A more general analytical theory of X‐ray beam propagation through compound refractive lenses (CRLs) than the earlier study by Kohn [(2003). JETP, 97, 204–215] is presented. The problem of nanofocusing with CRLs is examined in detail. For a CRL with a relatively large aperture the focusing efficiency is limited by the radiation absorption in the lens material. The aperture does not affect the focusing process and it is replaced by the effective aperture. The X‐ray transverse beam size at the focus is then by a factor of γ = β/δ times smaller than the transverse beam size just behind the CRL. Here, δ and β are the real and imaginary parts of the CRL material refractive index n = 1 − δ + iβ. In this instance, to improve focusing efficiency, it is advantageous to decrease the CRL aperture and increase the photon energy E. However, with increasing photon energy, the material absorption decreases, which results in the CRL aperture impact on the transverse beam size. The latter leads to the fact that with a proper CRL length the beam size is independent of both the aperture and photon energy but depends only on the CRL material electron density and is approximately equal to w_c = λ/(8δ)^1/2, where λ denotes the radiation wavelength, as predicted by Bergemann et al. [(2003). Phys. Rev. Lett, 91, 204801].

中文翻译：

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使用复合折射透镜进行X射线束纳米聚焦的可行性

X射线束通过复合折射透镜（CRL）传播的更广泛的分析理论比Kohn [（2003）的早期研究。JETP，97，204-215]给出。详细研究了CRL的纳米聚焦问题。对于具有较大孔径的CRL，聚焦效率受到透镜材料中辐射吸收的限制。光圈不影响聚焦过程，而是由有效光圈代替。然后，焦点处的X射线横向光束尺寸比CRL后面的横向光束尺寸小γ=β/δ倍。此处，δ和β是CRL材料折射率n = 1-δ+ i的实部和虚部β。在这种情况下，为了提高聚光效率，有利的是减小CRL孔和增加光子能量ë。但是，随着光子能量的增加，材料的吸收会减少，这会导致CRL孔径对横向光束尺寸的影响。后者导致这样一个事实，即在具有适当的CRL长度的情况下，光束大小与孔径和光子能量均无关，而仅取决于CRL材料的电子密度，并且大约等于w _c =λ/（8δ）^1/2， λ表示辐射波长，如Bergemann等人所预测。[（（2003）。物理 牧师快报，91，204801]。