Final answer:
The peak wavelength of synchrotron radiation is determined by the speed of the charged particle and the strength of the magnetic field within the synchrotron which accelerates particles and contains them in a fixed-radius path.
Step-by-step explanation:
The peak wavelength of synchrotron radiation is controlled by the speed of the charged particle and the magnetic field strength. These two factors influence how the charged particles emit synchrotron radiation as they are accelerated to very high energies in the synchrotron. Synchrotron radiation is significant in the context of particle accelerators like the ones found at CERN and SLAC, where particles are sped up to velocities that could be a substantial fraction of the speed of light. In synchrotrons, the magnetic field is synchronized with the increasing speed of the particles to keep their path at a fixed radius, hence the name synchrotron.