Abstract
Transverse instability of a bunched beam is investigated with synchrotron oscillations, space charge tune shift, and resistive wall wakefield taken into account. A boxcar model is used for a general analysis, and truncated Gaussian distribution is invoked for details. The beam spectrum, instability growth rate, and effects of chromaticity are studied in a wide range of parameters, both with head-tail and collective bunch interactions included. Influence of internal bunch oscillations on the collective instabilities is investigated thoroughly. Landau damping caused by the space charge tune spread is discussed, and the instability thresholds of different modes of truncated Gaussian bunch are estimated.
Highlights
Transverse instability of a bunched beam in a ring accelerator has been considered independently by Pellegrini [1] and Sands [2] with synchrotron oscillations and some internal degrees of freedom of the bunch taken into account (‘‘head-tail instability’’)
The role of the bunch space charge was studied in Refs. [4,5], where it has been shown that the space charge produced tune spread can suppress many of the head-tail modes due to Landau damping, acting on instability much like other sources of the incoherent tune spread
First results have been obtained with an assumption that the space charge tune shift is significantly less than synchrotron tune
Summary
Transverse instability of a bunched beam in a ring accelerator has been considered independently by Pellegrini [1] and Sands [2] with synchrotron oscillations and some internal degrees of freedom of the bunch taken into account (‘‘head-tail instability’’). [5] has led to the conclusion that almost all head-tail modes are prone to Landau damping until when the space charge tune shift is about less than the synchrotron tune. A more general theory is developed in this paper where a bunched beam with an arbitrary number of bunches is examined taking into account the space charge, intrabunch, and bunch-to-bunch interactions. Both of these interactions affect the beam eigenmodes including the instability growth rate, one or the other can dominate in specific situations resulting in different effects. It is assumed that the external field is linear; nonlinearity of the space charge field is taken into account at the analysis
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