  The inverse Compton scattering of laser light on high-energetic twisted
electrons is investigated with the aim to construct spatially structured x-ray
beams. In particular, we analyze how the properties of the twisted electrons,
such as the topological charge and aperture angle of the electron Bessel beam,
affects the energy and angular distribution of scattered x-rays. We show that
with suitably chosen initial twisted electron states one can synthesize
tailor-made x-ray beam profiles with a well-defined spatial structure, in a way
not possible with ordinary plane-wave electron beams.
