Betatron modulation of microwave instability in small isochronous ring

TL;DR

This paper investigates how betatron oscillations influence microwave instability in small isochronous rings, revealing the significant role of longitudinal space charge effects and their impact on beam dynamics.

Contribution

It introduces the coupling between transverse betatron motion and microwave instability, highlighting the importance of longitudinal coherent dipole modes in the isochronous regime.

Findings

Longitudinal space charge fields induce betatron oscillations in spectra.

Betatron motion affects the evolution of charge density spectra.

Simulation and theory confirm the role of centroid wiggles in instability.

Abstract

A novel coupling of the transverse betatron motion to the longitudinal microwave instability is studied. Besides the radial coherent dipole mode space charge field, simulation and theoretical studies in this paper show that the longitudinal coherent dipole mode space charge field due to centroid wiggles also plays an important role in the isochronous regime, it induces betatron oscillation frequencies in temporal evolutions of spectra of longitudinal charge densities, radial centroid offsets and coherent energy deviations of local centroids.