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Vortex $\gamma$ photons with intrinsic orbital angular momenta (OAM) possessa wealth of applications in various fields, e.g.-strong-laser physics, nuclearphysics, particle physics and astrophysics-yet their generation remainsunsettled. In this work, we investigate the generation of vortex $\gamma$photons via nonlinear Compton scattering of ultrarelativistic electrons in acircularly polarized laser pulse. We develop a quantum electrodynamicsscattering theory that explicitly addresses the multiphoton absorption and theangular momentum transfer mechanism. In pulsed laser fields, we unveil thevortex phase structure of the scattering matrix element, discuss how the vortexphase could be transferred to the radiated photon, and derive the radiationrate of the vortex $\gamma$ photon. We numerically examine the energy spectraand beam characteristics of the radiation, while also investigating theinfluence of finite laser pulses on the angular momentum and energydistribution of the emitted vortex $\gamma$ photons.

Vortex $\gamma$ photon generation via spin-to-orbital angular momentum transfer in nonlinear Compton scattering