The studies of incoherent single-particle and collective multi-particle effects are, in general, separated in accelerator beam dynamics in that the two dynamical phenomena involve quite different time scales. Recent experimental measurements indicate that in some parameter regime, the small-angle, multiple scattering effects within a high-brightness electron beam can have a strong influence on microbunched beam dynamics. In this paper, we apply our recently developed semi-analytical kinetic analysis to investigate the collective phase space microbunched dynamics in the presence of incoherent single-particle effects. Particular emphasis will be placed on evaluation of the intrinsic or slice energy spread. An example of two linear beam transport lines, followed by two identical, interleaving bunch compressor chicanes, is then presented. The semi-analytical calculations are consistent with particle tracking simulations. Moreover, the threshold condition is derived, indicating the relation among relevant physical quantities. At threshold, the incoherent effect can be beneficial for effective suppression of the collective microbunching instability. We expect that this work could shed light on high-brightness electron transport beamline design to improve short-wavelength free-electron laser performance.
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