Single-Shot Reconstruction of Electron Beam Longitudinal Phase-Space in a Laser Wakefield Accelerator

Laser wakefield accelerator (LWFA) is promising for many applications such as future TeV e⁺ - e^- colliders and XFELs. These applications, generally, require high beam quality in terms of energy spread, emittance, shot-to-shot stability, etc. To achieve high beam quality, one has to precisely diagnose the beam dynamics in LWFA. This is difficult owing to the highly nonlinear acceleration process and the sub-μm, sub-fs spatial-temporal diagnostic requirements. Here, we report on a single-shot longitudinal phase-space reconstruction diagnostic for electron beams in a laser wakefield accelerator via the experimental observation of distinct periodic modulations in the angularly resolved spectra. Such modulated angular spectra arise as a result of the direct interaction between the ultra-relativistic electron beam and the laser driver in the presence of the wakefield. A constrained theoretical model for the coupled oscillator, assisted by a genetic algorithm, was used to recreate the experimental electron spectra, and fully reconstruct the longitudinal phase-space distribution of the electron beam with a temporal resolution of ~1.3 fs. In particular, it revealed the slice energy spread of the electron beam, which is important to measure for applications such as XFELs. In our experiment, the root-mean-square slice energy spread retrieved is bounded at 9.9 MeV corresponding to a 0.9-3.0% relative spread, despite the overall GeV energy beam having ~100% relative energy spread. Our method could also be applied for electron beams from traditional accelerators, providing un-precedented temporal resolution, which could, therefore, substantially advance diagnostics for the whole accelerator community.