Conical geometry for sagittal focusing as applied to x rays from synchrotrons

Abstract

We describe a method for simultaneously focusing and monochromatizing x rays from a fan of radiation having as high as 15-mrad divergence in one dimension. This geometry is well suited to synchrotron radiation sources at magnifications of 1/5 to 2 and is efficient for x-ray energies between 3 and 40 keV (0.48 and 6.4 fJ). The method uses crystals bent to part of a cone for sagittal focusing and permits the collection of a larger divergence with less mixing of the horizontal into the vertical divergence than is possible with x-ray mirrors. We describe the geometry required for achieving the highest efficiency when a conical crystal follows a flat crystal in a nondispersive two-crystal monochromator. At a magnification of 1/3, the geometry is identical to that of a cylindrical focusing design described previously [ Nucl. Instrum. Methods172, 237 ( 1980)]. A simple theoretical calculation is shown to agree well with ray-tracing results. Minimum aberrations are observed at magnifications near 1. Applications of the conical focusing geometry to existing and future synchrotron radiation facilities is discussed.