A setup of a unique x-ray source is put forward employing a relativistic electron beam interacting with two counter-propagating laser pulses in the nonlinear few-photon regime. In contrast to Compton scattering (CS) sources, the envisaged x-ray source exhibits an extremely narrow relative bandwidth of $10^{-5}$ to $10^{-4}$, comparable to the x-ray free-electron laser (XFEL). The brilliance of the x-rays can be $2 - 3$ orders of magnitude higher than a state-of-the-art CS source, while the angle spreading of the radiation is much smaller. By tuning the laser intensities and the electron energy, one can realize either a single peak or a comb-like x-ray source around keV energy. The laser intensity and the electron energy in the suggested setup are rather moderate, rendering this scheme compact and table-top size, as opposed to XFEL and synchrotron infrastructures.
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