One-dimensional longitudinal space charge calculation based on integrated green function approach

Abstract

For fast longitudinal electron beam dynamics study or optimization in an x-ray free electron laser (FEL) linear accelerator, the one-dimensional longitudinal space charge (1D LSC) impedance, assuming a round cylinder beam with uniform transverse distribution is extensively used in both analytical analysis and numerical simulation. In this paper, instead of employing the impedance model in the frequency domain, we directly calculate the longitudinal electric field by convolving the longitudinal beam density with the slice green function, i.e., the longitudinal electric field generated by a slice beam. For high-energy electron beam, the slice green function rapidly diminishes to zero within a distance significantly smaller than the bunch length. In order to resolve the sharp variation, we report on a fast and high-precision method by applying the integrated green function (IGF) approach to compute the 1D LSC field numerically with few grid points, therefore, providing us with an alternative approach to the impedance model.