Space charge effects on the third order coupled resonance

Abstract

The effect of space charge on bunched beams has been the subject of numerous numerical and experimental studies in the first decade of 2000. Experimental campaigns performed at the CERN Proton Synchrotron in 2002 and at the GSI SIS18 in 2008 confirmed the existence of an underlying mechanism in the beam dynamics of periodic resonance crossing induced by the synchrotron motion and space charge. In this article we present an extension of the previous studies to describe the effect of space charge on a controlled coupled (2D) third order resonance. The experimental and simulation results of this latest campaign shed a new light on the difficulties of the 2D particle dynamics. We find striking experimental evidence that space charge and the coupled resonance create an unusual coupling in the phase space, leading to the formation of an asymmetric halo. Moreover, this study demonstrates a clear link between halo formation and fixed-lines.

Incoherent effects of space charge and sum resonances on particle beams in a storage ring

“…However, the recent study in Ref. [22] has shown that fixed lines play a fundamental role in determining the dynamics of halo formation in high-intensity bunched beams. Next, adopting a perturbative approach, the theory of sum coupled resonances including a frozen model of space charge modeling a Gaussian beam will be discussed.…”

“…It is considered a working example with Δ r0 ¼ 0.056, D r;sc ¼ −0.174 corresponding to the settings, beam sizes, and space charge tune shifts of the CERN-PS measurements of Ref. [22]. With these settings, the parameters of incoherence are I x;l ≃ I y;l ≃ 5, somehow justifying the use of the frozen model.…”

“…For the specific example of the experimental settings of Ref. [22], the scaled driving term is ρ s ≃ 10 −5 .…”

Numerical investigation of space charge effects on the positions of beamlets for transversely split beams

“…In recent years, the interplay between nonlinear effects generated by external fields and those produced by selffields and the interaction with the boundaries has been considered by several authors in studies addressing numerical [16][17][18], experimental [19][20][21][22], and theoretical [23,24] aspects. It is worth stressing that the challenge arises whenever one considers the combined effect of relatively weak external sources of nonlinearities, leading to a sizeable impact on the long-term beam dynamics, and space charge.…”

Comment on “Empirical condition of betatron resonances with space charge”

“…We refer to published data from carefully conducted high intensity beam dynamics experiments using sextupole errors at the GSI SIS18 [3] and the CERN Proton Synchrotron [4]-none of them referenced by the authors. In the comprehensive SIS18 benchmarking campaign, with results shown in below Fig.…”