  We demonstrate that a mm-scale free electron laser can operate in the X-ray
range, in the interaction between a moderately relativistic electron bunch, and
a transverse high intensity optical lattice. The corrugated light-induced
ponderomotive potential acts simultaneously as a guide and as a low-frequency
wiggler, triggering stimulated Raman scattering. The gain law in the small
signal regime is derived in a fluid approach, and confirmed from
Particle-In-Cell simulations. We describe the nature of bunching, and discuss
the saturation properties. The resulting all-optical Raman X-ray laser opens
perspectives for ultra-compact coherent light sources up to the hard X-ray
range.
