Abstract
Two new methods of computer simulation of synchrotron radiation nanofocusing with planar compound refractive lenses (PCRLs) are presented. The methods are based on the results of analytical theory. In contrast to previous works, the new methods take into account the PCRL aperture. It is especially important at high photon energies, when absorption is low and the calculations based on analytical theory, i.e. without taking into account the aperture, give incorrect results. A computer program was created and specific results were obtained for a silicon PCRL having an aperture of 50 µm, element length of 102 µm and minimum thickness of 2 µm. For an energy of 50 keV and number of elements 300, it focuses the beam to 31 nm size at a distance of one and a half times its length. Analysis of the calculation accuracy for the proposed methods is performed, as well as a demonstration of the capabilities of the computer program.
Highlights
Focusing of X-ray beams due to refractive effects was realized only a hundred years after the discovery of X-rays (Snigirev et al, 1996)
The three calculation methods (CLA, smeared lenses approach (SLA) and approximate smeared lenses approach (ASLA)) considered in the preceding section were implemented in the computer program XRWP11, which is permanently being developed to simulate the propagation of a synchrotron radiation (SR) beam through all elements of the optical scheme at stations of third- and fourth-generation SR sources and X-ray free-electron lasers
We have considered a simple example of calculating the focusing of an X-ray beam using a nanofocusing planar compound refractive lenses (PCRLs) only for the purpose of demonstrating the operation of the program
Summary
Focusing of X-ray beams due to refractive effects was realized only a hundred years after the discovery of X-rays (Snigirev et al, 1996). It is very difficult to accurately manufacture a parabolic surface with a small radius of curvature and a long length along the optical axis This shape is needed for X-ray lenses because the refraction of hard X-rays is very weak. In works by Kohn (2009, 2012), another approach was developed, which did not take into account the PCRL aperture, but used the compressed lens approximation In this model, refraction and absorption took place in a thin transverse layer in the middle of the element length, and this is the same as for the full thickness of the element. The first attempt to take into account the aperture within the framework of the analytical theory was made by Kohn & Folomeshkin (2021), where it was shown that the minimum beam size at the focus can be obtained only at high photon energies, when absorption is minimal. The new calculation methods are implemented in the framework of a universal computer program, which is permanently under development with the aim of using it on SR sources and X-ray free-electron lasers to simulate all optical phenomena
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