  We demonstrate, theoretically and experimentally, that a traveling electric
charge passing from one photonic crystal into another generates edge waves --
electromagnetic modes with frequencies inside the common photonic bandgap
localized at the interface -- via a process of transition edge-wave radiation
(TER). A simple and intuitive expression for the TER spectral density is
derived and then applied to a specific structure: two interfacing photonic
topological insulators with opposite spin-Chern indices. We show that TER
breaks the time-reversal symmetry and enables valley- and spin-polarized
generation of topologically protected edge waves propagating in one or both
directions along the interface. Experimental measurements at the Argonne
Wakefield Accelerator Facility are consistent with the excitation and
localization of the edge waves. The concept of TER paves the way for novel
particle accelerators and detectors.
