Fig. 1. Schematic layout of the self-seeded FEL with OAM.

Fig. 2. Temporal power of the FEL pulse at (a) the end of the first stage and (c) the entrance of the second stage decomposed into OAM modes. The corresponding transverse profiles of the pulse at these two positions are shown in (b) and (d), respectively.

Fig. 3. Gain curves of different OAM modes along the second stage.

Fig. 4. Transverse profile of the FEL pulse at the end of (a) the fifth cell and (b) the second stage. (c) Transverse phase distribution at the position of maximum power in the pulse. (d) Temporal power profile of the pulse at the end of the second stage.

Fig. 5. (a) Variation of the different OAM modes with the change of the imprinted total phase shift. (b) Gain curves of different OAM modes at the second stage starting from a weaker seed pulse.