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Gamma-ray beams with large angular momentum are a very valuable tool to studyastrophysical phenomena in a laboratory. We investigate generation ofwell-collimated $\gamma$-ray beams with a very large orbital angular momentumusing nonlinear Compton scattering of a strong laser pulse of twisted photonsat ultra-relativistic electrons. Angular momentum conservation among absorbedlaser photons, quantum radiation and electrons are numerically demonstrated inthe quantum radiation dominated regime. We point out that the angular momentumof the absorbed laser photons is not solely transferred to the emitted$\gamma$-photons, but due to radiation reaction shared between the$\gamma$-photons and interacting electrons. The efficiency of the angularmomentum transfer is optimized with respect to the laser and electron beamparameters. The accompanying process of electron-positron pair production isfurthermore shown to enhance the orbital angular momentum gained by the$\gamma$-ray beam.

Gamma-ray beams with large orbital angular momentum via nonlinear Compton scattering with radiation reaction