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It is shown theoretically that the asymmetric or inclined double-crystal X-ray monochromator may be used for X-ray pulse compression if the pulse is properly chirped. By adjusting the mutual distance of the two asymmetric or inclined crystals it should be possible to achieve even a sub-femtosecond compression of a chirped free-electron laser pulse. The small d-spacing of the crystal enables a more compact scheme compared with the currently used grating compression scheme. The asymmetric cut of the crystal enables the acceptance of a larger bandwidth. The inclined cut has larger tunability.

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