Abstract
Author(s): Venturini, M | Abstract: The effect of rf harmonic cavities on the transverse mode-coupling instability (TMCI) is still not very well understood. We offer a fresh perspective on the problem by proposing a new numerical method for mode analysis and investigating a regime of potential interest to the new generation of light sources where resistive wall is the dominant source of transverse impedance. When the harmonic cavities are tuned for maximum flattening of the bunch profile we demonstrate that at vanishing chromaticities the transverse single-bunch motion is unstable at any current, with growth rate that in the relevant range scales as the 6th power of the current. With these assumptions and radiation damping included, we find that for machine parameters typical of 4th-generation light sources the presence of harmonic cavities could reduce the instability current threshold by more than a factor two.
Highlights
A distinctive feature of the new generation of storagering light sources is a narrow vacuum chamber to accommodate high-gradient magnets and high performance insertion devices, significantly enhancing the resistive wall (RW) impedance
We provide a demonstration that in the absence of radiation damping the transverse motion at vanishing chromaticities is always unstable, regardless of bunch current, with growth rate varying from a 6 b dependence at small bunch current Ib to Im Ω ∼ Ib for larger Ib, the former being more likely to be encountered in the physical systems of interest
In the absence of harmonic cavities (HCs) it is well known that the transverse mode-coupling instability (TMCI) current threshold scales proportionally to the synchrotron tune, see Eq (10)
Summary
A distinctive feature of the new generation of storagering light sources is a narrow vacuum chamber to accommodate high-gradient magnets and high performance insertion devices, significantly enhancing the resistive wall (RW) impedance. The method we employ here is still based on mode analysis of the linearized Vlasov equation—the workhorse of all beam instability studies It differs from the traditional approach in two important respects: first, the radial dependence of the modes is represented by values on a grid, rather than through an expansion in orthogonal basis functions; second, the determination of the growth rate of the unstable modes is not cast in the form of a linear eigenvalue problem but entails the search for the roots of a more complicated secular equation. We assume the single-particle motion in the longitudinal plane to be unaffected by collective effects, integrable, and describable in terms of the action-angle variables ðJz; φzÞ, implying thatφz 1⁄4 ωsðJzÞ, the synchrotron oscillation frequency, is a function of Jz only (or a constant independent of Jz if the motion is purely linear). Note that (6) is more conveniently phrased in terms of the amplitude r rather than the action
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