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# Documents  82D10 | enregistrements trouvés : 33

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## The geometrical gyro-kinetic approximation Frénod, Emmanuel | CIRM H

Post-edited

Research talks;Partial Differential Equations;Mathematical Physics

At the end of the 70', Littlejohn [1, 2, 3] shed new light on what is called the Gyro-Kinetic Approximation. His approach incorporated high-level mathematical concepts from Hamiltonian Mechanics, Differential Geometry and Symplectic Geometry into a physical affordable theory in order to clarify what has been done for years in the domain. This theory has been being widely used to deduce the numerical methods for Tokamak and Stellarator simulation. Yet, it was formal from the mathematical point of view and not directly accessible for mathematicians.
This talk will present a mathematically rigorous version of the theory. The way to set out this Gyro-Kinetic Approximation consists of the building of a change of coordinates that decouples the Hamiltonian dynamical system satisfied by the characteristics of charged particles submitted to a strong magnetic field into a part that concerns the fast oscillation induced by the magnetic field and a other part that describes a slower dynamics.
This building is made of two steps. The goal of the first one, so-called "Darboux Algorithm", is to give to the Poisson Matrix (associated to the Hamiltonian system) a form that would achieve the goal of decoupling if the Hamiltonian function does not depend on one given variable. Then the second change of variables (which is in fact a succession of several ones), so-called "Lie Algorithm", is to remove the given variable from the Hamiltonian function without changing the form of the Poisson Matrix.
(Notice that, beside this Geometrical Gyro-Kinetic Approximation Theory, an alternative approach, based on Asymptotic Analysis and Homogenization Methods was developed in Frenod and Sonnendrücker [5, 6, 7], Frenod, Raviart and Sonnendrücker [4], Golse and Saint-Raymond [9] and Ghendrih, Hauray and Nouri [8].)
At the end of the 70', Littlejohn [1, 2, 3] shed new light on what is called the Gyro-Kinetic Approximation. His approach incorporated high-level mathematical concepts from Hamiltonian Mechanics, Differential Geometry and Symplectic Geometry into a physical affordable theory in order to clarify what has been done for years in the domain. This theory has been being widely used to deduce the numerical methods for Tokamak and Stellarator s...

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## Towards complex and realistic tokamaks geometries in computational plasma physics Ratnani, Ahmed | CIRM H

Post-edited

Research talks;Mathematical Physics

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## Exact conservation laws for gyrokinetic Vlasov-Poisson equations Tronko, Natalia | CIRM H

Post-edited

Research talks;Partial Differential Equations;Mathematical Physics

The momentum transport in a fusion device such as a tokamak has been in a scope of the interest during last decade. Indeed, it is tightly related to the plasma rotation and therefore its stabilization, which in its turn is essential for the confinement improvement. The intrinsic rotation, i.e. the part of the rotation occurring without any external torque is one of the possible sources of plasma stabilization.
The modern gyrokinetic theory [3] is an ubiquitous theoretical framework for lowfrequency fusion plasma description. In this work we are using the field theory formulation of the modern gyrokinetics [1]. The main attention is focussed on derivation of the momentum conservation law via the Noether method, which allows to connect symmetries of the system with conserved quantities by means of the infinitesimal space-time translations and rotations.
Such an approach allows to consistently keep the gyrokinetic dynamical reduction effects into account and therefore leads towards a complete momentum transport equation.
Elucidating the role of the gyrokinetic polarization is one of the main results of this work. We show that the terms resulting from each step of the dynamical reduction (guiding-center and gyrocenter) should be consistently taken into account in order to establish physical meaning of the transported quantity. The present work [2] generalizes previous result obtained in [4] by taking into the account purely geometrical contributions into the radial polarization.
The momentum transport in a fusion device such as a tokamak has been in a scope of the interest during last decade. Indeed, it is tightly related to the plasma rotation and therefore its stabilization, which in its turn is essential for the confinement improvement. The intrinsic rotation, i.e. the part of the rotation occurring without any external torque is one of the possible sources of plasma stabilization.
The modern gyrokinetic theory [3] ...

