Modeling and Numerical Methods for Hot Plasmas II

Bordeaux, 12-14 October 2015


Organizing comitee

Jérôme Breil
Stéphane Brull
Emmanuel D'Humières
Ingrid Rochel

Presentation of the workshop
This conference is devoted to modeling and scientific computing for the transport of charged particles in hot plasmas. 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.
The tools developed in this context are important to prepare and analyze experiments related to fusion. In the Bordeaux area, these tools are required to prepare experiments on the high power, high energy laser PETAL that will be operational in two years at CEA/CESTA.
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 Jérôme Breil, Stéphane Brull, Emmanuel d'Humières and Ingrid Rochel.

Crédits: photographies d'Ingrid Rochel


How to come to the workshop
IMB is located on the Université de Bordeaux 1 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 1
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 is mandatory even if there is no registration fee for the conference. You can register by sending an email to Stéphane Brull until the 25th of September .

Invited speakers:

Sever Hirstoaga (INRIA/Strasbourg): Particle-In-Cell simulations for highly oscillatory Vlasov-Poisson system talk.pdf
Abstract: We study the dynamics of charged particles under the influence of a strong magnetic field by solving numerically multi-scale Vlasov-Poisson and the guiding center models. First we propose an explicit scheme able to use large time steps with respect to the size of the solution's fast oscillations. Second we implement efficiently a PIC method in order to perform simulations with a large number of particles and we assess the code performance.

Yves Elskens (Marseille): Uniform derivation of Coulomb collisional transport thanks to Debye shielding talk.pdf

Mihai Bostan (Marseille) : Le système de Vlasov-Poisson effectif pour les plasmas fortement magnétisés
Abstract: Nous étudions le régime du rayon de Larmor fini pour le système de Vlasov-Poisson, dans le cas où la longueur de Debye est égale au rayon de Larmor. Le champ magnétique est supposé uniforme. Nous restreignons l'étude de ce problème non linéaire au cas bi-dimensionnel. Nous obtenons le modèle limite en appliquant les méthodes de gyro-moyenne. Nous donnons l'expression explicite du champ d'advection effectif de l'équation de Vlasov, dans laquelle nous avons substitué le champ électrique auto-consistant, via la résolution de l'équation de Poisson moyennée à l'échelle cyclotronique. Nous mettons en évidence la structure hamiltonienne du modèle limite et présentons ses propriétés: conservations de la masse, de l'énergie cinétique, de l'énergie électrique, etc.

Bruno Després (Paris 6): Advances in kinetic sheath modeling
Abstract: Sheath are stationary physical solutions in a plasma near a metallic wall, where a boundary layer is not locally neutral. We will show how to formulate the problem as a the "minimizer" of kinetic Vlasov equations (for i+ and e-) plus a non linear Poisson equation. It yields the existence of sheaths. The mathematical stability will be discussed, plus some extention to more challenging problems in plasma. This work has been done at LJLL-UPMC with Mehdi Badsi (PHD) and Martin Campos Pinto (CNRS).

Olivier Lafitte (Paris 13): Expression précisée du champ électromagnétique dans un plasma froid d'ions dans l'approximation fluide et transfert d'énergie laser: cas de l'incidence oblique talk.pdf

Vladimir Tikonchuk (Bordeaux): Multiscale models of laser-plasma interaction for the shock ignition scheme talk.pdf
Abstract: Laser-plasma interactions (LPI) in the context of Inertial Confinement Fusion (ICF) are prone to numerous nonlinear and kinetic processes. Although routinely studied at miscroscopic and mesoscopic scales with Particle-in-Cell and Paraxial Electromagnetic codes, these processes are hardly accounted for in the radiative hydrodynamics codes, which are usually limited to collisional absorption modeling. The direct drive advanced ICF schemes such as shock ignition, and laser plasma experiments at a nanosecond time scale require a more detailed description of LPI at hydrodynamic scales including the cross-beam energy transfer, parametric instabilities, high energy electron and ion transport and their effect on the ablation pressure and fusion ignition conditions. In this talk we present a novel macroscopic LPI model specially adopted for using in hydrocodes and its application to the shock ignition scheme. The model is based on the Paraxial Complex Geometrical Optics for stochastically distributed Gaussian optical beamlets. It is describing the laser beam refraction and diffraction in the plasma, laser energy absorption due to the collisional and resonant processes, energy exchange between the laser beams and hot electron generation due to the resonance absorption, the Stimulated Raman Scattering (SRS) and Two-Plasmon Decay (TPD). The hot electron transport is described in the multi-group continuous slowing down approximation, adapted to transversally Gaussian electron beams. The LPI model is validated against several experiments conducted on the PALS and OMEGA facilities, showing an extremely good agreement, simultaneously matching observables from hydrodynamic, hot electrons and reflectivity measurements. The role of hot electrons in the shock formation and preheat of the upstream plasma is demonstrated.

