The Berk-Breizman Model as a Paradigm for Energetic Particle-driven Alfven Eigenmodes

The achievement of sustained nuclear fusion in magnetically confined plasma relies on efficient confinement of high-energy ions produced by the fusion reaction. Such particles can excite Alfven Eigenmodes (AEs), which significantly degrade their confinement and threatens the vacuum vessel of future reactors. To develop diagnostics and control schemes, a better understanding of linear and nonlinear features of resonant interactions between plasma waves and high-energy particles, is required. In the case of an isolated single resonance, the problem is homothetic to the so-called Berk-Breizman (BB) problem, which is an extension of the classic bump-on-tail electrostatic problem, including external damping to a thermal plasma, and collisions. A semi-Lagrangian simulation code, COBBLES, is developed to solve the initial-value BB problem. The nonlinear behavior of instabilities in experimentally-relevant conditions is categorized into steady-state, periodic, chaotic, and frequency-sweeping (chirping) regimes. The chaotic regime is shown to extend into a linearly stable region, and a mechanism for such subcritical instabilities is proposed. Analytic and semi-empirical laws for nonlinear chirping characteristics, such as sweeping-rate, lifetime, and asymmetry, are developed and validated. Long-time simulations demonstrate the existence of a quasi-periodic chirping regime. Collisional drag and diffusion are shown to be essential to reproduce the alternation between major chirping events and quiescent phases, which is observed in experiments. Based on these findings, a fitting procedure between COBBLES simulations and chirping AE experiments is developped. This procedure, which yields local linear drive and external damping rate, is applied to Toroidicity-induced AEs (TAEs) on JT-60U and MAST tokamaks. This suggests the existence of TAEs relatively far from marginal stability

中性流体およびプラズマにおける亜臨界不安定性について

International audience亜臨界不安定性は，非線形不安定性の一種である．亜臨界不安定な系は，線形安定であっても非線形的に不安定となる．特徴として，不安定性が生じるための初期摂動の大きさに閾値が存在し，閾値以下の摂動は減衰し安定化する．亜臨界不安定性は，流体やプラズマにおいて広くみられる現象である．亜臨界不安定性は，乱流や構造形成，異常抵抗性や乱流輸送に本質的なインパクトを与えるため重要な問題である．この解説では，亜臨界不安定性の概念について解説し，様々な物理的局面における研究について紹介する

Subcritical Instabilities in Neutral Fluids and Plasmas

International audienceIn neutral fluids and plasmas, the analysis of perturbations often starts with an inventory of linearly unstable modes. Then, the nonlinear steady-state is analyzed or predicted based on these linear modes. A crude analogy would be to base the study of a chair on how it responds to infinitesimaly small perturbations. One would conclude that the chair is stable at all frequencies, and cannot fall down. Of course, a chair falls down if subjected to finite-amplitude perturbations. Similarly, waves and wave-like structures in neutral fluids and plasmas can be triggered even though they are linearly stable. These subcritical instabilities are dormant until an interaction, a drive, a forcing, or random noise pushes their amplitude above some threshold. Investigating their onset conditions requires nonlinear calculations. Subcritical instabilities are ubiquitous in neutral fluids and plasmas. In plasmas, subcritical instabilities have been investigated based on analytical models and numerical simulations since the 1960s. More recently, they have been measured in laboratory and space plasmas, albeit not always directly. The topic could benefit from the much longer and richer history of subcritical instability and transition to subcritical turbulence in neutral fluids. In this tutorial introduction, we describe the fundamental aspects of subcritical instabilities in plasmas, based on systems of increasing complexity, from simple examples of a point-mass in a potential well or a box on a table, to turbulence and instabilities in neutral fluids, and finally, to modern applications in magnetized toroidal fusion plasmas

Self-consistent gyrokinetic modelling of turbulent and neoclassical tungsten transport in toroidally rotating plasmas

