An apparatus for generating x-rays includes an electron beam generator and a first device arranged to apply an RF electric field to accelerate the electron beam from the generator. A photon source is arranged to provide photons to a zone to interact with the electron beam from the first device so as to generate x-rays via inverse-Compton scattering. A second device is arranged to apply an RF electric field to decelerate the electron beam after it has interacted. The first and second devices are connected by RF energy transmission means arranged to recover RF energy from the decelerated electron beam as it passes through the second device and transfer the recovered RF energy into the first device.