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Abstract: High-intensity X-ray free electron laser (XFEL) beams require optics made of materials with minimal radiation absorption, high diffraction efficiency, and high radiation hardness. Multilayer Laue lenses (MLLs) are diffraction-based X-ray optics that can focus XFEL beams, as already demonstrated with tungsten carbide/silicon carbide (WC/SiC)-based MLLs. However, high atomic number materials such as tungsten strongly absorb X-rays, resulting in high heat loads. Numerical simulations predict much lower heat loads in MLLs consisting of low atomic number Z materials, although such MLLs have narrower rocking curve widths. In this paper, we first screen various multilayer candidates and then focus on Mo2C/SiC multilayer due to its high diffraction efficiency. According to numerical simulations, the maximum temperature in this multilayer should remain below 300°C if the MLL made out of this multilayer is exposed to an XFEL beam of 17.5 keV photon energy, 1 mJ energy per pulse and 10 kHz pulse repetition rate. To understand the thermal stability of the Mo2C/SiC multilayer, we performed a study on the multilayers of three different periods (1.5, 5, and 12 nm) and different Mo2C to SiC ratios. We monitored their periods, crystallinity, and stress as a function of annealing temperature for two different heating rates. The results presented in this paper indicate that Mo2C/SiC-based MLLs are viable for focusing XFEL beams without being damaged under these conditions.
Keywords: x-ray optics, multilayer Laue lens, thermal stability, numerical simulation
Published in DiRROS: 20.12.2024; Views: 80; Downloads: 34
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Keywords: vine water stress, polyphenol biosynthesis, proanthocyanidin polymerization, galloylation, anthocynin
Published in DiRROS: 20.12.2024; Views: 71; Downloads: 15
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Keywords: potujoča trikotničarka, Dreissena polymorpha, zooplankton, DNA, Bohinjsko jezero
Published in DiRROS: 19.12.2024; Views: 69; Downloads: 0

Abstract: Given a closed subset $K$ in ${\mathbb R}$, the rational $K$-truncated moment problem ($K$-RTMP) asks to characterize the existence of a positive Borel measure $\mu$, supported on $K$, such that a linear functional ${\mathcal L}$, defined on all rational functions of the form ${f \over q}$, where $q$ is a fixed polynomial with all real zeros of even order and $f$ is any real polynomial of degree at most $2k$, is an integration with respect to ▫$\mu$▫. The case of a compact set ▫$K$▫ was solved by Chandler in 1994, but there is no argument that ensures that $\mu$ vanishes on all real zeros of $q$. An obvious necessary condition for the solvability of the $K$-RTMP is that ${\mathcal L}$ is nonnegative on every $f$ satisfying $f|_K \ge 0$. If ${\mathcal L}$ is strictly positive on every $0 \ne f|_K \ge 0$, we add the missing argument in Chadler's solution and also bound the number of atoms in a minimal representing measure. We show by an example that nonnegativity of ${\mathcal L}$ is not sufficient and add the missing conditions to the solution. We also solve the $K$-RTMP for unbounded $K$ and derive the solutions to the strong truncated Hamburger moment problem and the truncated moment problem on the unit circle as special cases.
Keywords: truncated moment problem, rational truncated moment problem, representing measure, moment matrix, localizing moment matrix, preordering
Published in DiRROS: 19.12.2024; Views: 75; Downloads: 26
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Published in DiRROS: 19.12.2024; Views: 73; Downloads: 21
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