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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., 26 pages, 10 figures, to be published

International audience

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．

Équipe 107 : Physique des plasmas chauds; International audience; In a collisionless plasma, it is known that linearly stable modes can be destabilized (subcritically) by the presence of structures in phase space. However, nonlinear growth requires the presence of a seed structure with a relatively large threshold in amplitude. We demonstrate that, in the presence of another, linearly unstable (supercritical) mode, wave-wave coupling can provide a seed, which is significantly below the threshold, but can still grow by (and only by) the collaboration of fluid and kinetic nonlinearities. By modeling the subcritical mode kinetically, and the impact of the supercritical mode by simple wave-wave coupling equations, it is shown that this new kind of subcritical instability can be triggered, even when the frequency of the supercritical mode is rapidly sweeping. The model is applied to the bursty onset of geodesic acoustic modes in a LHD experiment. The model recovers several key features such as relative amplitude, time scales, and phase relations. It suggests that the strongest bursts are subcritical instabilities, driven by this mechanism of combined fluid and kinetic nonlinearities.

Équipe 107 : Physique des plasmas chauds; International audience; We have tested the telegraph equation for transport dynamics in magnetized plasma by comparing its results with experimental observations in the Large Helical Device [S. Inagaki et al., Nucl. Fusion 53, 113006 (2013)]. The telegraph equation includes a finite relaxation time for turbulence intensity in response to the changes in global plasma parameters. This model was applied to nondiffusive radial heat pulse propagation under the periodic modulation of the heating power. The model showed some success in reproducing the amplitudes of higher harmonics. However, the phase relation between the temperature gradient and heat flux was opposite to that in experimental observations.

In the presence of wave dissipation, phase-space structures emerge in nonlinear Vlasov dynamics. Their dynamics can lead to a nonlinear continuous shifting of the wave frequency (chirping). This report summarizes my personal contribution to these topics in the fiscal year 2012. The effects of collisions on chirping characteristics were investigated, with a one-dimensional beam-plasma kinetic model. The long-time nonlinear evolution was systematically categorized as damped, steady-state, periodic, chaotic and chirping. The chirping regime was sub-categorized as periodic, chaotic, bursty, and intermittent. Existing analytic theory was extended to account for Krook-like collisions. Relaxation oscillations, associated with chirping bursts, were investigated in the presence of dynamical friction and velocity-diffusion. The period increases with decreasing drag, and weakly increases with decreasing diffusion. A new theory gives a simple relation between the growth of phase-space structures and that of the wave energy. When dissipation is modeled by a linear term in the field equation, simple expressions of a single hole growth rate and of the initial perturbation threshold are in agreement with numerical simulations., 8 pages, 11 figures

International audience; Wave-particle interaction is a defining paradigm of plasma physics. Nonlinear problems arise in the ITER-relevant context of energetic particle (EP) interaction with Alfvén waves, collisionless trapped electron mode turbulence and transport, trapped ion ITG instabilities, radio-frequency heating and magnetic reconnection. In this paper, we report on fundamental advances in the understanding of nonlinear trapping and its effects on stability, saturation, turbulence and transport. These results have broad implications for EP instabilities, drift-wave turbulence and transport, and many other applications to fusion physics.

Équipe 107 : Physique des plasmas chauds; International audience; Abrupt and strong excitation of a mode has been observed when the frequency of a chirping energetic-particle driven geodesic acoustic mode (EGAM) reaches twice the geodesic acoustic mode (GAM) frequency. The frequency of the secondary mode is the GAM frequency, which is a half-frequency of the primary EGAM. Based on the analysis of spatial structures, the secondary mode is identified as a GAM. The phase relation between the secondary mode and the primary EGAM is locked, and the evolution of the growth rate of the secondary mode indicates nonlinear excitation. The results suggest that the primary mode ( EGAM) contributes to nonlinear destabilization of a subcritical mode.

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.

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.; 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.