BriXSinO: Brilliant source of X-rays based on Sustainable and innOvative accelerators.

We present the design study of the innovative accelerator BriXSinO. BriXSinO is able to generate high repetition rate (multi-MHz-class) high-brightness electron beams by using a Super Conducting Linac, operating in Continuous Wave mode, equipped with an arc bringing the electrons back to the Linac. The electron beam travels therefore twice through the Super Conducting Linac, permitting to work either in energy recovering regime for sustainable operations or in the two-pass two-way mode, doubling the final energy. In addition to allowing the exploration of these fundamental and promising Beam Dynamical processes, BriXSinO drives two synchronized radiation sources: a Free-Electron Laser Oscillator producing terahertz waves and an Inverse Compton Scattering based on a laser in Fabry-P\'$e$rot cavity, delivering X-rays.