Emittance growth of kicked and mismatched beams due to amplitude-dependent tune shift

TL;DR

This paper derives evolution equations for Gaussian beam moments considering amplitude-dependent tune shifts, providing insights into emittance growth and error tolerances for beam injection.

Contribution

It introduces new analytical expressions for beam evolution and asymptotic emittance values under amplitude-dependent tune shifts, enhancing understanding of beam decoherence.

Findings

Derived equations for beam moment evolution

Provided asymptotic emittance expressions

Evaluated injection error tolerances

Abstract

We derive evolution equations for the first and second moments of an initially mismatched, coupled, and displaced arbitrary Gaussian phase-space distribution under the influence of decoherence due to amplitude-dependent tune shift. Moreover, we find expressions for the asymptotic values of the beam matrix and the emittance and use them to evaluate error tolerances for injection.