Concatenated analyses of phase space microbunching in high brightness electron beam transport

Abstract

Microbunching instability (MBI) has been a challenging issue in high-brightness electron beam transport for modern accelerators. The existing theoretical formulation of MBI for recirculating accelerators is based on the single-pass analysis. For multi-pass recirculation or a long beam transport line, the intuitive way of quantifying MBI by successive multiplication of individual scalar amplification gains from subsections of a beamline was found to underestimate the effect. More thorough analyses based on concatenation of gain matrices, aimed to combine the density, energy, and transverse–longitudinal modulations for a general linear transport line, will be developed in this paper. Inclusion of such cross-plane microbunching structures in semi-analytical Vlasov analysis is a crucial step to systematically characterize phase space modulations for a beamline complex in terms of concatenating individual beamline segments. In this paper we outline the concept of gain matrix and develop a semi-analytical formulation to include the microbunching structures in the aforementioned phase space modulations. Then we investigate the phase space microbunching dynamics in an example lattice of the recirculating beamline, compare the semi-analytical calculation with particle tracking simulations, and find that the microbunching amplification calculated from multiplication of concatenated gain matrices can be considered as upper limit to the start-to-end gains.