Phase-space reconstruction of the electron beam via modulated angular spectrum of the electron beam in a laser wakefield accelerator*

Laser wakefield accelerator (LWFA) is promising for many applications such as future TeV e⁺-e^- colliders and advanced radiation sources. These applications require  high beam quality in terms of energy spread, emittance, beam charge, shot-to-shot stability, dark current, etc. To achieve high beam qualities, one has to precisely control the beam dynamics in LWFA, which in turn can only be done with the detailed diagnostic of the beam dynamics. This is  difficult owing to the highly nonlinear acceleration process and the sub-μm, sub-fs spatial-temporal diagnostic requirements. We report on a phasespace diagnostic and reconstruction of the electron beam dynamics via the experimental observation of fishbone-like periodic modulated angular spectra of the electron beams. This is a result of the direct interaction between an electron beam and the laser driver in a laser wakefield accelerator. An analytical model  describes the betatron oscillations and the constant longitudinal acceleration to explain the experimental observation. The analytical model, assisted by a machine learning algorithm, can fully reconstruct the electron beam's transverse and longitudinal momentum distribution, the bunch shape, the pulse duration and the energy chirp. More importantly, it reveals the slice energy spread of the electron beam. The experimental observation and the theoretical model are confirmed by Particle-in-Cell simulations.