On the asymptotic limit of the three dimensional Vlasov-Poisson system for large magnetic field : formal derivation

TL;DR

This paper rigorously derives the long-term behavior of the 3D Vlasov-Poisson system under strong magnetic fields, revealing the guiding center approximation and drift velocities, especially considering non-constant magnetic fields.

Contribution

It provides a formal derivation of the asymptotic limit of the 3D Vlasov-Poisson system with strong magnetic fields, including non-constant fields, extending previous results.

Findings

Motion splits into stationary flow and guiding center drift

Classical drift velocities are recovered in the asymptotic limit

Effect of nonconstant magnetic fields is analyzed

Abstract

This paper establishes the long time asymptotic limit of the three dimensional Vlasov-Poisson equation with strong external magnetic field. The guiding center approximation is investigated in the three dimensional case with a non-constant magnetic field. In the long time asymptotic limit, the motion can be split in two parts : one stationary flow along the lines of the magnetic field and the guiding center motion in the orthogonal plane of the magnetic field where classical drift velocities are recovered. We discuss in particular the effect of nonconstant external magnetic fields.