Abstract
Direct numerical methods for solving the Vlasov equation offer some advantages over macroparticle simulations, as they do not suffer from the consequences of the statistical fluctuations inherent in using a number of macroparticles smaller than the bunch population. Unfortunately, these methods are more time consuming and generally considered impractical in a full 6D phase space. However, in a lower-dimension phase space they may become attractive if the beam dynamics is sensitive to the presence of small charge-density fluctuations and a high resolution is needed. In this paper we present a 2D Vlasov solver for studying the longitudinal beam dynamics in single-pass systems of interest for x-ray FELs, where characterization of the microbunching instability stemming from self-field amplified noise is of particular relevance.
Highlights
Lasing in an x-ray free electron laser (FEL) critically depends on electron-beam quality
Evaluation of the Fourier transform of the charge density in item (vi) and determination of the collective force is done by a fast-Fourier-transform algorithm (FFT) along the lines of Ref. [11]
A systematic application of our solver to the study of microbunching in the overall FERMI linac, as well as a close comparison with macroparticle simulations and a more thorough assessment of the applicability of the model presented in Sec
Summary
Lasing in an x-ray free electron laser (FEL) critically depends on electron-beam quality. A number of effects can spoil transverse emittance and energy spread as the electron beams are accelerated and compressed before entering the undulator. Of particular concern is the development of microbunching instabilities [1–. 5] stemming from the unavoidable irregularities present in the charge density at injection. Because of self-fields from radiation or space-charge, these irregularities may create energy fluctuations, which in turn feed further lumping in the charge density as the beam travels through a dispersive region. Minimizing the development of such instabilities is a significant part in the effort of designing an X-FEL. Modeling of beam dynamics is currently carried out using a combination of macroparticle simulations and semianalytical studies of the solutions of the linearized
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