All-vortex nonlinear Compton scattering in a polarized laser field

The process of all-vortex nonlinear Compton scattering in an intense and polarized laser field, in which the initial and final electrons and the emitted $\gamma$ photon are all in vortex states, is studied theoretically. We develop a formalism for the process, which allows us to study the exchanges of the orbital angular momentum (OAM) and spin angular momentum among the electron, $\gamma$ photon, and laser. A wave packet of the Bessel-Gaussian type is adopted to describe the initial vortex electron for the purpose of normalization. Both circularly and linearly polarized lasers are examined. Substantial numerical calculations are performed to reveal the physics of the exchanges of the OAM and spin angular momentum. The strong impact of the laser intensity and the opening angle of the initial vortex electron is demonstrated. Our results also suggest possible scenarios for the separation of the emitted $\gamma$ photons with different OAMs, as well as a possible way which could help to distinguish the OAM and spin of the vortex particle by the multi-peak structure in the spectrum of the emitted photon.