Well-Posedness of a Diffusive Gyrokinetic Model

Abstract

We study a finite Larmor radius model used to describe the ions distributions in the core of a toka-mak plasma, that consist in a gyro-kinetic transport equation, coupled with an electro-neutrality equation. Since the last equation do not provide enough regularity on the electric potential, we introduce a simple linear collision operator adapted to the finite Larmor radius approximation. Next we study the two-dimensional dynamics in the direction perpendicular to the magnetic field and prove thanks to the smoothing effects of the collisions and of the gyro-average the global existence of solutions, as well as short time uniqueness and stability.

Cited by in corpus (3)

• On the asymptotic limit of the three dimensional Vlasov-Poisson system for large magnetic field : formal derivation
• The Vlasov-Poisson System for Stellar Dynamics in Spaces of Constant Curvature
• Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective