The purpose of this school is to review the recent progresses and remaining challenges in the mathematical and numerical modeling of kinetic plasmas in the presence of a strong magnetic field, with an emphasis on Tokamak fusion plasmas.
The school will gather mathematicians and physicists working on the kinetic or hybrid modeling of plasmas confined by strong magnetic fields.
The presence of several small (or large) parameters in fusion plasmas (e.g. the small Debye length, the high electron mobility, the low collisionality and of course the large B field) is indeed the source of many difficulties in the design of efficient models. To avoid wasting computational resources it is necessary to develop numerical models that behave well in the regimes where these parameters are small but not zero, and sometimes vary throughout the simulation domain. Such models include gyrokinetic approximations, hybrid fluid-kinetic descriptions, asymptotic-preserving methods for e.g. quasi-neutral regimes and self-consistent models for the charged boundary layers (plasma sheaths) close to the walls. They all require a good understanding of the physical plasma properties that follow from the presence of these small parameters.
The school will therefore present a review of the recent progresses made in this direction and highlight some of the remaining challenges that should be adressed with high priority in the next future.
The school will consist of two parts.
1. Four lectures given by recognized experts on these fields, including applied mathematicians and plasma physicists (click the title for a summary):
Josh BURBY (Courant Institute, New York)
Discrete collisionless kinetics: how far we've come and where we're going
Mohammed LEMOU (CNRS IRMAR, Rennes)
Averaging techniques and uniformly accurate numerical approximations of Vlasov equations with strong magnetic field
Giovanni MANFREDI (CNRS IPCMS, Strasbourg) Kinetic modelling of the plasma-wall transition in magnetized fusion plasmas
Eric SONNENDRÜCKER (TUM and Max-Planck IPP, Garching) Part I: Introduction to Finite Element Exterior Calculus Part II: A discrete variational framework for the Vlasov-Maxwell equations Part III: Modern gyrokinetic theory and its implementation
The focus will be on modeling the physics related to the fast gyration of charged particles along magnetic field lines, but other consequences of intense magnetic fields will be addressed (eg their influence on the plasma sheaths close to the walls).
2. Short presentations by the participants, to foster discussions and exchange of ideas.
Martin Campos Pinto
Martin Campos Pinto (CNRS LJLL, Paris)
Frédérique Charles (UPMC LJLL, Paris)
Bruno Després (UPMC LJLL, Paris)
Omar Maj (Max-Planck IPP, Garching)
Claudia Negulescu (UPS, IMT, Toulouse)