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Using the hydrodynamic model in the electrostatic approximation, we describe the formation of graphene surface plasmons when a charge is in motion either perpendicular or parallel to a graphene sheet. In the first case, the electron-energy loss (EEL) spectrum of the electron is computed, showing that the resonances in the spectrum are linked to the frequency of the graphene surface plasmons. In the second case, we discuss the formation of plasmonic wakes due to the dragging of the surface plasmons induced by the motion of the charge. This effect is similar to Coulomb drag between two electron gases at a distance from each other. We derive simple expressions for the electrostatic potential induced by the moving charge on graphene. We find an analytical expression for the angle of the plasmonic wake valid in two opposite regimes. We show that there is a transition from a Mach-type wake at high speeds to a Kelvin-type wake at low ones and identify the Froude number for plasmonic wakes. We show that the Froude number can be controlled externally tunning both the Fermi energy in graphene and the dielectric function of the environment, a situation with no parallel in ship wakes. Using EEL we propose a source of graphene plasmons, based on a graphene drum built in a metallic waveguide and activated by an electron beam created by the tip of an electronic microscope. We also introduce the notion of a plasmonic billiard.

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Assuming a two-component quasar structure model consisting of a central compact source and an extended outer feature, we produce microlensing simulations for a population of compact masses in the lensing galaxy of Q2237+0305. Such a model is a simplified version of that adopted to explain the brightness variations observed in Q0957. The microlensing light curves generated for a range of source parameters were compared to the light curves obtained in the framework of the Optical Gravitational Lensing Experiment program. With a large number of trials, we built, in the domain of the source structure parameters, probability distributions to find 'good' realizations of light curves. The values of the source parameters which provide the maximum of the joint probability distribution calculated for all the image components have been accepted as estimates for the source structure parameters. The results favour the twocomponent model of the quasar brightness structure over a single compact central source model, and in general the simulations confirm the Schild-Vakulik model that previously described successfully the microlensing and other properties of Q0957. Adopting 3300 km s −1 for the transverse velocity of the source, the effective size of the central source was determined to be about 2 × 10 15 cm, and ε ≈ 2 was obtained for the ratio of the integral luminosity of the outer feature to that of the central source.