Transverse Instabilities of Coasting Beams with Space Charge

TL;DR

This paper investigates the transverse stability of coasting beams under space charge effects, analyzing the limitations of the rigid-beam model and providing practical stability thresholds for Gaussian beams with tune spreads.

Contribution

It extends the analysis of beam stability by deriving simple fits for stability thresholds considering chromatic and octupole tune spreads under realistic conditions.

Findings

Landau damping rate computed for relevant parameter regimes

Schottky spectra analyzed with space charge effects

Stability thresholds provided for Gaussian beams with tune spreads

Abstract

Transverse beam stability is strongly affected by the beam space charge. Usually it is analyzed with the rigid-beam model. However this model is only valid when a bare (not affected by the space charge) tune spread is small compared to the space charge tune shift. This condition specifies a relatively small area of parameters which, however, is the most interesting for practical applications. The Landau damping rate and the beam Schottky spectra are computed assuming that validity condition is satisfied. The results are applied to a round Gaussian beam. The stability thresholds are described by simple fits for the cases of chromatic and octupole tune spreads.