Radiation with the same properties of typical Cherenkov radiation can be created by structures of electric current that travel faster than light. By manipulating density profiles in plasma acceleration setups, structures up to nanocoulombs of charge are created and may travel faster than the speed of light and emit optical shocks at the Cherenkov angle. Electrons are still subluminal, hence the electrons that compose the structure at a time t = t 0 are different from the electrons in the structure at a time t > t 0.