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## Modelling of magnetic fusion plasmas: from fluid to kinetic description: kinetic MHD Garbet, Xavier | CIRM H

Post-edited

Research talks;Mathematical Physics

This lecture will present a short overview on kinetic MHD. The advantages and drawbacks of kinetic versus fluid modelling will be summarized. Various techniques to implement kinetic effects in the fluid description will be introduced with increasing complexity: bi-fluid effects, gyroaverage fields, Landau closures. Hybrid formulations, which combine fluid and kinetic approaches will be presented. It will be shown that these formulations raise several difficulties, including inconsistent ordering and choice of representation. The non linear dynamics of an internal kink mode in a tokamak will be used as a test bed for the various formulations. It will be shown that bi-fluid effects can explain to some extent fast plasma relaxations (reconnection), but cannot address kinetic instabilities due to energetic particles. Some results of hybrid codes will be shown. Recent developments and perspectives will be given in conclusion. This lecture will present a short overview on kinetic MHD. The advantages and drawbacks of kinetic versus fluid modelling will be summarized. Various techniques to implement kinetic effects in the fluid description will be introduced with increasing complexity: bi-fluid effects, gyroaverage fields, Landau closures. Hybrid formulations, which combine fluid and kinetic approaches will be presented. It will be shown that these formulations raise ...

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## The equation of state in astrophysicsproceedings of IAU colloquium n° 147June 14-18 Chabrier, Gilles ; Schatzman, Evry | Cambridge University Press 1994

Congrès

ISBN 978-0-521-47260-9

IAU colloquium , 0147

Localisation : Colloque 1er étage (SAIN)

approche en molécule d'Onsager du potentiel de bilindage dan # blindage de réaction nucléaire en astrophysique # champ magnétique # convection turbulente # cristallisation de mélange ionique binaire dense # croûte d'étoile neutronique # effondrement gravitationnel ou explosion thermonucléaire de # formalisme d'intégral de chemin # haute pression # hydrogène fluide à haute densité # hélioséismologie et séismologie de Jupiter # mécanique statistique de plasma quantique # naine brune # observation # planète géante # plasma stellaire # processus de transport # refroidissement de naine blanche # structure ou évolution stellaire # thermodynamique et opacité # transition de phase de plasma # variable cataclysmique # équation d'état en astrophysique approche en molécule d'Onsager du potentiel de bilindage dan # blindage de réaction nucléaire en astrophysique # champ magnétique # convection turbulente # cristallisation de mélange ionique binaire dense # croûte d'étoile neutronique # effondrement gravitationnel ou explosion thermonucléaire de # formalisme d'intégral de chemin # haute pression # hydrogène fluide à haute densité # hélioséismologie et séismologie de Jupiter # mécanique ...

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## Numerical solution of ordinary and partial differential equationsbased on a summer schoolAug. - Sept. Fox, L. | Pergamon Press 1962

Congrès

Localisation : Colloque 1er étage (OXFO)

méthode de Monte-Carlo # neutron # plasma # réacteur nucléaire # solution numérique # équation aux dérivées partielles # équation de transport linéaire # équation différentielle ordinaire # équation elliptique # équation intégrale # équation parabolique quasi-linéaire

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## An asymptotic regime for the Vlasov-Poisson system Miot, Evelyne | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

We investigate the gyrokinetic limit for the two-dimensional Vlasov-Poisson system in a regime studied by F. Golse and L. Saint-Raymond. First we establish the convergence towards the Euler equation under several assumptions on the energy and on the norms of the initial data. Then we provide a first analysis of the asymptotics for a Vlasov-Poisson system describing the interaction of a bounded density with a moving point charge.

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## From Vlasov-Poisson-Fokker-Planck to incompressible Euler equations Barré, Julien | CIRM

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

Vlasov-Poisson-Fokker-Planck equations provide a simplified model for a cloud of cold atoms in a Magneto Optical Trap. The strong field, or quasi-neutral regime, where the repulsive interaction dominates, is often relevant for experiments. Motivated by this example and more generally by trapped non neutral plasmas, we study this quasi-neutral limit, and show under certain conditions the convergence of the solution of Vlasov-Poisson-Fokker-Planck equations to the solution of incompressible Euler equation.
For an infinite or periodic system, this limit has already been studied by Y. Brenier and N. Masmoudi. New difficulties arise here from the Fokker-Planck operator, and especially from the boundary conditions (Joint work with D. Chiron, T. Goudon et N. Masmoudi).
Vlasov-Poisson-Fokker-Planck equations provide a simplified model for a cloud of cold atoms in a Magneto Optical Trap. The strong field, or quasi-neutral regime, where the repulsive interaction dominates, is often relevant for experiments. Motivated by this example and more generally by trapped non neutral plasmas, we study this quasi-neutral limit, and show under certain conditions the convergence of the solution of Vlasov-Poisson-Fokker-Planck ...

