Modeling microbunching from shot noise using Vlasov solvers

Unlike macroparticle simulations, which are sensitive to unphysical statistical fluctuations when the number of macroparticles is smaller than the bunch population, direct methods for solving the Vlasov equation are free from sampling noise and are ideally suited for studying microbunching instabilities evolving from shot noise. We review a 2D (longitudinal dynamics) Vlasov solver we have recently developed to study the microbunching instability in the beam delivery systems for X-ray FELs and present an application to FERMI@Elettra. We discuss, in particular, the impact of the spreader design on microbunching.