Abstract
The resistive wall impedance is one of the expected main drivers of transverse beam instabilities in the proposed Future Circular Collider hadron-hadron option (FCC-hh). We obtain the resistive wall impedance for the FCC-hh beam screen from a two-dimensional finite element solver. The impedances and resulting growth rates are compared to the LHC, using similar models for the resistivity of the copper layer. Similar to the LHC and in addition to active feedback, dedicated octupole magnets together with a finite chromaticity should be employed for Landau damping, as a cure against transverse beam instabilities. The stability boundary provided by an LHC-like octupoles configuration in combination with an electron lens is obtained from a dispersion relation including the two-dimensional tune spreads. The prediction from the simple dispersion relation are compared to the corresponding beam transfer function and to the stability boundaries reconstructed using particle tracking with an effective impedance. The electron cloud induced tune spreads and their scaling with higher energy and smaller beam pipe radius are estimated. Besides the important estimation of growth rates and stability threshold for FCC-hh we also try to improve the understanding of the scaling of coherent instabilities and their thresholds with energy towards a possible highest-collider limit, using the example of two high-energy colliders, the existing LHC and the proposed FCC-hh.
Highlights
: The resistive wall impedance is one of the expected main drivers of transverse beam instabilities in the proposed Future Circular Collider hadron-hadron option (FCC-hh)
The stability boundary provided by an LHC-like octupoles configuration in combination with an electron lens is obtained from a dispersion relation including the two-dimensional tune spreads
The smaller effective beam pipe radius in the FCC-hh potentially increases the threshold for electron cloud (EC) buildup
Summary
The FCC-hh and LHC parameters used in this study are given in table 1. We will focus on the transverse impedance of the FCC-hh beam pipe and the resulting resistive wall instabilities. In the FCC-hh the increase of the pipe impedance at the lowest betatron sideband outweighs the benefit of the larger rigidity for the instability growth rate, as we will see later more in detail. The LHC beam screen transverse size is 36.8 mm in the vertical plane and 46.4 mm in the horizontal plane. The thickness of the stainless steel screen is 1 mm and the thickness of copper coating is 75 μm. The FCC-hh beam screen transverse size is supposed to be 24.44 mm in the vertical plane and 27.65 mm in the horizontal plane.
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