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## Simulation of kinetik electrostatic electron nonlinear (KEEN) waves with variable velocity resolution grids and high-order time-splitting Mehrenberger, Michel | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

KEEN - Vlasov plasmas - acoustic waves - semi-Lagrangian scheme - Vlasov-Poisson equation; - BGK mode

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## High magnetic field averaged models for plasma physics Bostan, Mihaï | CIRM H

Multi angle

Research talks;Mathematical Physics

The subject matter of this talk concerns the derivation of the Finite Larmor radius approximation, when collisions are taken into account.
Several studies are performed, corresponding to different collision kernels. The main motivation consists in computing the gyro-average of the Fokker-Planck- Landau operator, which plays a major role in plasma physics. We determine its equilibria and derive the fluid approximation around them, leading to a new Euler type system of conservation laws.
The main technique applies for studying highly anisotropic parabolic problems, for example the heat equation with disparate diffusion coeffcients with respect to the parallel and perpendicular directions.
The subject matter of this talk concerns the derivation of the Finite Larmor radius approximation, when collisions are taken into account.
Several studies are performed, corresponding to different collision kernels. The main motivation consists in computing the gyro-average of the Fokker-Planck- Landau operator, which plays a major role in plasma physics. We determine its equilibria and derive the fluid approximation around them, leading to a ...

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## From Vlasov-Poisson to Euler in the gyrokinetic limit Miot, Evelyne | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

We investigate the gyrokinetic limit for the two-dimensional Vlasov-Poisson system in a regime studied by F. Golse and L. Saint-Raymond [1, 3]. First we establish the convergence towards the Euler equation under several assumptions on the energy and on the norms of the initial data. Then we analyze the asymptotics for a Vlasov-Poisson system describing the interaction of a bounded density of particles with a moving point charge, characterized by a Dirac mass in the phase-space. We investigate the gyrokinetic limit for the two-dimensional Vlasov-Poisson system in a regime studied by F. Golse and L. Saint-Raymond [1, 3]. First we establish the convergence towards the Euler equation under several assumptions on the energy and on the norms of the initial data. Then we analyze the asymptotics for a Vlasov-Poisson system describing the interaction of a bounded density of particles with a moving point charge, characterized by ...

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## 5D full-$f$ gyrokinetic simulation for ion turbulence and transport barrier in tokamak plasmas Imadera, Kenji | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

Gyrokinetic simulation is considered to be an essential tool to study turbulent transport driven by micro-scale instabilities in tokamak plasmas. It is roughly categorized into two approaches; delta-$f$ local and full-$f$ global approaches. In full-$f$ approach, both turbulent transport and profile evolutions are solved self-consistently under the power balance between external heat source/sink. In this talk, we address (A) numerical technique to treat such full-$f$ gyrokinetic Vlasov-Poisson equations [1] and (B) characteristics of global ion-scale turbulence and transport barrier [2]. We also discuss (C) the role of stable modes in collisionless or weakly collisional plasmas [3]. Gyrokinetic simulation is considered to be an essential tool to study turbulent transport driven by micro-scale instabilities in tokamak plasmas. It is roughly categorized into two approaches; delta-$f$ local and full-$f$ global approaches. In full-$f$ approach, both turbulent transport and profile evolutions are solved self-consistently under the power balance between external heat source/sink. In this talk, we address (A) numerical technique ...

