The general framework of this topic is the study of ITER or LMJ type instabilities in fusion plasmas.

Instabilities evolve non-linearly towards turbulence. This turbulence allows the transport of heat and matter, reducing plasma confinement. The aim is thus to determine the nature of underlying instabilities, to demonstrate their non-linear saturation processes and to set up possible control methods.

To that end, it is necessary to solve Maxwell equations and calculate the response of the plasma to field perturbations. To evaluate this response, physicists have the choice between a fluid description and a kinetic one.

The fluid model (3D) involves moments of the distribution function and requires an appropriate "closure" relationship. This relationship is difficult to justify when the plasma is collisionless, which is the case for fusion plasmas.

In the kinetic approach (6D), the evolution of the distribution function in time and space is studied. For collisionless hot plasmas, the Vlasov equation governs the evolution of the distribution function. The numerical treatment of the kinetic model is more demanding than that of the fluid model, but it correctly describes the Landau effect.

Furthermore, it gives transport associated with the turbulent fluctuations that is closer to the experimental reality than that provided by the fluid models. It also allows the problem of the closure hypothesis of the fluid model to be avoided.