Abstract
In synchrotrons, nonuniform fill patterns, which give rise to beam phase transients and a spread in synchrotron tune between bunches, have been observed to damp longitudinal coupled-bunch instabilities driven by higher-order modes in rf cavities. The transients are especially large in the presence of Landau cavities, which are used commonly in storage-ring light sources and particularly in the new generation of diffraction-limited storage rings. A method has recently been devised to predict the beam transient including complex form factors for the different bunches. This has now been extended to accurately predict the growth-rates and oscillation frequencies of coupled-bunch modes for arbitrary fill patterns, taking the individual complex form factors and equilibrium phases of the different bunches into account. In this paper, the extended method is presented and the theory is outlined. For a case with significant transient beam loading, predictions of the resulting beam transient and bunch profiles are compared to measurements. Predictions of coupled-bunch mode behavior are then benchmarked against results from the macroparticle tracking code mbtrack with good agreement. Finally, the method is used to predict the behavior of coupled-bunch modes as a function of the fields in passive Landau cavities.
Highlights
In synchrotron storage rings, rf cavities are used to return the energy that a charged-particle beam has lost to synchrotron radiation
In electron storage rings used as dedicated sources of synchrotron radiation, Landau cavities are sometimes used to flatten the center of this potential [1], thereby lengthening the electron bunches
This paper explores the effects of the transient beam loading of Landau cavities in a synchrotron where HOMdriven coupled-bunch instabilities dominate in the longitudinal plane
Summary
Rf cavities are used to return the energy that a charged-particle beam has lost to synchrotron radiation. The MAX IV 3 GeV ring is unique in that Landau cavities were included from the conceptual design stage for the reasons mentioned previously and with the knowledge that it would help stabilize the beam against coupled-bunch instabilities both longitudinally and transversely [10] by introducing synchrotron-tune spread and reducing the overlap of the beam spectrum with that of the main driving impedances by lengthening the bunches. It is a machine where HOMs in the normal-conducting. It is important to evaluate these independently because, in some cases, they may be a limiting factor in the use of Landau cavities for bunch lengthening [17]
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