Bremsstrahlung in synchrotrons In synchrotons electrons are accelerated by undulators or wigglers. However, I don't get how you produce Bremsstrahlung, because Bremsstrahlung is a 3-particle process: charged particles, ions and photons are needed. The ions are needed for momentum conservation, because photons which are generated have a bigger momentum than electrons. 
But where do we have ions in a synchrotron? 
I thought only electrons were accelerated by undulators and wigglers, and the breaking electrons produce photons when they collide with ions. But where do we have those ions in synchrotrons?
 A: OK, following discussion in the comments I think I see where your confusion originates.

You can draw one box and say 

"this reaction between a photon, an electron, and a nucleus is isolated and conserves momentum", 

but you could also draw a slightly different box and say 

"this reaction between a photon and an electron is subject to an external force which is why it doesn't conserve momentum"1

where the force is provided by the field of a nucleus. But in the latter view view you don't need the nucleus, you need the field.
In the context of interactions between ionizing radiation and matter Bremsstrahlung involves a nucleus and is usually discussed in terms like the former. Because nuclei are the source of strong fields that is present in those contexts.
But if we, as experimentors provide a wiggler (or even just a bending or focusing magnet) we are providing the field in places where there are a negligible number of nuclei present (in the evacuated beam pipe), so we need to view the process in the latter terms.

1 This is a place where the strict language distinction between "conserves [X]" and "total [X] of the system is constant" that some authors are making these days leads to really excessive wordiness. Of course, gloabal momentum is conserved; but some is carried away from the eletron/photon system in the form of a non-trivial Poynting vector in the field.
A: First of all in order to dissipate confusion I would like to point out that the magnets of wigglers and undulators (insertion devices) in a synchrotron are assembled in a way that they produce strongly focalized synchrotron radiation (i.e. their magnetic fields act on the electrons in a way so that they radiate synchrotron radiation). This type of radiation is not considered as bremsstrahlung.
However, wigglers and undulators can also be source of bremsstrahlung if an electron out of the foreseen orbit hits them and gets desaccelerated thereby producing bremsstrahlung. This scenario is not as seldom as it might seem. The magnets of insertion devices are vertically much closer to beam than the walls of the vacuum chamber the beam is usually guided in outside of these devices. So in order to get through the insertion devices the beam has to be more strongly focussed vertically than outside of the insertion devices.
This shows the importance of strong focalisation of the electron beam which however leads to secondary effects, for instance intra-bunch scattering of electrons kicks electrons out of the phase space they need to be in for staying on the orbit. Such electrons can hit the magnets of the insertion devices and create strong bremsstrahlung.
Moreover, another source of bremsstrahlung are indeed rest-gas of rest ions in the "vacuum"
which electrons can hit on their orbit. The collision leads to emission of bremsstrahlung. They will be always some ions in the vacuum chamber because the vacuum chamber is exposed to synchrotron radiation which facilitates the desorption of ions from the vacuum chamber walls.
Finally, controlled or uncontrolled beam losses moves electrons from their usual orbit so that they can hit insertion devices or vacuum chamber walls. Both collisions also lead to bremsstrahlung.
All of these processes are undesired and therefore synchrotrons are constructed in a way that they are suppressed as much as possible. Nevertheless the effects cannot be completely avoided and therefore bremsstrahlung remains of most important source of radiation exposure of a synchrotron.
