A new class of focusing crystal shapes for Bragg spectroscopy of small, point-like, x-ray sources in laser produced plasmas

This paper describes a new class of focusing crystal forms for the x-ray Bragg crystal spectroscopy of small, point-like, x-ray sources. These new crystal forms are designed with the aid of sinusoidal spirals, a family of curves, whose shapes are defined by only one parameter, which can assume any real value. The potential of the sinusoidal spirals for the design x-ray crystal spectrometers is demonstrated with the design of a toroidally bent crystal of varying major and minor radii for measurements of the extended x-ray absorption fine structure near the Ta-L3 absorption edge at the National Ignition Facility.