Abstract
In the Brazilian synchrotron light source (LNLS---Laborat\'orio Nacional de Luz S\'{\i}ncrotron), we observed that modulating the phase of the accelerating fields at approximately twice the synchrotron frequency suppressed remarkably well a longitudinal coupled-bunch mode of the beam driven by a higher order mode in one of the radiofrequency (rf) cavities. In this work, we present the results of a set of systematic measurements, in single and multibunch mode, aimed at characterizing the effects of rf phase modulation on the beam. We compare those experiments with the results of tracking simulations and of a theoretical model in which Landau damping is the stabilizing mechanism that explains the suppression of the longitudinal coupled-bunch instability. We also measure the frequency of the stable islands created in longitudinal phase space by phase modulation and the longitudinal beam transfer function as a function of the modulation frequency and amplitude. The experimental results are in good agreement with theoretical expectations.
Highlights
Studies related to the effects of phase or amplitude modulation of the accelerating radiofrequency fields in circular accelerators date back to the early 1990’s when a series of classical experiments were performed with the aim of understanding basic aspects of nonlinear longitudinal beam dynamics at low current in hadron machines [1
Those early works laid the basic theoretical foundations for subsequent interest in applying rf phase or voltage modulation to electron storage rings used as synchrotron light sources [6,7] as a tool to control electron bunch density [8,9], increase beam lifetime [10], and reduce the amplitude or even suppress coupled-bunch instabilities [10 –12], resulting in relevant improvement to the performance of those machines
Some of those previous works analyzed the effects of rf phase modulation at the first and third harmonics of the synchrotron frequency
Summary
Studies related to the effects of phase or amplitude modulation of the accelerating radiofrequency (rf) fields in circular accelerators date back to the early 1990’s when a series of classical experiments were performed with the aim of understanding basic aspects of nonlinear longitudinal beam dynamics at low current in hadron machines [1–. Apart from the fundamental interest of those experiments, related to the possibility of direct observations of nonlinear phenomena such as the formation of islands in phase space and measurement of synchrotron tune variations with amplitude, the main applications envisaged by those works were related to issues such as lifetime limitations due to rf noise, the development of superslow extraction techniques, and the use of parametric feedback for multibunch instabilities Those early works laid the basic theoretical foundations for subsequent interest in applying rf phase or voltage modulation to electron storage rings used as synchrotron light sources [6,7] as a tool to control electron bunch density [8,9], increase beam lifetime [10], and reduce the amplitude or even suppress coupled-bunch instabilities [10 –12], resulting in relevant improvement to the performance of those machines.
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