| Summary: | Focusing of high-power X-rays is still a great challenge and the intensity of X-ray attained in existing focusing schemes is still far below the relativistic threshold. Here, we propose that solid density plasma lens can potentially focus X-ray lasers at very high power levels. The interaction of high-power X-ray laser with solid-density plasmas is systematically studied. It is theoretically shown that there exists a certain range of wavelengths for X-ray lasers that can be focused in solid-density plasmas when the input power and plasma density are determined. To avoid the essential laser-plasma instabilities and obtain high-gain intensity amplification for X-ray, we design concave structured plasma lens. Particle-in-cell simulation results show that such regime can effectively avoid the instabilities and focus X-ray of micrometer-sized spot and multi-TW power, and thus lead to the generation of relativistic intensity X-ray. The parameters of the concave structures and the effects of quantum electrodynamics are also discussed and it indicates that our scheme is quite robust. We further demonstrate that the relativistic X-ray laser interacting with thin-foil leads to high-quality attosecond electron bunches.
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