The effect of toroidal rotation on both turbulent and neoclassical transport of tungsten (W) in tokamaks is investigated using the flux-driven, global, nonlinear 5D gyrokinetic code GYSELA. Nonlinear simulations are carried out with different levels of momentum injection that drive W to the supersonic regime, while the toroidal velocity of the main ions remains in the subsonic regime. The numerical simulations demonstrate that toroidal rotation induces centrifugal forces that cause W to accumulate in the outboard region, generating an in-out poloidal asymmetry. This asymmetry enhances neoclassical inward convection, which can lead to central accumulation of W in cases of strong plasma rotation. The core accumulation of W is mainly driven by inward neoclassical convection. However, as momentum injection continues, roto-diffusion, proportional to the radial gradient of the toroidal velocity, becomes significant and generate outward turbulent flux in the case of ion temperature gradient (ITG) turbulence. Overall, the numerical results from nonlinear GYSELA simulations are in qualitative agreement with the theoretical predictions for impurity transport, as well as experimental observations.Comment: 26 pages, 10 figures, to be publishe

Nonlinear excitation of subcritical fast ion-driven modes

International audienc

On the relationship between residual zonal flows and bump-on tail saturated instabilities

A connection is established between two classical problems: the non linear saturation of a bump-on tail instability in collisionless regime, and the decay of a zonal flow towards a finite amplitude residual. Reasons for this connection are given and commented

Gyrokinetics

DoctoralGyrokinetics is a self-consistent kinetic model of magnetised plasmas that applies to dynamical systems characterised by typical frequencies lower than the cyclotron frequency. Any gyrokinetic theory proceeds in two steps. The first one is the derivation of a gyrokinetic Vlasov equation for each charged species. This is done by building a new adiabatic invariant of motion, the magnetic moment, associated with a virtual particle, the gyrocentre, slightly shifted from the particle guiding-centre. It relies on a near-identity change of variables in a 8D extended phase space. This change of variables is not unique. Several options are discussed in this lecture note. The second part is the derivation of particle charge and current densities that enter the Maxwell equations, knowing the gyrocentre distribution functions. It appears that a magnetised plasma behaves as a medium that is both electrically polarised and magnetised. The resulting model encompasses one kinetic equation per species and the Maxwell equations. It can be used to address any self-consistent electromagnetic problem in magnetised plasmas, in particular instabilities and turbulent transport. Sections labelled with a star "*" can be skipped in a first reading. Notations can be found in Appendix A

The Berk-Breizman Model as a Paradigm for Energetic Particle-driven Alfvén Eigenmodes

