Abstract
In this study, the observation of three simultaneously rotating beams in the SOLEIL storage ring is reported. This event occurred in November 2007 while operating in a low momentum compaction factor mode. The dynamics of the three beams is simulated using the longitudinal equations of motion and the longitudinal phase-space Hamiltonian which are extended to include higher-order terms of momentum compaction factor up to the third order. The effect of the transverse oscillation amplitude of the particles is also included in this work. It is shown that this term, which is experimentally very difficult to compensate for very low momentum compaction factor optics, can strongly affect the longitudinal beam dynamics. Finally, an extended formula of the variation of synchrotron frequency with respect to the relative variation of the rf frequency is derived and is used to deduce the higher-order terms of the momentum compaction factor from experimental data.
Highlights
INTRODUCTIONA series of experiments has been conducted since 2007 at the SOLEIL synchrotron light source [1] to obtain picosecond electron bunch length conditions to produce infrared coherent synchrotron radiation in the Terahertz region and, at the same time, to allow time-resolved x-ray experiments [2,3]
A series of experiments has been conducted since 2007 at the SOLEIL synchrotron light source [1] to obtain picosecond electron bunch length conditions to produce infrared coherent synchrotron radiation in the Terahertz region and, at the same time, to allow time-resolved x-ray experiments [2,3].In the low bunch current regime, disregarding collective beam effects, the bunch length scales with the square root of the momentum compaction factor
It is shown that this term, which is experimentally very difficult to compensate for very low momentum compaction factor optics, can strongly affect the longitudinal beam dynamics
Summary
A series of experiments has been conducted since 2007 at the SOLEIL synchrotron light source [1] to obtain picosecond electron bunch length conditions to produce infrared coherent synchrotron radiation in the Terahertz region and, at the same time, to allow time-resolved x-ray experiments [2,3]. To understand these experimental observations, the longitudinal equations of motion and the corresponding Hamiltonian have been expanded up to the third-order momentum compaction factor 3 as well as taking into account the particle transverse excursion amplitude This momentum-independent path lengthening term which can be compensated, in principle, by the rf frequency, becomes a more critical parameter at lower values and its compensation is more challenging for extremely low- optics. Storing three beams in a circular accelerator can be understood theoretically when higher orders of the momentum compaction factor are included in the model providing that the bucket energy acceptance is large enough and that the chromatic closed orbit of each beam stays within the physical aperture of the accelerator
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