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X-ray radiation of relativistic electrons passing through the crystal lattice(in case of channeling radiation) requires electrons with energies just fromtens up to hundreds MeV, but has a drawback: low number of emitted X-rayquanta. However, the brightness of such a source could be potentially increasedif the current density of the electron bunch is high enough to initiate theself amplified spontaneous emission (SASE) process. The conditions at whichthis phenomenon could take place for the case of axial channeling are analyzedin the present paper within the first order perturbation theory. The transitionfrom spontaneous to SASE regime is described, the requirements for bunchcurrent parameters initiating SASE process are determined taking into accountthe periodic structure of the crystal medium. It is also shown that satisfyingBragg diffraction conditions could enhance self amplification. Numericalresults for the case of axial channeling in Si, Ge and C crystals are presentedas an example.

Self amplification of channeling radiation at Bragg diffraction conditions