the difference in the dynamics of the described flows, they share the same nonlinear saturation mechanism: the mean flow distortion.

EPFL2015

Suprathermal electron studies in Tokamak plasmas by means of diagnostic measurements and modeling

Josef Kamleitner

To achieve reactor-relevant conditions in a tokamak plasma, auxiliary heating systems are required and can be realized by waves injected in the plasma that heat ions or electrons under certain conditions. Electron cyclotron resonant heating (ECRH) is a very flexible and robust technique featuring localized power deposition and current drive (CD) capabilities. Its fundamental principles such as damping on the cyclotron resonance are well understood and the application of ECRH is a proven and established tool; electron cyclotron current drive (ECCD) is regularly used to develop advanced scenarios and control magnetohydrodynamics (MHD) instabilities in the plasma by tailoring the current profile. There remain important open questions, such as the phase space dynamics, the observed radial broadening of the suprathermal electron distribution function (e.d.f.) and discrepancies in predicted and experimental CD efficiency. These are addressed in this thesis. One of its main goals is indeed to improve the understanding of wave-particle interaction in plasmas and current drive mechanisms. This was accomplished by combined experimental and numerical studies, strongly based on the conjunction of hard X-ray (HXR) bremsstrahlung measurements and Fokker-Planck modeling, characterizing the suprathermal electron population. The hard X-ray tomographic spectrometer (HXRS) diagnostic was purposely developed to perform these studies, in particular by investigating spatial HXR emission asymmetries in the co- and counter-current directions and within the poloidal plane. The system uses cadmium-telluride (CdTe) detectors and digital acquisition to store the complete time history of incoming photon pulses. An extensive study of digital pulse processing algorithms was performed and its consequent application allows the HXRS to handle high count rates in a noisy tokamak environment. Numerous other numerical tools were developed in the course of this thesis, among others to improve the time resolution by conditional averaging and to obtain local information with the general tomographic inversion (GTI) package. The interfaces of the comparatively new LUKE code and well-established CQL3D Fokker-Planck (F-P) code to the tokamak à configuration variable (TCV) data were refurbished and a detailed benchmarking of these two codes was performed for the first time. Indeed, the theory-predicted toroidal and poloidal emission asymmetries could be consistently verified by experiment and modeling in many cases, including scans of a variety of plasma and wave parameters. The effects of supra-thermal electron diffusion and radio frequency (RF) wave scattering, both resulting in a radial broadening of the HXR emission, were separated by a poloidal deposition location angle scan. Furthermore, previous results on anomalous diffusion and CD efficiency were reproduced with increased confidence arising from enhanced diagnostic specifications. The plasma response to electron cyclotron (EC) absorption and the role of quasi-linear effects were investigated using the coherent averaging capabilities of the HXRS. Several MHD instabilities can occur in the plasma center and better understanding of these modes and events is indispensable for their mitigation in order to prevent their negative effects on confinement and stability. Sawtooth crashes are such a major instability and localized at the q=1 surface. They can be described as the evolution of an internal m=1 kink mode leading to [...]

EPFL2015

Instability of two-phase co-axial jets at small Reynolds number

Laura Augello

A precise knowledge of co-axial flow dynamics and a better understanding of the mechanisms that act to destabilize the interface between the two fluids is of fundamental interest in many industrial applications like lubricated transport, injection devices, atomization and controlled microdroplet production. The flow is in general unstable, since at least two mechanisms act to destabilize the cylindrical interface: shear and capillary instabilities. While these two mechanisms are active in a jet issuing from a tap, their respective influence strongly depends on the Reynolds number, the Ohnesorge number, but also on the viscosity, density, and aspect ratios. In this thesis, the global stability characteristics of two-phase co-axial flow are determined. The stability analysis follows two successive steps. First the steady base flow is determined, via the resolution of the nonlinear Navier-Stokes equations together with the location of the free interface. Second, these equations are linearized around the base flow and the dominant eigenmodes determined. The novelty lies in the formulation of models that can describe both the qualitative and quantitative characteristics of the two-phase flow configuration and the adaptation of the tools of global stability analysis for this configuration. We find that the dripping to jetting regime transition depends on the Capillary number, the degree of the confinement and the viscosity ratio, and we show that, surprisingly, the nozzle geometry does not affect the stability properties of the flow. Finally, the influence of surface viscosity on these coaxial flows has been considered. The governing and constitutive equations describing the continuum mechanics of the surface in the axisymmetric case are derived. With the addition of surface viscosity at the interface, the base flow evolves over a lengthscale which is much larger than the entry length in the Stokes regimes and than the typical unstable wavelength. We show that while the flow becomes eventually more convectively unstable once it reaches the fully developed profile, the surface viscosity creates an absolute region at the inlet, that is expected to promote droplet formation.

