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# Documents  82D10 | enregistrements trouvés : 10

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## Post-edited  Modelling of magnetic fusion plasmas: from fluid to kinetic description: kinetic MHD Garbet, Xavier (Auteur de la Conférence) | CIRM (Editeur )

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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## Post-edited  Exact conservation laws for gyrokinetic Vlasov-Poisson equations Tronko, Natalia (Auteur de la Conférence) | CIRM (Editeur )

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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## Post-edited  Towards complex and realistic tokamaks geometries in computational plasma physics Ratnani, Ahmed (Auteur de la Conférence) | CIRM (Editeur )

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## Post-edited  The geometrical gyro-kinetic approximation Frénod, Emmanuel (Auteur de la Conférence) | CIRM (Editeur )

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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## Multi angle  5D full-$f$ gyrokinetic simulation for ion turbulence and transport barrier in tokamak plasmas Imadera, Kenji (Auteur de la Conférence) | CIRM (Editeur )

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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## Multi angle  From Vlasov-Poisson to Euler in the gyrokinetic limit Miot, Evelyne (Auteur de la Conférence) | CIRM (Editeur )

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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## Multi angle  High magnetic field averaged models for plasma physics Bostan, Mihaï (Auteur de la Conférence) | CIRM (Editeur )

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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## Multi angle  Simulation of kinetik electrostatic electron nonlinear (KEEN) waves with variable velocity resolution grids and high-order time-splitting Mehrenberger, Michel (Auteur de la Conférence) | CIRM (Editeur )

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

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## Multi angle  From Vlasov-Poisson-Fokker-Planck to incompressible Euler equations Barré, Julien (Auteur de la Conférence) | CIRM (Editeur )

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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## Multi angle  An asymptotic regime for the Vlasov-Poisson system Miot, Evelyne (Auteur de la Conférence) | CIRM (Editeur )

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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