Well-Posedness of a Diffusive Gyrokinetic Model

TL;DR

This paper proves the well-posedness of a gyrokinetic model for plasma ions, incorporating a collision operator to address regularity issues, and demonstrates global existence and stability of solutions.

Contribution

It introduces a linear collision operator to improve regularity and establishes global existence, uniqueness, and stability results for the gyrokinetic model.

Findings

Global existence of solutions proven

Short time uniqueness established

Stability results demonstrated

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.