EPFL2015

Experimental investigation into localized instabilities of mixed Rayleigh-Bénard-Poiseuille convection

Emeric Grandjean

An experimental study of the stability of the Rayleigh-Bénard-Poiseuille flow was performed in a large transverse aspect ratio channel. The onset for the transverse thermo-convective rolls was determined as a function of the Reynolds number for two different fluids (water: Pr = 6.5 and mineral oil: Pr = 450). Then, the system impulse response was studied and a good agreement with theory was found for the convective/absolute instability transition. Finally the response of the system to localized heating was observed and compared with analytical and numerical results by Martinand, Carrière and Monkewitz (2004 & 2006): experimental thermo-convective global modes are found to correspond to the saturated "steep" variety constructed by Pier, Huerre and Chomaz (2001).

EPFL2008

Understanding the destabilizing role for surface tension in planar shear flows in terms of wave interaction

Luca Biancofiore, François Gallaire

Both surface tension and buoyancy force in stable stratification act to restore perturbed interfaces back to their initial positions. Hence, both are intuitively considered as stabilizing agents. Nevertheless, the Taylor-Caulfield instability is a counterexample in which the presence of buoyancy forces in stable stratification destabilize shear flows. An explanation for this instability lies in the fact that stable stratification supports the existence of gravity waves. When two vertically separated gravity waves propagate horizontally against the shear, they may become phase locked and amplify each other to form a resonance instability. Surface tension is similar to buoyancy but its restoring mechanism is more efficient at small wavelengths. Here, we show how a modification of the Taylor-Caulfield configuration, including two interfaces between three stably stratified immiscible fluids, supports interfacial capillary gravity whose interaction yields resonance instability. Furthermore, when the three fluids have the same density, an instability arises solely due to a pure counterpropagating capillary wave resonance. The linear stability analysis predicts a maximum growth rate of the pure capillary wave instability for an intermediate value of surface tension corresponding to We(-1) = 5, where We denotes the Weber number. We perform direct numerical nonlinear simulation of this flow and find nonlinear destabilization when 2

Amer Physical Soc2017

Improving the Turbulence Coupling between High Resolution Numerical Weather Prediction Models and Lagrangian Particle Dispersion Models

Balazs Szintai

For the modelling of the transport and diffusion of atmospheric pollutants during accidental releases, sophisticated emergency response systems are used. These modelling systems usually consist of three main parts. The atmospheric flow conditions can be simulated with a numerical weather prediction (NWP) model. The evolution of the pollutant cloud is described with a dispersion model of variable complexity. The NWP and the dispersion models have to be coupled with a so-called meteorological pre-processor. This means that all the necessary – in most cases turbulence related – variables which are not available from the standard output of the NWP model have to be diagnosed. The main difficulty of the turbulence coupling is that these subgrid scale variables of NWP models are not routinely verified and thus little is known concerning their quality and impact on dispersion processes. The general aim of the present work is to better understand and improve this coupling mechanism. For this purpose all the three main components of the emergency response system of MeteoSwiss are carefully evaluated and possible improvement strategies are suggested. In the first part, the NWP component of the system, namely the COSMO model, is investigated focusing on the model performance in the Planetary Boundary Layer (PBL). Three case studies, representing both unstable and stable situations, are analyzed and the COSMO simulations are validated with turbulence measurements and Large Eddy Simulation (LES) data. It is shown that the COSMO model is able to reproduce the main evolution of the boundary layer in dry convective situations with the operational parameter setting. However, it is found that the COSMO model tends to simulate a too moist and too cold PBL with shallower PBL heights than observed. During stable conditions the operational parameter setting has to be significantly modified (e.g., the minimum diffusion coefficient) to obtain a good model performance. The turbulence scheme of COSMO, which carries a prognostic equation for Turbulent Kinetic Energy (TKE), is studied in detail to understand the shortcomings of the simulations. The turbulent transport term (third order moment) in the TKE equation is found to be significantly underestimated by the COSMO model during unstable situations. This results in inaccurate TKE profiles and hence missing entrainment fluxes at the top of the PBL. A solution to increase the TKE transport in the PBL is proposed in the present work and evaluated during a three-month continuous period. While improving the TKE profile substantially, the modification is demonstrated to not impair other model output characteristics. The second component of the emergency response system, namely the meteorological pre-processor, is also validated on case studies and a continuous period. The main objective of this analysis is to compare the currently operational coupling approach, which is based on the direct usage of the prognostic TKE from the COSMO model, to a classical approach based on similarity theory considerations, thereby using turbulence measurements on the one hand and LES data on the other hand. To be able to use similarity theory approaches for the determination of turbulence characteristics, the PBL height has first to be diagnosed from the NWP model. In the present study, several approaches for the determination of PBL height have been implemented and validated with radio sounding measurements. Based on the verification results and the operational convenience, the method based on the bulk Richardson number method has been chosen for the diagnosis of the PBL height. Validation results of post-diagnosed turbulence characteristics show that during convective situations, the similarity approach tends to overestimate the turbulence intensity, while the approach based on the direct usage of TKE yields more accurate results. For stable conditions the different approaches are closer to each other and both give reasonable predictions. It is found that the main drawback of the direct approach is the isotropic assumption in the horizontal direction. A new hybrid method is proposed which uses similarity considerations for the partitioning of horizontal TKE between along-wind and cross-wind directions. In the last part, pollutant dispersion in complex terrain is studied using a new scaling approach for TKE that is suited for steep and narrow Alpine valleys. This scaling approach is introduced in the interface between COSMO and a Lagrangian particle dispersion model (LPDM), and its results are compared to those of a classical similarity theory approach and to the operational coupling type, which uses the TKE from the COSMO model directly. For the validation of the modelling system, the TRANSALP-89 tracer experiment is used, which was conducted in highly complex terrain in southern Switzerland. The ability of the COSMO model to simulate the valley-wind system is assessed with several meteorological surface stations. The dispersion simulation is evaluated with the measurements from 25 surface samplers. The sensitivity of the modelling system towards the soil moisture, horizontal grid resolution, and boundary layer height determination is investigated. It is shown that if the flow field is correctly reproduced, the new scaling approach improves the tracer concentration simulation compared to the classical coupling methods.

