An alternative view of coherent synchrotron radiation induced microbunching development in multibend recirculation arcs

Coherent synchrotron radiation (CSR) induced microbunching instability has been one of the most challenging issues in the design of modern accelerators. We recently developed a semi-analytical Vlasov solver and applied it to the investigation of the physical processes associated with microbunching amplification for several types of recirculation arc lattices. In this study, we build on the concept of stage gain, proposed by Huang and Kim (2002), and develop an alternative view to characterize CSR microbunching development in terms of stage orders. The stage orders enable a fair and quantitative comparison of the impact of lattice optics on the microbunching development for different lattices under similar initial beam parameters. The multibend arcs considered in this study have a distinguishing feature of multistage amplification. The CSR microbunching gain grows as a six-stage amplification for the presented recirculation arcs with a total of 24 dipoles, while two-stage amplification was previously concluded for a three-dipole bunch compressor chicane. We also attempt to relate the lattice optics pattern with the obtained stage gain functions through a physical interpretation. The investigation in this paper may serve as a complementary discussion to our previous work (Tsai et al., 2017).