So different sources can result of the radiation of different types of particles (note this is a bit different than considering photons as radiation like you do in E&M).
As far as I know, for circular accelerators like the LHC, the idea is to get the collision energy high enough to create particles of interest based on the collision alone, so particles below a certain mass range can be created by an accelerator of a given energy.
For the linear accelerators I know of, the idea is to accelerate some nucleus and collide it with a target of a given material. You then typically get a variety of…