Analytical solution of crystal diffraction intensity

Plasma density and temperature can be diagnosed by x-ray line emission measurement with crystal, and bent crystals such as von Hamos and Hall structures are proposed to improve the diffraction brightness. In this study, a straightforward solution for the focusing schemes of flat and bent crystals is provided. Simulations with XOP code are performed to validate the analytical model, and good agreements are achieved. The von Hamos or multi-cone crystal can lead to several hundred times intensity enhancements for a 200μm plasma source. This model benefits the applications of the focusing bent crystals.