The X-ray optics of singly and doubly curved crystals are studied using a vector procedure and rotation matrices and general relations for the angular deviation from the Bragg angle over the crystal surface with a source aligned or misaligned on the Rowland circle. Hence, the effective scattering area, collection solid angle and diffracted X-ray intensity profile on the crystal surface are derived. The effective areas and the diffracted X-ray intensity profiles on the crystal surface for both aligned and misaligned source cases are plotted and compared. It is argued that the introduced point-focusing crystal configuration confirms the radii that have been obtained previously by a trial and error method by optimizing the crystal collection solid angle.

The propagation of arbitrary amplitude dust ion acoustic waves (DIAWs) in a magnetized collisional dusty plasma including hot electrons, with kappa velocity distribution for electrons, warm ions and dust particles has been studied. In the presence of immobile massive dust particulates, DIAWs have been investigated through the Sagdeev pseudopotential method. It is demonstrated that the amplitude and width of the pseudo-potential are increased with the ion density and also with Directional cosines. It is shown that the behaviors of the amplitude and the width of the wave in terms of all of plasma parameters is similar to the our recently work, and the spectral index has a little effect on the wave.

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The focusing properties of several bent crystal geometries, including the newly introduced Pestehe & Askari general point‐focusing system [Pestehe & Askari Germi (2012), Opt. Soc. Am. A, 29, 68–77; Pestehe & Askari Germi (2012), J. Appl. Cryst.45, 890–901], on an arbitrarily positioned detector plane are investigated and illustrated. The properties of the focal points and the generated images are theoretically related to the local, ℓ, and directional, γ, positions of the detector plane for a given position of a point source on the Rowland circle. A general relation is derived for the detector positioning to obtain a specially focused image. This formula for the polar position of the detector plane, given by the two ℓ and γ variables, enables the exact determination of the system astigmatism and the exact calculation of the sagittal and meridional image positions for the spectrometer under study. The astigmatisms of the above‐mentioned bent crystal geometries have been studied, and their sagittal and meridional focal positions and characteristics have been obtained and are illustrated. It is also shown that there is a possibility of designing a spectrometer to focus rays from a linear source onto a point on the Rowland circle.