Revisiting the `magic condition' on the basis of the Takagi–Taupin theory

A numerical framework based on the integral solution of the Takagi–Taupin equations has been developed for cylindrically bent Laue crystals. On the basis of this framework, diffraction geometries that satisfy the `magic condition' have been studied from the perspective of dynamical theory. The numerical findings indicate that, in certain diffraction geometries, the focusing behaviour of cylindrically bent Laue crystals will be notably influenced by dynamical effects and the foci of different energies will not converge as predicted by the `magic condition', which is derived from geometric optics theory. These dynamical effects are further explained through a direct numerical analysis of the influence function.