Temporal transition radiation

We establish the temporal analogue of transition radiation, when space boundary effects are ignored, and only temporal transitions are considered. We study the radiation spectrum emitted by a bunch of charged particles when they move in a medium where the refractive index abruptly changes in time. We apply it to the case of vacuum-plasma transitions due, for instance, to the sudden ionization of a neutral gas, and determine the spectral range of expected radiation. The case of Rydberg ultracold plasmas is also considered, where the spectral range of emitted radiation is considerably enhanced.