Two-dimensional Finite Larmor Radius approximation in canonical gyrokinetic coordinates
This work offers a new mathematical perspective on gyrokinetic approximations for plasma physics, but is incremental as it refines existing proofs.
The paper provides a new proof of the 2D finite Larmor radius approximation of the Vlasov-Poisson system with a strong magnetic field using two-scale convergence in canonical gyrokinetic coordinates, extending previous work by Frénod, Sonnendrücker, and Bostan.
In this paper, we present some new results about the approximation of the Vlasov-Poisson system with a strong external magnetic field by the 2D finite Larmor radius model. The proofs within the present work are built by using two-scale convergence tools, and can be viewed as a new slant on previous works of Frénod and Sonnendrücker and Bostan on the 2D finite Larmor Radius model. In a first part, we recall the physical and mathematical contexts. We also recall two main results from previous papers of Frénod and Sonnendrücker and Bostan. Then, we introduce a set of variables which are so-called canonical gyrokinetic coordinates, and we write the Vlasov equation in these new variables. Then, we establish some two-scale convergence and weak-* convergence results.