Modeling and Numerical Methods for Hot Plasmas III

Bordeaux, 12-13 October 2017



Organizing comitee


Denise Aregba Denise.Aregba@math.u-bordeaux.fr
Stéphane Brull Stephane.Brull@math.u-bordeaux.fr






Presentation of the workshop
This conference is devoted to modeling and scientific computing for the transport of charged particles in hot plasmas fusion with or without wall interaction. These plasmas are motivated by inertially or magnetically confined fusion plasmas. The goal of this meeting is to review recent advances in this field. A particular attention will be drawn to the use of kinetic equations to describe these phenomena.
This workshop will allow to present recent results on various topics related to the transport of particles in hot plasmas, at the interface between applied mathematics and plasma physics. It will be an opportunity to gather scientists from these communities.

Organization of the workshop
This workshop is organized by Denise Aregba and Stéphane Brull



















Crédits: photographies d'Ingrid Rochel

Arrival:

How to come to the workshop
IMB is located on the Université de Bordeaux campus in the city of Talence.
From the Bordeaux train station (Saint-Jean Station), take the C Tramway Line to the Quinconces Station and then the B Line (Pessac Centre direction) until you reach the Forum Station.
From the Bordeaux Mérignac airport, a shuttle leaves every 45 minutes during the day. Take the shuttle until you reach the Office du Tourisme Station, then take the B Line (Pessac Centre direction) until you reach the Forum Station. You can also take a taxi (around 40 euros for a one-way trip).

By car:
From the North of Bordeaux (Paris, Nantes, A10...), take the East Rocade in the direction of Toulouse, then take Exit 16 (Talence, Domaine Universitaire). Continue on the Cours de la Libération until you reach number 351 (on your left after the Casino supermarket, next to the Peixotto Parc).
From the South-East of Bordeaux (Toulouse), take the Rocade in the Bayonne direction, then take Exit 16 (Talence, Domaine Universitaire). Continue on the Cours de la Libération until you reach number 351 (on your left after the Casino supermarket, next to the Peixotto Parc).
From the South of Bordeaux (Bayonne), take the Rocade in the Toulouse direction, then take Exit 16 (Talence, Domaine Universitaire). Turn left to go over the Rocade. Continue on the Cours de la Libération until you reach number 351 (on your left after the Casino supermarket, next to the Peixotto Parc).

You can also locate IMB using Google Maps.
Institut de Mathématiques de Bordeaux
Building A33
Université Bordeaux
351 cours de la Libération
33405 TALENCE cedex
Tél : (33)/(0) 5 40 00 60 70
Fax : (33)/(0) 5 40 00 21 23

Registration

Registration is mandatory even if there is no registration fee for the conference. You can register by sending an email to Stéphane Brull until the 30th of September .


Programme


jeudi 12 octobre

9h00-10h00 Q. Wargnier
10h00-10h30 Pause café
10h30-11h30 P. Helluy
11h30-12h30 X. Lhébrard
12h30-14h00 Buffet en salle de détente
14h00-15h00 A. Nouri
15h00-16h00 M. Bostan
16h00-16h30 Pause café
16h30-17h30 P. Ghendrih
20h00 Dîner au café du port


vendredi 13 octobre

9h30-10h30 Y. Elskens
10h30-11h00 Pause café
11h00-12h00 O. Lafitte
12h00-14h00 Buffet en salle de détente
14h00-15h00 F. Filbet
15h00-16h00 B. Fornet

Orateurs:


Francis Filbet (Toulouse): Particle methods for the three dimensional Vlasov-Poisson system with a large magnetic field
Abstract: We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson system with a strong and inhomogeneous external magnetic field with fixed direction. In this regime, the time step can be subject to stability constraints related to the smallness of Larmor radius and plasma frequency. To avoid this limitation, our approach is based on first and higher-order semi-implicit numerical schemes already validated on dissipative systems and for homogeneous magnetic fields. Thus, when the magnitude of the external magnetic field becomes large, this method provides a consistent PIC discretization of the guiding-center system taking into account variations of the magnetic field. We carry out some theoretical proofs and perform several numerical experiments that establish a solid validation of the method and its underlying concepts.

Xavier Lhebrard (CELIA): Etude du système d'Euler bitempérature avec champ magnétique transverse.
Abstract:Cet exposé est consacré à l'étude du système d'Euler bitempérature avec champs magnétique transverse. En effet dans le contexte de la fusion par confinement inertiel, on s'intéresse à la magnéto-hydrodynamique des électrons et des ions hors équilibre thermique. On introduit dans un premier temps un modèle cinétique couplé aux équations de Maxwel. Le modèle fluide est alors établi par une procédure de Chapman-Enskog. On présente ensuite une méthode numérique élaborée grâce à la résolution d'un système de relaxation associé. On montre ensuite la robustesse de la méthode sous des contraintes sur le pas de temps (conditions CFL). Plus précisément on donne des conditions suffisantes sur les vitesses d'onde pour que le schéma numérique préserve la positivité des densités et des énergies électroniques et ioniques, et satisfasse une inégalité d'entropie discrète.

Mihai Bostan (Marseille): Modèles gyro-cinétiques en temps long
Abstract: Nous étudions les équations de Vlasov-Poisson en présence d'un champ magnétique extérieur très intense. Nous souhaitons analyser le comportement de ces solutions en temps long. Nous montrons la convergence forte vers un profil, solution d'un système de Vlasov-Poisson homogènéisé par rapport au mouvement rapide cyclotronique, et pour toute densité de présence (pas nécessairement bien pr\'eparée). On montre aussi que le système limite est bien posé, et on \'etudie ses principales propriétés.

