The AugerPrime upgrade represents a significant enhancement in the capability of the Pierre Auger Observatory to detect air showers. Central to this advancement is the installation of a radio antenna atop each existing Surface Detector station, constituting the Radio Detector (RD). The RD enhances the sensitivity of the Surface Detector to the electromagnetic component of air showers. Hence, the new detector presents an opportunity for the discovery of rare particles such as ultra-high-energy photons. This contribution shows the development efforts towards an RD trigger with focus on the detection of rare particles. The radio trigger designed for the detection of photon-induced events will be outlined, and the challenge of a radio background consisting of human-made noise is discussed. The trigger efficiency and reconstruction accuracy are studied with simulations. The presentation will conclude by summarizing the effectiveness of the new detector component
