Development of a 2D Vlasov Solver for Single-Pass Systems

Abstract

Direct numerical methods for solving the Vlasov equationoffer some advantages over macroparticle simulations, as they do notsuffer from the numerical noise inherent in using a number ofmacroparticles smaller than the bunch population. Unfortunately thesemethods are more time-consuming and generally considered impractical in afull 6D phase space. However, in a lower-dimension phase space they maybecome attractive if the beam dynamics is sensitive to the presence ofsmall charge-density fluctuations and a high resolution is needed. Inthis paper we present a 2D Vlasov solver for studying the longitudinalbeam dynamics in single-pass systems of interest for X-FEL's, wherecharacterization of the microbunching instability is of particularrelevance. The solver includes a model to account for the smearing effectof a finite horizontal emittance on microbuncing. We explore the effectof space charge and coherent synchrotron radiation (CSR). The numericalsolutions are compared with results from linear theory and good agreementis found in the regime where linear theory applies.