Abstract
Studies of the longitudinal beam dynamics in the small isochronous ring (SIR) at Michigan State University revealed a fast, space-charge driven instability that did not fit the model of the negative mass instability. The observed beam behavior can be explained by the transverse horizontal component of the coherent space-charge force and its effect on the longitudinal motion. This force effectively modifies the slip factor, shifting the isochronous point and enhancing the negative mass instability. This paper presents results of numerical and experimental studies of the longitudinal beam dynamics in SIR and proposes a simple analytical model explaining these results.
Highlights
Experimental and numerical studies of space-charge effects in the small isochronous ring (SIR) conducted at Michigan State University revealed a fast, space-charge driven longitudinal instability [1,2]
We demonstrate that the transverse spacecharge field can noticeably affect the longitudinal beam dynamics in the isochronous regime in Sec
The small isochronous ring (SIR) is a compact, lowenergy storage ring designed to simulate the dynamics of intense beams in the isochronous regime
Summary
Experimental and numerical studies of space-charge effects in the small isochronous ring (SIR) conducted at Michigan State University revealed a fast, space-charge driven longitudinal instability [1,2]. Transverse effects were limited to the defocusing caused by the incoherent space-charge field and the corresponding effective increase of the dispersion function (Umstatter effect [5]). None of those models could reproduce the observed beam behavior. The instability observed in SIR can be explained by the transverse horizontal component of the coherent spacecharge field and its effect on the coherent longitudinal motion. This field, caused by a deformation of the beam shape, enhances the negative mass instability.
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