Sébastien Guisset (Bordeaux): Around the electronic M1 model talk.pdf

Holger Heumann (INRIA/Sophia Antipolis): Quasi-static Free-Boundary Equilibrium of Toroidal Plasma: Computational Methods and Applications talk.pdf
Abstract: We present a comprehensive survey of the various computational methods for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilibria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized non-linear problem to tackle the various non-linearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we discuss as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate performance and application areas.

Roland Duclous (CEA/Bruyères): Descriptions cinétiques déterministes et stochastiques du Bremsstrahlung electron-ion: du régime thermique au régime non thermique

Bruno Fornet (Nuclétudes): Charge conserving DGTD-PIC methods on nonconforming cartesian grids and related issues
Abstract: In this talk, we will be interested in specific issues appearing in the simulation of plasmas described by a Vlasov-Maxwell system. The investigated numerical methods are obtained by weakly coupling a DGTD method for the Maxwell system and a Particle In Cell (PIC) approach to account for the dynamics of charged particles. Discontinuous Galerkin in Time Domain (DGTD) Methods are powerful tools to compute the sharp behavior of electromagnetic fields satisfying Maxwell equations. One of the very nice features of DGTD is the ability to accomodate meshes with hanging nodes and possibly bad aspect ratio over the mesh. This is an edge for multiscale modelling because only the fine parts have to be meshed in a detailed manner. Another good point of DGTD methods is their ability to go high order easily. However, problems known as "charge conservation issues" are likely to arise in the coupling of DGTD and PIC methods, whenever performed without much care. These issues have first been much studied in FDTD (Finite Difference in Time Domain), then in FETD (Finite Elements in Time Domain)-PIC and finally in DGTD-PIC in a less extensive manner. We will detail the problem of charge conservation, the main solutions proposed to handle it, and then describe a novel DGTD-PIC approach, validated for nonconforming cartesian grids, preserving the attractive aspects of the DGTD method.

Philippe Ghendrih (CEA/Cadarache): Maitriser les complexités dans ITER talk.pdf

Denise Aregba (Bordeaux): Le système d'Euler bi-température non conservatif: propriétés entropiques et approximation numérique. talk.pdf

Anne Nouri (Marseille): Sur une équation cinétique modélisant un plasma du coeur de tokamak
Abstract: On étudie une équation cinétique utilisée dans l'étude de plasmas de tokamaks, en particulier pour ITER. Elle a la particularité d'être bien posée quand on la considère dans les directions perpendiculaires aux lignes de champ magnétique, et mal posée au sens d'Hadamard quand on la considère dans la direction parallèle aux lignes de champ magnétique.

Confirmed Participants:

Denise Aregba Olivier Lafitte Mihai Bostan
Jérôme Breil Stéphane Brull Holger Heumann
Roland Duclous Emmanuel d'Humières Bruno Després
Bruno Dubroca Rachel Nuter Thana Nguyen Bui
Nicolas Popoff Sébastien Guisset Xavier Lhebrard
Yves Elskens Nicolas Popoff Sever Hirstoaga
Vladimir Tikonchuk Philippe Ghendrih Bruno Fornet
Jean-Luc Feugeas Anne Nouri Guillaume Duchateau
Rodolphe Turpault Philippe Nicolaï Gabriel Georges
Arnaud Colaitis Dario Del Sorbo Céline Barranger
Hélène Hivert Mathieu Patrizio Bourgeade Antoine
Rafick Imekraz Corentin Audiard Franck Sueur