Focusing of betatron radiation from a laser-wakefield accelerator for XANES studies of warm dense matter

The x-rays produced by a laser wakefield accelerator could be an invaluable source for x-ray absorption near-edge spectroscopy (XANES) measurements of warm dense matter due to their large spectral bandwidth and femtosecond pulse durations. Femtosecond x-ray absorption spectroscopy can provide time-resolved information on the ultrafast dynamics of the non-equilibrium transition of a metal foil from solid to the warm dense matter state: an opportunity to provide information to better describe and understand astrophysical and fusion plasmas. This work portrays the focusing of laser-wakefield acceleration produced betatron radiation for sub-100 fs XANES snapshots of the L-edge (707 eV) of laser-heated iron. The betatron was focused with a toroidal mirror to a spot size of ≈ 50 × 35 μm. The laser heated spot size is ≈ 300 μm enabling all photons emitted by the source to probe a homogeneous region of the warm dense sample, minimizing temperature and density gradients for accurate XANES measurements. We present a ray-tracing model used to compare the performance of the focusing system with the experimental betatron spot measurement, as well as an analysis of the XANES spectra of an unheated thin (50 nm) iron sample.