Experimental requirements for X-ray compact free electron lasers with a laser wiggler

In this paper we specify the experimental parameters required to operate a Free Electron Laser with a laser wiggler in the Angstrom region. Both the quantum and the classical regimes are discussed. The quantum regime of SASE can be reached with more realistic parameters than the classical one. The fundamental feature of the quantum SASE is the extremely narrow single-line radiation spectrum, whose line width can be four orders of magnitude smaller than the bandwidth of the classical spiky SASE spectrum.