Fig. 1. Scheme to generate an optical vortex with multiple topological charges based on an HGHG setup.

Fig. 2. Optical setup in this scheme.

Fig. 3. (a) Transverse intensity and (b) corresponding phase of seed laser in the focal plane.

Fig. 4. (a) Longitudinal phase space of the electron beam after the modulator. The vertical axis p represents the energy modulation amplitude, which is defined as the ratio of the electron’s deviation from the central energy to the initial energy spread. (b) Transverse phase of the local microbunching .

Fig. 5. (a) Evolution of the power along the radiator. (b) Evolution of the bunching factor along the radiator. (c) The longitudinal power and (d) its spectrum at the radiator exit.

Fig. 6. (a) The transverse intensity and (b) its corresponding phase of radiation at the radiator exit.

Fig. 7. (a) Evolution of the power along the radiator. (b) The transverse phase of radiation at the radiator exit.

Table 1. Main parameters of the simulation.