Olivier Lafitte (Paris 13): The hybrid singularity in the oblique incidence case: Bessel-type solution for the general case
Abstract: We generalize the results obtained by Despres, Imbert-Gerard and Lafitte for the heating of a plasma by a magnetic field in the cold model approximation for the oblique incidence case (meaning that the projection of the incident wave vector on the direction of the imposed magnetic field is non zero. In this case, the Maxwell system of equations transforms into a system of four differential equations of order 1, which are coupled. After a review of the traditional cut-off and resonance singularities of the wave in the plasma, we analyze the solution in the neighborhood of the hybrid resonance by proving that the system is equivalent to the coupling of a singular second order system and of a regular second order system, yielding the same type of solution as in DIL

Anne Nouri (Marseille): Sur un système de Vlasov-Poisson en dimension 1 d'espace
Abstract: On considère un système de Vlasov-Poisson en domaine borné unidimensionnel avec des conditions au bord de réflection directe pour les fonctions de distribution électonique et ionique. On étudie sa limite quasi-neutre. On compare le système obtenu en considérant les électrons adiabatiques.

Philippe Helluy (Strasbourg): Palindromic Discontinuous Galerkin Method
Abstract: This work is devoted to a general approach for solving hyperbolic systems of conservation laws. In many applications the time scale of the interesting phenomena is very different from the time scale imposed by the explicit CFL condition. The PDG method is a general implicit (but matrix-free) high order method for approximating systems of conservation laws. It is unconditionally stable and has the complexity of an explicit scheme. It relies on a vectorial kinetic interpretation of the conservation laws proposed in Aregba, Natalini, Discrete kinetic schemes for multidimensional systems of conservation laws, 2000. The kinetic system is approximated with an asymptotic-preserving high order DG method. The method is well adapted to parallel optimizations. We will review the task-based implementation of the method, based on the StarPU runtime library, and some applications to fluid mechanics and plasma physics. Some results of the presentation are also given in Badwaik et al., Task-based parallelization of an implicit kinetic scheme, 2017.

Bruno Fornet (Nucletude): Vers l'industrialisation du DGTD(-PIC) pour la simulation de plasmas non collisionnels
Abstract: La simulation numérique de phénomènes physiques en contexte industriel nécessite l'utilisation de chaînes de calcul efficaces et ergonomiques, dont le solveur n'est qu'un maillon. Des problématiques spécificiques apparaissent lorsque ce solveur est d'ordre éléveé, conduisant souvent les utilisateurs à préférer l'utilisation des méthodes à bas ordre si cela est compatible avec la précision recherchée. Nous nous intéresserons plus particulièrement à deux problématiques relevant des mathématiques appliquées qui émergent lors de l'élaboration d'une chaîne de calcul pour la simulation instationnaire de plasmas non collisionnels (équations de Maxwell-Vlasov), à savoir la réduction drastique des temsp de calcul DGTD sur maillage cartésien et la conception d'un générateur automatique de maillages HP solveurs-optimisés.

Quentin Wargnier (Ecole Polytechnique-CMAP): Simulation of multicomponent plasma in thermal non-equilibrium with application to magnetic reconnection in solar physics: multiscale modeling from kinetic theory and numerical treatment of the non-conservative product.
Abstract: This contribution deals with the fluid modeling of fully and partially ionized collisional multicomponent magnetized plasma in thermal and chemical non-equilibrium for the purpose of simulating and predicting magnetic reconnections in the chromosphere of the sun. We first introduce a derivation of the fluid model from kinetic theory using a multi-scale Chapman-Enskog expansion based on a proper scaling of the Boltzmann equations, where the small ratio of mass between the electron and heavy species is taken into account in the small parameter as well as the Knudsen number (Graille, Magin, Massot 2009). We also focus on the numerical simulation of a simplified model in order to properly investigate the influence of the presence of a non-conservative product in the electron energy equation for shock solutions, derive jump conditions and propose an original numerical treatment in order to avoid non-physical shocks in the numerical solution.

Yves Elskens (Marseille): Phase mixing importance for both Landau instability and damping
Abstract: We discuss the self-consistent dynamics of plasmas by means of hamiltonian formalism for a system of N near-resonant electrons interacting with a single Langmuir wave. The connection with the Vlasov description is revisited through the numerical calculation of the van Kampen-like eigenfrequencies of the linearized dynamics for many degrees of freedom. Both the exponential-like growth as well as damping of the Langmuir wave are shown to emerge from a phase mixing effect among beam modes, revealing unexpected similarities between the stable and unstable regimes.

Philippe Ghendrih (CEA-Cadarache): Two species kinetic response to an external drive by electrostatic waves to investigate Lower Hybrid hot spot generation in tokamak plasmas




Participants:


Denise Aregba Stéphane Brull Xavier Lhébrard
Corentin Prigent Bruno Fornet Olivier Lafitte
Francis Filbet Philippe Helluy Bruno Dubroca
Anne Nouri Mihai Bostan Quentin Wargnier
Thana Nguyen Bui Philippe Ghendrih Teddy Pichard
Paul Geniet Krisztian Benyo Stefano Pezzano
Andrea Ferrero Philippe Nicolaï Kevin Santugini
Jerôme Breil Jean-Luc Feugeas Philippe Thieullen
Edouard Le Bel Marc Massot































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