  The present state of progress in laser wakefield acceleration encourages
considering it as a practical alternative to conventional particle
accelerators. A promising application would be to use a laser-plasma
accelerator as an injector for a synchrotron light source. Yet, the energy
spread and jitter of the laser-plasma beam pose a significant difficulty for an
efficient injection. In this paper we propose a design of a prototype injector
to deliver 500 MeV low-intensity electron bunches to the DESY-II electron
synchrotron. The design utilizes presently available conventional accelerator
technology, such as a chicane and an X-band radio frequency cavity, to reduce
the energy spread and jitter of the electron beam down to a sub-per-mille
level.