en français : Le succès de la fusion nucléaire par confinement magnétique repose sur un confinement efficace des particules alpha, qui sont des ions hautement énergétiques produits par les réactions de fusion. De telles particules peuvent exciter des instabilités dans le domaine de fréquence des modes d'Alfvén (AEs) qui dégradent leur confinement et risquent d'endommager l'enceinte à vide de réacteurs futurs. Afin de développer des diagnostiques et moyens de contrôle, une meilleure compréhension des comportements linéaire et non-linéaire des interactions résonantes entre ondes plasma et particules énergétiques, qui constitue le but de cette thèse, est requise. Dans le cas d'une résonance unique et isolée, la description de la déstabilisation des AEs par des ions énergétiques est homothétique au problème de Berk-Breizman (BB), qui est une extension du problème classique de l'instabilité faisceau, incluant un amortissement externe vers un plasma thermique, et des collisions. Un code semi-Lagrangien, COBBLES, est développé pour résoudre le problème aux valeurs initiales de BB selon deux approches, perturbative (delta f) et auto-cohérente (full-f). Deux modèles de collisions sont considérés, à savoir un modèle de Krook, et un modèle qui inclue la friction dynamique et la diffusion dans l'espace des vitesses. Le comportement non-linéaire de ces instabilités dans des conditions correspondantes aux expériences est catégorisé en régimes stable, périodique, chaotique, et de balayage en fréquence (sifflet), selon le taux d'amortissement externe et la fréquence de collision. On montre que le régime chaotique déborde dans une région linéairement stable, et l'on propose un mécanisme qui résout le paradoxe que constitue l'existence de telles instabilités sous-critiques. On développe et valide des lois analytiques et semi-empiriques régissant les caractéristiques non-linéaires de sifflet, telles que la vitesse de balayage, la durée de vie, et l'asymétrie. Des simulations de longue durée démontrent l'existence d'un régime de sifflets quasi-périodiques. Bien que ce régime existe quel que soit l'un des deux modèles de collision, la friction et la diffusion sont essentielles pour reproduire l'alternance entre sifflets et périodes de repos, telle qu'observée expérimentalement. Grâce à ces découvertes, on développe une nouvelle méthode pour analyser des paramètres cinétiques fondamentaux du plasma, tels que le taux de croissance linéaire et le taux d'amortissement externe. Cette méthode, qui consiste à faire correspondre les simulations de COBBLES avec des expériences d'AEs qui présentent des sifflets quasi-périodiques, ne requiert aucun diagnostique interne. Cette approche est appliquée à des AEs induits par la toroidicité (TAEs) sur les machines JT-60 Upgrade et Mega-Amp Spherical Tokamak. On obtient des estimations de paramètres cinétiques locaux qui suggèrent l'existence de TAEs relativement loin de la stabilité marginale. Les résultats sont validés en recouvrant la croissance et décroissance de l'amplitude des perturbations mesurées, et en estimant les fréquences de collision à partir des données expérimentales d'équilibre.en anglais : The achievement of sustained nuclear fusion in magnetically confined plasma relies on efficient confinement of alpha particles, which are high-energy ions produced by the fusion reaction. Such particles can excite instabilities in the frequency range of Alfven Eigenmodes (AEs), which significantly degrade their confinement and threatens the vacuum vessel of future reactors. In order to develop diagnostics and control schemes, a better understanding of linear and nonlinear features of resonant interactions between plasma waves and high-energy particles, which is the aim of this thesis, is required. In the case of an isolated single resonance, the description of AE destabilization by high-energy ions is homothetic to the so-called Berk-Breizman (BB) problem, which is an extension of the classic bump-on-tail electrostatic problem, including external damping to a thermal plasma, and collisions. A semi-Lagrangian simulation code, COBBLES, is developed to solve the initial-value BB problem in both perturbative (delta f) and self-consistent (full-f) approaches. Two collision models are considered, namely a Krook model, and a model that includes dynamical friction (drag) and velocity-space diffusion. The nonlinear behavior of instabilities in experimentally-relevant conditions is categorized into steady-state, periodic, chaotic, and frequency-sweeping (chirping) regimes, depending on external damping rate and collision frequency. The chaotic regime is shown to extend into a linearly stable region, and a mechanism that solves the paradox formed by the existence of such subcritical instabilities is proposed. Analytic and semi-empirical laws for nonlinear chirping characteristics, such as sweeping-rate, lifetime, and asymmetry, are developed and validated. Long-time simulations demonstrate the existence of a quasi-periodic chirping regime. Although the existence of such regime stands for both collision models, drag and diffusion are essential to reproduce the alternation between major chirping events and quiescent phases, which is observed in experiments. Based on these findings, a new method for analyzing fundamental kinetic plasma parameters, such as linear drive and external damping rate, is developed. The method, which consists of fitting procedures between COBBLES simulations and quasi-periodic chirping AE experiments, does not require any internal diagnostics. This approach is applied to Toroidicity-induced AEs (TAEs) on JT-60 Upgrade and Mega-Amp Spherical Tokamak devices, which yields estimations of local kinetic parameters and suggests the existence of TAEs relatively far from marginal stability. The results are validated by recovering measured growth and decay of perturbation amplitude, and by estimating collision frequencies from experimental equilibrium data.PALAISEAU-Polytechnique (914772301) / SudocSudocFranceF