Efficient model for low-energy transverse beam dynamics in a nine-cell 1.3 GHz cavity

TL;DR

This paper presents an efficient, low-energy transverse beam dynamics model for nine-cell 1.3 GHz cavities, enabling rapid analysis of beam stability and misalignments in facilities like FLASH and European XFEL.

Contribution

The paper introduces a novel low-energy transverse beam dynamics model using transfer matrices and coupler kick coefficients, validated against experiments and simulations.

Findings

Model accurately predicts intra-bunch-train trajectory variations.

Enables comprehensive numerical studies of misalignments and RF parameter effects.

Supports deduction of misalignments from multibunch experiments.

Abstract

FLASH and the European XFEL are SASE-FEL user facilities, at which superconducting TESLA cavities are operated in a pulsed mode to accelerate long bunch-trains. Several cavities are powered by one klystron. While the low-level rf system is able to stabilize the vector sum of the accelerating gradient of one rf station sufficiently, the rf parameters of individual cavities vary within the bunch-train. In correlation with misalignments, intrabunch-train trajectory variations are induced. An efficient model is developed to describe the effect at low beam energy, using numerically adjusted transfer matrices and discrete coupler kick coefficients, respectively. Comparison with start-to-end tracking and dedicated experiments at the FLASH injector will be shown. The short computation time of the derived model allows for comprehensive numerical studies on the impact of misalignments and variable rf parameters on the transverse intra-bunch-train beam stability at the injector module. Results from both, statistical multibunch performance studies and the deduction of misalignments from multibunch experiments are presented.