Fig. 1. (a) Schematic diagram of an intense Laguerre–Gaussian laser pulse interaction with a micro-droplet target. Here, the map in the plane presents the projection of electron density and the red curve in the plane shows the photon density distribution along the laser axis. The U-shaped red arrow shows the scattering process of a counterstreaming linearly polarized Gaussian laser pulse off a rotating relativistic electron sheet. (b) Transverse electron density distribution at , 20 and 30, respectively. (c), (d) Electron divergence angle at and evolution of the electron energy spectrum. (e), (f) Electron distribution in the phase space and at . Here, the magenta arrows in (b) denote the average transverse momentum of electrons at each cell. The red curves in (e) and (f) represent electron numbers with respect to the longitudinal velocity and dephasing rate , respectively.

Fig. 2. (a) Normalized longitudinal electric field and (b) Q factor with respect to . The red, black, blue and green curves correspond to the cases of CEP , , and , respectively. Evolution of with respect to when the CEP equals (c) , (d) , (e) and (f) in the case of (dashed) and (solid), respectively.

Fig. 3. (a)–(d) Electron density distribution at and (e)–(h) corresponding electron energy distribution at in the plane when , , and , respectively.

Fig. 4. (a) Density distribution, (b) angular distribution, (c) energy distribution and (d) energy spectrum and brilliance of high-energy -photons with energy of more than 1 MeV at . Here, the magenta arrows in (a) denote the average transverse momentum of -photons at each cell. The black double-headed arrow in (b) denotes the polarization direction.

Fig. 5. (a) Evolution of energy and BAM for electrons and -photons. (b) Distribution of the average OAM along energy . (c) Spectrum of for electrons and -photons. Influence of the laser intensity on the (d) energy and BAM conversion efficiency and , (e) energy spectrum and (f) brilliance of -photons.