Tsai, C.-Y. Li, R. JACoW Geneva, Switzerland 978-3-95450-180-9 10.18429/JACoW-NAPAC2016-THPOA35 English 1177-1180 THPOA35 ion bunching simulation electron lattice Contribution to a conference proceedings 2017 2017-01 http://dx.doi.org/10.18429/JACoW-NAPAC2016-THPOA35 https://jacow.org/napac2016/papers/thpoa35.pdf Microbunching instability (MBI) has been a challenging issue in high-brightness electron beam transport for modern accelerators. The existing Vlasov analysis of MBI is based on single-pass configuration*. For multi-pass recirculation or a long beamline, the intuitive argument of quantifying MBI, by successive multiplication of MBI gains, was found to underestimate the effect**. More thorough analyses based on concatenation of gain matrices aimed to combine both density and energy modulations for a general beamline**. Yet, quantification still focuses on characterizing longitudinal phase space; microbunching residing in (x,z) or (x',z) was observed in particle tracking simulation. Inclusion of such cross-plane microbunching structures in Vlasov analysis shall be a crucial step to systematically characterize MBI for a beamline complex in terms of concatenating individual beamline segments. We derived a semi-analytical formulation to include the microbunching structures in longitudinal and transverse phase spaces. Having numerically implemented the generalized formulae, an example lattice*** is studied and reasonable agreement achieved when compared with particle tracking simulation.