The gyrokinetic limit for the Plasma-Charge model in $\mathbb{R}^2$

In this article, we investigate the gyrokinetic limit for the two-dimensional Vlasov-Poisson system with point charges. We show that the solution converges to a measure-valued solution of the Euler equation with a defect measure, which extends the results in [Miot, Nonlinearity, 2019] to the case of multi-point charges and removes the small condition $\sup_{0<\varepsilon<1}\|f_{\varepsilon}^0\|_{L^1}<1$.
Comment: 23 pages