Imaging electron trajectories in a laser-wakefield accelerator by measuring the betatron x-ray spectrum angular dependence*

We have performed experiments using the 200 TW Callisto laser system at LLNL to produce GeV-class electron beams and keV Betatron x-rays. The laser was focused into various gas cells with sizes ranging from 3 to 10 mm that contained a mixure of gases (He, N, Ar). We demonstrate that it is possible to do a tomographic reconstruction of electron trajectories inside the channel of the laser-wakefield accelerator from the angular dependence of the Betatron x-ray spectrum, using an image plate-based spectrometer with differential filtering. Experimental results are benchmarked against a code that solves the equation of motion of electrons oscillating in the plasma wake and by calculating the corresponding x-ray radiation spectrum and profile. This combined single-shot, simultaneous spectral and spatial x-ray analysis allows for a 3D reconstruction of electron trajectories in the plasma with micrometer resolution.