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## Une introduction aux problèmes inverses elliptiques et paraboliques Choulli, Mourad | Springer;Société de Mathématiques Appliquées et Industrielles 2009

Ouvrage

- xix; 249 p.
ISBN 978-3-642-02459-7

Mathématiques & applications , 0065

Localisation : Collection 1er étage

problème inverse # équation elliptique linéaire # équation parabolique linéaire et semilinéaire # solution géométrique optique # continuation unique # estimation de Carleman

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## Physique des tokamaks Rax, Jean-Marcel | Les Editions de l'Ecole Polytechnique 2011

Ouvrage

- 426 p.
ISBN 978-2-7302-1580-0

Localisation : Enseignement RdC (RAX)

tokamak # plasma # fusion nucléaire # énergie thermonucléaire # système de particules chargées # confinement magnétique

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## Physique des plasmas:cours et applications Rax, Jean-Marcel ; Bigot, Bernard | Dunod 2005

Ouvrage

- xii; 426 p.
ISBN 978-2-10-007250-7

Sciences sup

Localisation : Enseignement RdC (RAX)

plasmas # technique des plasmas

82D10

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## Numerical models for fusion Degond, P. ; Grandgirard, V. ; Sarazin, Y. ; Jardin, S. C. ; Villani, C. ; Crouseilles, N. ; Guillard, H. ; Nkonga, Boniface ; Sonnendrücker, E. | Société Mathématique de France 2013

Ouvrage

Panoramas et synthèses , 0039;0040

Localisation : Collection 1er étage

amortissement Landau # dynamique galactique # écho plasma # eulérien # fréquence cyclotron # fusion # limite faible nombre de Mach # longueur de Debye # magnétohydrodynamique # modèles fluides de plasmas # méthode de Newton # méthodes computationnelles # nombre de Mach # particle-in-cell # physique des plasmas # plasma de fusion magnétique # quasi-neutralité # régime de dérive-fluide # schémas conservatifs # schémas de capture de chocs # schémas implicites # schémas `Asymptotic-Preserving' # semi-lagrangien # simulations de calcul haute performance # théorie gyrocinétique # théorie KAM # tokamak # transport turbulent # Vlasov-Poisson. amortissement Landau # dynamique galactique # écho plasma # eulérien # fréquence cyclotron # fusion # limite faible nombre de Mach # longueur de Debye # magnétohydrodynamique # modèles fluides de plasmas # méthode de Newton # méthodes computationnelles # nombre de Mach # particle-in-cell # physique des plasmas # plasma de fusion magnétique # quasi-neutralité # régime de dérive-fluide # schémas conservatifs # schémas de capture de chocs # schémas ...

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## Réarrangement relatif : un instrument d'estimations dans les problèmes aux limites Rakotoson, Jean-Michel | Springer 2008

Ouvrage

- xv, 292 p.
ISBN 978-3-540-69117-4

Mathématiques & applications , 0064

Localisation : Collection 1er étage

analyse mathématique # inégalité de Polya-Szegö # réarrangement relatif # réarrangement monotone # C_alpha-arrangement # inégalité ponctuelle de Poincaré-Sobolev # espace normé

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## Microscopic dynamics of plasmas and chaos Elskens, Yves ; Escande, Dominique | Institute of Physics Publishing 2003

Ouvrage

- xix; 308 p.
ISBN 978-0-7503-0612-6

Series in plasma physics

Localisation : Ouvrage RdC (ELSK)

plasma # mécanique statistical # réseau neural # théorie cinétique # chaos hamiltonnien # processus de diffusion

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## Topics in kinetic theory Passot, Thierry ; Sulem, Catherine ; Sulem, jean-Louis | American Mathematical Society 2005

Ouvrage

- 312 p.
ISBN 978-0-8218-3723-8

Fields institute communications , 0046

Localisation : Collection 1er étage

théorie cinétique des gazs # mécanique statistique # cinétique mécanique des fluides # équation de Boltzmann # système de Vlasov-Maxwell # plasma # processus de transport

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## The Cauchy problem in kinetic theory Glassey, Robert T. | SIAM 1996

Ouvrage

- 241 p.
ISBN 978-0-89871-367-1

Localisation : Ouvrage RdC (GLASS)

problème de Cauchy # théorie cinétique des gaz # équation de la physique # équation de Boltzmann # flot plasmique # plasma # mécanique statistique # système de Vlasov-Poisson # Système de Vlasov-Maxwell

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Ressources Electroniques (Depuis le CIRM)

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