Finite-difference solution of parabolic equation and numerical simulation for X-ray focusing

• Autorzy: Elsawy M. H. R. A. , Leble S.
• Języki publikacji: EN

Abstrakty

EN

In this paper we apply the finite-difference method to solve a parabolic equation of a general problem of short wave diffraction in a conducting medium. It is based on the implicit Runge-Kutta method of the second order combined with the iterative procedure. We also present new numerical simulations for X-rays focusing using the mentioned approach. We consider CRLs with a parabolic profile with a radius of curvature up to 0.2 mm. The main goal of this work is to elaborate an X-ray calculator for a PC which would present new possibilities compared to conventional ones. The correspondent code is written in FORTRAN to obtain the focal distance and diffraction spot profiles. Simulations for two cases were performed, the first one with 33 Al lenses for X-ray energy 15 keV, the results showed that we needed to consider more than 50000 points in each direction which forced us to consider a one-dimensional simulation only. For the second case we performed a simulation for several lenses, up to 15 Al lenses to perform the 2-d simulation. We have good agreement with the experimental data for the focal distance, and for the intensity at the focal plane while, for the spot size, we have smaller FWHM for the Gaussian beam at the detector than in the experimental data. We believe that the FWHM we have is smaller as our lenses are ideal without any defects.

Słowa kluczowe

EN

finite difference model; focusing X-rays; Runge-Kutta

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2014
• Tom: Vol. 18, No 1
• Strony: 101--111
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

Twórcy

autor

Elsawy M. H. R. A.

• Faculty of Applied Physics and Applied Mathematics Gdansk University of Technology Narutowicza 11/12, 80-223 Gdansk, Poland
• Im. Kant Baltic Federal University A. Nevskogo 14, 236041 Kaliningrad, Russia

autor

Leble S.

• Im. Kant Baltic Federal University A. Nevskogo 14, 236041 Kaliningrad, Russia

Bibliografia

• [1] Lengeler B, Schroer Ch, Tummler J, Benner B, Richwin M, Snigirev A, Snigireva I and Drakopoulos M 1999 J. Synchrotron Rad. 6 1153
• [2] Snigirev J, Kohn V, Snigireva I, Souvorov A and Lengeler B 1998 Optical Society of America
• [3] Kohn V G 2003 Journal of Experimental and Theoretical Physics 97 (1) 204
• [4] Snigirev A, Filseth B, Elleaume P, Klocke T, Kohn V, Lengeler B, Snigireva I, Souvorov A and Tummler J 1997 Proc. SPIE High Heat Flux and Synchrotron Radiation Beamlines (ed. Macrander A M K A T) 3151 164
• [5] Bass M, McDonald C, Li G, DeCusatis C M and Mahaja V N Handbook of Optics, Volume V, Atmospheric Optics, Modulators, Fiber Optics, X-Ray and Neutron Optic, third edition, ISBN: 978-0-07-163314-7
• [6] Kshevetskij S and Wojda P 2013 On finite-difference algoritm of X-ray focusing. II Baltic School of solid state physics: ”Methods and Tools X-ray studies”, Im. Kant BFU
• [7] Butcher J C Numerical Methods for Ordinary Differential Equations, Second Edition, Chapter 3. Runge-Kutta Methods