Reduction of SAXS Signal due to Doppler Broadening Induced Loss of Coherence

TL;DR

This paper analyzes how Doppler broadening in laser-heated plasmas reduces SAXS signal coherence, affecting intensity and spectral features, with implications for plasma diagnostics and XFEL applications.

Contribution

It provides an analytical and numerical framework to quantify Doppler-induced coherence loss in SAXS signals and its impact on measurements in high-temperature plasmas.

Findings

Doppler broadening reduces SAXS intensity and broadens Bragg peaks.

Coherence loss is manageable for SASE XFELs but significant in seeded setups.

The study offers criteria for including Doppler effects in SAXS data analysis.

Abstract

We present an analytical and numerical study of how Doppler-induced spectral broadening in laser-heated plasmas degrades the coherence of small-angle X-ray scattering (SAXS) signals, and show that the resulting loss of temporal coherence reduces the SAXS intensity. Applying this formalism to two benchmark geometries - single density steps (wires) and periodic gratings -- we obtain analytic estimates. For gratings, finite coherence simultaneously lowers Bragg-peak heights and broadens their widths, whereas for isolated steps only the overall scaling with q affected. We map the parameter space relevant to current SASE and self-seeded XFELs, revealing that Doppler effects remain managable for the trieval of geometry parameters (less than few 10 % error) for SASE bandwidths but become the dominant error source in seeded configurations or above-keV temperatures. Practical consequences for density-gradient retrieval and interface-sharpness measurements are quantified. The results supply clear criteria for when Doppler broadening must be included in SAXS data analysis and offer a route to infer electron temperature directly from coherence-loss signatures.