A high-accuracy method of computation of X-ray waves propagation through an optical system consisting many lenses

• Autorzy: Kshevetskii S. , Wojda P.

Identyfikatory

DOI

10.17466/TQ2016/20.2/F

• Języki publikacji: EN

Abstrakty

EN

The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated mathematically and investigated. The presented results for equations show that in order to establish a high accuracy computation a much smaller number of points is needed to solve the problem of X-ray waves propagation through a multi-lens system when the method for the second equation is used. The reason for such a result is that the electric field of a wave after passing through many lenses is a quickly oscillating function of coordinates, while the electric field phase is a quickly increasing, but not oscillating function. Therefore, a very detailed difference grid, which is necessary to approximate the considered electric field can be replaced by not such a detailed grid, when computations are made for the complex wave of the electric field. The simulation error of both suggested methods is estimated. It is shown that the derived equation for a phase function allows efficient simulation of propagation of X-rays for the multi-lens optical system.

Słowa kluczowe

EN

X-ray wave; X-ray optic; lens; non-uniform medium; focusing; numerical method; simulation; finite differences; stability; numerical error; wave phase; electromagnetic wave; fast oscillating function

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2016
• Tom: Vol. 20, No 2
• Strony: 171--186
• Opis fizyczny: Bibliogr. 16 poz., rys., tab.

Twórcy

autor

Kshevetskii S.

• Baltic I. Kant Federal University Al. Nevsky 14, Kaliningrad, Russia

autor

Wojda P.

• Gdansk University of Technology Narutowicza 11/12, 80-233 Gdansk, Poland

Bibliografia

• [1] Snigirev A, Kohn V, Snigireva I and Lengeler B 1996 Nature 384 49
• [2] Kohn V, Snigireva I, Snigirev A 2003 Optics Communications 216 247
• [3] Kohn V G 2002 Letters in JETPH 76 (10) 701
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• [5] Artemiev A, Snigirev A V I, Artemiev N, Grigoriev M, Peredkov S, Glikin L, Levtonov M V, Zabelin A, and Maevskiy A 2006 Review of Scientific Instruments 77, 063113-1
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• [9] Kohn V G 2012 J. Synchrotron Rad 19 84
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• [11] Kohn V G 2009 A. surface, X-ray, synchrotron and neutron researches 5 32
• [12] Leontovich M A 1944 Izvestiya AN SSSR, Ser. Phys. 8 16
• [13] Babich V M and Buldyrev V S 1972 Asymptotic methods in problems of diffraction of short waves
• [14] Kshevetskii S P and Wojda P 2014, Proc. SPIE 9209, Advances in Computational Methods for X-Ray Optics III 92090Q
• [15] Berezin I S and Zydkov N P 1966 Computing Methods 3rd ed. 1; 1962 2nd ed. 2
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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę