  In vacuum with an induced by strong electromagnetic wave refraction index
larger than unity, an ultra-relativistic electron emits Cherenkov radiation.
During the interaction with this wave the electron also radiates photons via
the Compton scattering. Synergic Cherenkov-Compton process can be observed by
colliding laser accelerated electrons with a high intensity electromagnetic
pulse. Extremely high energy photons cannot be emitted via the Cherenkov
radiation because the vacuum refraction index tends to unity at these energies.
Experiments on studying these phenomena will reveal the properties of vacuum
predicted by nonlinear quantum electrodynamics.
