On the Geometrical Gyro-Kinetic theory

Long Time Behaviour of an Exponential Integrator for a Vlasov-Poisson System with Strong Magnetic Field

“…It is interesting to notice that the trajectories followed by the macroparticles of the PIC method used to solve system (5.31)-(5.33) are the ones given by equation (4.3), but with X ε replaced by C ε . We learn from Littlejohn [19,20] and Frénod, Lutz [10] that it is indeed possible to do that, since X ε and C ε remain close on the long term. We refer also to Frénod, Sonnendrücker [13] and Golse, Saint-Raymond [15], where a kinetic equation version of this approximation is studied, even when the self-induced electric eld is considered.…”

Can One Hear Whistler Waves?

“…Then, the analysis is already more complicated than in the constant case. There are special phenomena at stake, see for instance the articles [8,12,14,16,17].…”

“…These motions have long been of interest to both mathematicians [3,4,12,14,32] and physicists [5,28]. Their description raises difficulties known under the name of the Störmer problem, with actual continuations in the direction of chaos [10].…”

“…The asymptotic study of (1.5) falls under the scope of KAM theory [1,4,21,28] or gyrokinetic theory [5,12,32]. There are three adiabatic invariants (gyro, bounce and drift), providing a qualitative description of the motions.…”

Homogenization-based numerical methods

“…Up to now, actual Tokamak plasma kinetic simulation is based on the Gyro-Kinetic approximation (see [35], [24], [43], [44], [38,39,40] [34], [7], [10], [22], [27], [28], [45,46,47], [25,26], [18,19]) that is a five-dimensional approximated model Figure 1. Starting points, the project targeted points and solution pathways, for the target applications.…”