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X-Ray Propagation Simulation

X-Ray Propagation Simulation. Student: Jing Yee Chee Advisors: Kenneth D. Finkelstein David Sagan Georg H. Hoffstaetter. Motivation. The ultimate goal of BMAD Track both charged particles and photons from source (electron gun) through the beamline to the sample

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X-Ray Propagation Simulation

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  1. X-Ray Propagation Simulation Student: Jing Yee Chee Advisors: Kenneth D. Finkelstein David Sagan Georg H. Hoffstaetter

  2. Motivation • The ultimate goal of BMAD • Track both charged particles and photons from source (electron gun) through the beamline to the sample • Build up a subroutine library that users can easily use to write programs

  3. Tracking particles from electron gun to beamlines! • Need to extend into photon optics and weakly relativistic particles • Mirror element already implemented by previous REU student and David • This project aims to add 1 more element to BMAD’s library

  4. Crystal Element • Perfect crystals are an important element in x-ray optics • Frequently used as monochromators • Diffracts (reflects) according to Bragg’s Law • However, this is only an approximate law

  5. Dynamical Diffraction • A more accurate account of diffraction was developed in the 20th century • Some pioneers include Sir Charles Galton Darwin, Max von Laue, Paul Peter Ewald • Summarized in Batterman and Cole, a very well cited 1964 paper • Basically it involves solving Maxwell’s equations in a region of periodic electron density

  6. Some results from the theory For symmetric Bragg reflection, Bragg’s Law: Diagram greatly exaggerates deviations from Bragg’s Law

  7. Some results from the theory For symmetric Bragg reflection,

  8. Some results from the theory For symmetric Bragg reflection, • Equation still holds, but for wave vectors inside crystal. • Dispersion surface gives allowed wave vectors • Reflectivity can be determined by determining which point on dispersion surface is active

  9. Some results from the theory (cont’d) • However, things are complicated by the fact that the crystal is rarely cut perfectly • i.e. ns is not in the direction of H • The case where H, kin, ns, are coplanar is known as asymmetric Bragg reflection • Very well studied, eg. by Matsushita and Kaminaga

  10. How do we describe single photons? • Similar description to charged particle optics • Or equivalently, if defined relative to some reference particle with energy λ • Add in ϑ for polarization and I for intensity of radiation.

  11. 2 stage algorithm • Firstly, find the center of reflection • Output the required graze angle of the crystal to achieve the center of reflection • Output orientations of the outgoing reference basis • Track individual photons as they diffract • Coordinates to be transformed into the outgoing basis

  12. Current Progress • 1st stage of the algorithm has been written and debugged • Results for the simpler cases compared to output from xop • 2nd stage is on its way…

  13. Future Work • Curved optical elements • Eg. capillaries • Time-evolution of short pulses of radiation • Tracking of phase fronts

  14. Questions?

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