The gyrokinetic limit for the Vlasov-Poisson system with a point charge

TL;DR

This paper investigates the behavior of a 2D Vlasov-Poisson system with a point charge under a large magnetic field, demonstrating convergence to a measure-valued Euler solution with a defect measure in an asymptotic regime.

Contribution

It establishes the gyrokinetic limit for the Vlasov-Poisson system with a point charge, linking kinetic and fluid descriptions in a novel setting.

Findings

Solution converges to a measure-valued Euler solution

Demonstrates the effect of large magnetic fields on plasma dynamics

Introduces a framework for analyzing singular interactions in kinetic systems

Abstract

We consider the asymptotics of large external magnetic field for a 2D Vlasov-Poisson system governing the evolution of a bounded density interacting with a point charge. In a suitable asymptotical regime, we show that the solution converges to a measure-valued solution of the Euler equation with a defect measure.