Numerical simulation of diffraction of synchrotron radiation in a single-crystal tungsten.
The influence of pulsed heat load on the tungsten wall of the divertor in a fusion reactor is expected to cause cracks, which will lead to the appearance of plastic deformations. In order to understand how these deformations are formed, and how to avoid it, one has to measure their dynamics during a pulsed heat load. Currently, the diagnostic of the dynamic of such deformations based on the method of fast diffractometry is under development at the BINP SB RAS. The method of fast diffractometry consists in measuring the diffraction pattern of a synchrotron radiation beam (SR) scattered on a sample of a single-crystal, and then in reconstruction of the deformation of the sample according to the form of a diffractograms. The work was carried out in the Laue back reflection method; a mosaic single-crystal tungsten was used as a sample. The model takes into account the absorption of SR, mosaicism of sample, and the kinematic theory of diffraction was used. Firstly, an analytical calculation of SR beam propagation in the sample was carried out, as a result of it an integral expression for the intensity distribution of the scattered radiation was obtained. This expression determined the geometry of scattered SR. The next step was to take into account the mosaicism of a single-crystal tungsten by introducing a model distribution function which describes the orientation of crystal planes in a single-crystal. After that, the convolution of these two expressions was carried out by using numerical methods. Pulsed heat load leads to compression and stretching of the surface that as a result is expressed in a rotation of the "reflecting" crystalline plane. The same effect can be achieved by sample rotation. That’s why final expression is determined by the angle of the sample position relatively to the SR beam and the distribution function parameters. Wolfram Mathematica program was created to simulate the scattering of the SR beam in a mosaic single-crystal tungsten to calculate the instrument functions of the problem of the deformation reconstruction in a sample according to the form of diffractograms. Numerical calculations and comparison with experimental data were carried out, and as a result, revealed a discrepancy in the shape of the interference peak. This discrepancy was reduced by using a more appropriate distribution function.