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. K: Accelerator modelling and simulations (multi-particle dynamics; single-particle dynamics); Coherent instabilities

A pulsed electron lens produces a betatron tune shift along a hadron bunch as a function of the longitudinal coordinates, which is a longitudinal detuning. An example of transverse detuning are the tune shifts due to octupole magnets. This paper considers a pulsed electron lens as a measure to mitigate the head-tail instabilities. Using a detailed analytical description within a Vlasov formalism, the coherent properties of the longitudinal and transverse detuning are presented. The analytical predictions are compared with the results of the particle tracking simulations. A pulsed electron lens is demonstrated to be a source of tune spread with two components: a static one, leading to Landau damping; and a dynamic one, leading to an effective impedance modification, which we demonstrate analytically and in our particle tracking simulations. The effective impedance modification can be important for beam stability due to devices causing a longitudinal detuning, especially for nonzero head-tail modes. The Vlasov formalism is extended to include the combination of longitudinal and transverse detuning. As a possible application at the SIS100 heavy-ion synchrotron (Facility for Antiproton and Ion Research (FAIR) at GSI Darmstadt, Germany), a combination of a pulsed electron lens with octupole magnets is considered.

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