Reduction of SAXS signal due to Doppler broadening induced loss of coherence

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 is affected. We map the parameter space relevant to current self-amplified spontaneous emission (SASE) and self-seeded x-ray free electron lasers, revealing that Doppler effects remain manageable for the retrieval 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.