EPFL2010

High Intensity Beam Issues in the CERN Proton Synchrotron

Sandra Aumon

This PhD work is about limitations of high intensity proton beams observed in the CERN Proton Synchrotron (PS) and, in particular, about issues at injection and transition energies. With its 53 years, the CERN PS would have to operate beyond the limit of its performance to match the future requirements. Beam instabilities driven by transverse impedance and aperture restrictions are important issues for the operation and for the High-Luminosity LHC upgrade which foresees an intensity increase delivered by the injectors. The main subject of the thesis concerns the study of a fast transverse instability occurring at transition energy. The proton beams crossing this energy range are particularly sensitive to wake forces because of the slow synchrotron motion. This instability can cause a strong vertical emittance blow-up and severe losses in less than a synchrotron period. Experimental observations show that the particles at the peak density of the beam longitudinal distribution oscillate in the vertical plane due to a short range wake field and following a travelling wave of about 700 MHz. In order to perform measurements, a dedicated single bunch beam was set up with a zero chromaticity plateau around transition energy. Extensive measurements were performed of the dynamics of instability in order to compute rise times and intensity thresholds. These measurements were done for several peak densities and the results show that the longer the bunch length, the higher is the threshold in intensity. Other measurements performed with a small negative chromaticity and another working point show that the intensity threshold can be pushed at higher values—in this case, the threshold was increased by 20%. The particularity of this work is that the instability is triggered during the acceleration. At transition energy, the momentum compaction factor is zero and the exchange of particles between the head and the tail of the beam from synchrotron motion, which is a natural way to damp instabilities, vanishes for few turns. Therefore the measurements at which η the instability is triggered are fundamental to know in which longitudinal regime the instability develops. Macro particle simulations were performed in order reproduce the dynamics of the instability with the HEADTAIL code, that simulates the beam interaction with the impedance of the machine. In the case of the PS, a very detailed impedance model does not exist, therefore a very simple resonator impedance was considered. The parameters of the code were adapted in order to simulate the beam as close as possible to the experimental conditions. The simulations showed that the travelling wave is well reproduced and therefore rise times were extracted for different beam intensities and compared to the measurements. A good agreement is found for a such simple impedance model. The intensity thresholds are reproduced for zero chromaticity within 30% and it is clear that some damping mechanisms occurring in the measurements are not reproduced by the code. In particular, octupolar components of the field, non-linear coupling and transverse space charge are not taken into account. These limitations could cause some discrepancies between model and measurements. This study allows to establish a broadband impedance model which can be use to predict the dynamics of the instability. A few experiments were done also with the use a gamma transition jump. In this case, the instability appears in the adiabatic regime and the rising of the instability is following the peak density of the beam. Both the intensity threshold measurements and the simulations show that the gamma jump is by far the most efficient way to increase significantly the intensity threshold. The choice of adequate working point appears also to be a cure of the instability. This study with the support of measurements provides a rough impedance model confirmed by simulations and an understanding of the different mechanisms triggering the instability. The last part of the thesis is dedicated to proton beam losses studies at injection energy. An eventual upgrade of the high intensity beam is limited by large beam losses at injection in the PS. Losses were measured with the current beam loss monitor system of the PS that they occur while the incoming beam enters in the machine and then during several hundred turns while the beam is circulating. Optics measurements were performed to check the mismatch of the transfer line between the PSBooster and the PS. A significant horizontal dispersion mismatch was found and in particular a difference in optics between the four injection lines of the PS. Aperture bottlenecks were found at the injection septum in both transverse planes and at the maximum of the injection bump. With the help of Monte Carlo simulations, the high radiation outside the ring induced by the losses was understood. However, the mismatch does not explain the continuous losses after the beam is injected. A possible explanation is that the space charge forces contribute to make particles cross resonances and are lost while they are oscillating at high amplitudes. The transverse phase space is refilled due to the combination of the synchrotron motion and space charge. Several solutions were proposed to improve the situation. A new optics of the transfer line and at injection could make the beam size smaller. Some special quadrupoles already installed in the PS could be used to adapt the optics of the incoming beam. Increase the injection energy from 1.4 GeV to 2 GeV kinetic would cause a gain of 65% in space charge forces, and these studies are currently ongoing for the upgrade of the PS in the framework of high-intensity LHC upgrade project. High intensity beams are also perturbed by space charge forces and transverse instabilities. Coherent tune shift measurements were performed at injection and extraction in order to evaluate the transverse imaginary part of the impedance and the contribution of the space charge to betatron frequency shift with the beam intensity.

