  The coherent synchrotron radiation (CSR) of a high brightness electron beam
traversing a series of dipoles, such as recirculation or transport arcs, may
lead to the microbunching instability. We extend and develop a semi-analytical
approach of the CSR-induced microbunching instability for a general lattice,
based on the previous formulation with 1-D CSR model [Phys. Rev. ST Accel.
Beams 5, 064401 (2002)] and apply it to investigate the physical processes of
microbunching amplification for two example transport arc lattices. We find
that the microbunching instability in transport arcs has a distinguishing
feature of multistage amplification (e.g, up to 6th stage for our example arcs
in contrast to two stage amplification for a 3-dipole chicane). By further
extending the concept of stage gain as proposed by Huang and Kim [Phys. Rev. ST
Accel. Beams 5, 074401 (2002)], we developed a method to quantitatively
characterize the microbunching amplification in terms of iterative or staged
orders that allows the comparison of optics impacts on microbunching gain for
different lattices. The parametric dependencies and Landau damping for our
example lattices are also studied. Excellent agreement of the gain functions
and spectra from Vlasov analysis with results from ELEGANT is achieved which
helps to validate our analyses.
