A FOUR-DIMENSIONAL VLASOV SOLVER FOR MICROBUNCHING INSTABILITY INTHE INJECTION SYSTEM FOR X-RAY FELS

The micro-bunching instability (MBI) is seeded by small charge-density fluctuations in the electron bunches, and is successively amplified by the combined effect of space charge and coherent synchrotron radiation, as the beam travels through magnetic compressors. The quantitative understanding of this effect demands for accurate numerical simulations. Here we report on the progress of an upgrading of a 2D Vlasov solver code toward a 4D grid-based Vlasov solver, including also the transversedynamics. The goal is to provide an accurate characterization of the MBI seeded by random noise present in the bunch distribution. We also comment on the advantages of our procedure with respect to other approaches, e.g. macroparticle simulations