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In the paper, we consider the Cauchy problem on the spatially one-dimensionalVlasov-Poisson-Landau system modelling the motion of ions under a generalizedBoltzmann relation. Let the Knudsen number and the Debye length be given as$\varepsilon>0$ and $\varepsilon^{b}$ with $\frac{3}{5}\leq b\leq 1$,respectively. As $\varepsilon\to 0$ the formal Hilbert expansion gives thefluid limit to the quasineutral compressible Euler system. We start from thesmall-amplitude rarefaction wave of the Euler system that admits a smoothapproximation with a parameter$\delta\sim\varepsilon^{\frac{3}{5}-\frac{2}{5}a}$, where the wave strength isindependent of $\varepsilon$ and we take $\frac{2}{3}\leq a\leq 1$ if$\frac{2}{3}\leq b\leq 1$ and $4-5b\leq a\leq 1$ if $\frac{3}{5}\leq b<\frac{2}{3}$. Under the scaling $(t,x)\to(\varepsilon^{-a}t,\varepsilon^{-a}x)$, for well-prepared initial data weconstruct the unique global classical solution to the Vlasov-Poisson-Landausystem around the rarefaction wave in the vanishing limit $\varepsilon\to 0$and also obtain the global-in-time convergence of solutions toward therarefaction wave with rate$\varepsilon^{\frac{3}{5}-\frac{2}{5}a}|\ln\varepsilon|$ in the$L^{\infty}_xL^2_v$ norm. The best rate is$\varepsilon^{\frac{1}{3}}|\ln\varepsilon|$ with the choice of $a=\frac{2}{3}$and $\frac{2}{3}\leq b\leq 1$. Note that the nontrivial electric potential inthe solution connects two fixed distinct states at the far fields $x=\pm\infty$for all $t\geq 0$ and tends asymptotically as $\varepsilon\to 0$ toward aprofile determined by the macro density function under the quasineutralassumption. Our strategy is based on an intricate weighted energy methodcapturing the quartic dissipation to give uniform bounds of the nonlineardynamics around rarefaction waves.

Global quasineutral Euler limit for the Vlasov-Poisson-Landau system with rarefaction waves