Long Time Behavior of Collisional Multi-Species Equations for Strongly Magnetized Plasmas with Mass-Disparate Particles

We consider the long-time behavior of the Vlasov–Poisson–Fokker–Planck equations modeling the dynamics of two-species charged particles (e.g., electrons and ions) in a plasma under the strong effect of magnetic fields while also taking into account their small mass ratio. We derive a fluid model for both electrons and ions. In three space dimensions, a constraint occurs along the parallel direction of the magnetic field lines for each species. When neglecting the curvature of the magnetic lines and focusing on the plane motion of a plasma subjected to a magnetic field orthogonal to the plane, we provide a rigorous mathematical justification of the formally derived system in the two-dimensional setting. Our proofs rely on the modulated energy method.