RF gymnastics with transfer matrices

TL;DR

This paper introduces transfer matrices to model particle motion near fixed points in phase space, enabling analysis of bunch transfer between RF systems and effects on longitudinal emittance and injection tolerances.

Contribution

It presents a novel transfer matrix formalism for analyzing particle dynamics near fixed points and their impact on beam transfer and emittance in RF systems.

Findings

Transfer matrices effectively describe particle motion near fixed points.

Decoherence due to amplitude-dependent tune shift impacts emittance.

Tolerances for injection are assessed using the formalism.

Abstract

We introduce transfer matrices to describe the motion of particles in the vicinity of the stable and unstable fixed points of longitudinal phase space and use them to analyze the transfer of bunches between radio-frequency systems operating at different harmonics and voltages. We then apply this formalism to analyze the decoherence due to amplitude-dependent tune shift on the asymptotically achievable longitudinal emittance and assess tolerances for the injection.