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Framework for systematic modelling of magnetized plasmas.

par Caroline CHAMPENOIS - publié le

séminaire au laboratoire
mercredi 13 décembre à 10:00, en 361

Natalia Tronko

Max-Planck-Institut für Plasmaphysik and Technische Universität München, Fakultät der Mathematik, Garching, Germany,

abstract :

Strongly magnetized plasmas, such as astrophysical and laboratory ones, represent complex multi-scaled systems in space and time. Building up reduced models : both kinetic and fluid allows one to access physical mechanisms in different regimes (e.g., turbulent, collisional) and geometry configurations.
Since more than three decades now, reduced kinetic models like gyrokinetics, resulting from the elimination of the fast scales of motion associated with the particle rotation around magnetic field lines, is the focus of intense research, both theoretical and numerical. Such an approach allows a drastical reduction of computational time for numerical simulations. The gyrokinetic reduction provides access to accurate prediction of long-scale processes such as transport which is one of the main issues for fusion plasma confinement [1]. For astrophysical plasmas, the gyrokinetic theory is also of interest [2]. Recently, gyrokinetic simulations have been used to access small scale spectra, in order to fill the gaps in prediction of solar wind behavior when magnetohydrodynamics approximations fail.
Building up a solid theoretical basis following consistent derivation of the reduced equations with careful handling of orderings is an ultimate starting point for development of trustworthy numerical simulations. A systematic derivation, which guarantees the energetic consistency of gyrokinetic models requires advanced mathematical tools such as differential geometry (perturbative Lie-transformation techniques) as well as advanced variational calculus on functional spaces.
The gyrokinetic Lagrangian is the central object of the derivation, it contains information about all the approximations and orderings, which will be naturally transferred to the equations of motion and associated conserved quantitites. Furthermore, the Noether theorem can be applied to the gyrokinetic Vlasov-Maxwell system issued from the variational formulation for derivation of the associated conserved quantities. In particular, the energy invariant represents a special interest for verification of quality of numerical simulations.
In this talk a systematic approach developed within the European enabling research project VeriGyro for verification of major European gyrokinetic codes both theoretically [3] and numerically [4] will be presented. An example of implementation of energy conservation law into the Particle- In-Cell gyrokinetic code ORB5 will be considered for verification of quality of simulations[5].
[1] X. Garbet, Y. Idomura, L. Villard, and T. H. Watanabe. Gyrokinetic simulations of turbulent transport. Nuclear Fusion, 50:043002, 2010.
[2] A. A. Schekochihin, S. C. Cowley, W. Dorland, G. W. Hammett, G. G. Howes, E. Quataert, and T. Tatsuno. Astrophysical gyrokinetics : kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophysical Journal Supplement, 182:310, 2009.
[3] N. Tronko, T. Bottino, A. Goerler, E. Sonnendru ̈cker, D. Told, and L. Villard. Verification of gyrokinetic codes : theoretical background and applications. Physics of Plasmas, 24:056115, 2017.
[4] T. Goerler, N. Tronko, W. A. Hornsby, A. Bottino, R. Kleiber, C. Norcini, V. Grandgirard, F. Jenko, and E. Sonnendru ̈cker. Intercode comparison of gyrokinetic global electromagnetic modes. Physics of Plasmas, 23:072503, 2016.
[5] N. Tronko, A. Bottino, and E. Sonnendru ̈cker. Second order gyrokinetic theory for Particle-In- Cell codes. Physics of Plasmas, 23:082505, 2016.

contact : Magali Muraglia


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