EPFL2012

TRANSVERSE MODE COUPLING INSTABILITY MEASUREMENTS AT TRANSITION CROSSING IN THE CERN PS

Sandra Aumon

Transition crossing in the CERN PS is critical for the stability of high intensity beams, even with the use of a second order gamma jump scheme. The intense single bunch beam used for the neutron Time-of-Flight facility (n-ToF) needs a controlled longitudinal emittance blowup at flat bottom to prevent a fast single-bunch vertical instability from developing near transition. This instability is believed to be of Transverse Mode Coupling (TMCI) type. A series of measurements taken throughout 2009 and 2010 aims at using this TMCI observed on the ToF beam at transition, as a tool for estimating the transverse global impedance of the PS. For this purpose, we compare the measurement results with the predictions of the HEADTAIL code and find the matching parameters. This procedure allows a better understanding of the different mechanisms involved and can suggest how to improve the gamma jump scheme for a possible intensity upgrade of the n-ToF beam.

2010

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We study the linear spatiotemporal stability of an infinite row of equal point vortices under symmetric confinement between parallel walls. These rows of vortices serve to model the secondary instability leading to the merging of consecutive (Kelvin-Helmholtz) vortices in free shear layers, allowing us to study how confinement limits the growth of shear layers through vortex pairings. Using a geometric construction akin to a Legendre transform on the dispersion relation, we compute the growth rate of the instability in different reference frames as a function of the frame velocity with respect to the vortices. This approach is verified and complemented with numerical computations of the linear impulse response, fully characterizing the absolute/convective nature of the instability. Similar to results by Healey on the primary instability of parallel tanh profiles [J. Fluid Mech. 623, 241 (2009)], we observe a range of confinement in which absolute instability is promoted. For a parallel shear layer with prescribed confinement and mixing length, the threshold for absolute/convective instability of the secondary pairing instability depends on the separation distance between consecutive vortices, which is physically determined by the wavelength selected by the previous (primary or pairing) instability. In the presence of counterflow and moderate to weak confinement, small (large) wavelength of the vortex row leads to absolute (convective) instability. While absolute secondary instabilities in spatially developing flows have been previously related to an abrupt transition to a complex behavior, this secondary pairing instability regenerates the flow with an increased wavelength, eventually leading to a convectively unstable row of vortices. We argue that since the primary instability remains active for large wavelengths, a spatially developing shear layer can directly saturate on the wavelength of such a convectively unstable row, by-passing the smaller wavelengths of absolute secondary instability. This provides a wavelength selection mechanism, according to which the distance between consecutive vortices should be sufficiently large in comparison with the channel width in order for the row of vortices to persist. We argue that the proposed wavelength selection criteria can serve as a guideline for experimentally obtaining plane shear layers with counterflow, which has remained an experimental challenge.

2018