Launching of surface plasmons by swift electrons has long been utilized in electron-energy-loss spectroscopy (EELS) to investigate plasmonic properties of ultrathin, or two-dimensional (2D), electron systems. However, its spatio-temporal process has never been revealed. This is because the impact of an electron will generate not only plasmons, but also photons, whose emission cannot be achieved at a single space-time point, as fundamentally determined from the uncertainty principle. Here, we propose that such a space-time limitation also applies to surface plasmon generation in EELS experiment. On the platform of graphene, we demonstrate within the framework of classical electrodynamics that the launching of 2D plasmons by an electrons impact is delayed after a hydrodynamic splashing-like process, which occurs during the plasmonic formation time when the electron traverses the formation zone. Considering this newly revealed process, we show that previous estimates on the yields of graphene plasmons in EELS have been overestimated.
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