Impedance updates and stability simulations with Vlasov solvers

Impedance updates and stability simulations with Vlasov solvers in FCC-hh Sergey Arsenyev, Nico Klinkenberg* Euro. Cir. Col meeting 2018 in Karlsruhe 17 October, 2018 *Bachelor’s thesis: https: //cds. cern. ch/record/2640156

Part 1: impedance 2

Impedance updates since FCC week 2018 V I Currently included impedance sources: • Beamscreen: resistive wall • Beamscreen: coating for e-cloud • Beamscreen: pumping holes • Warm beam pipe: resistive wall • Collimators: geometrical impedance • Interconnects: geometrical impedance • 400 MHz RF cavities • Crab cavities 3

Impedance updates: tighter beamscreen be am beam The tighter vertical aperture of 12. 22 mm is accepted from the impedance point of view (13. 2 mm previously) or AC 85% of circumference for longitudinal impedance for transverse impedance Cubic scaling 4

Impedance updates: crab cavities *Data from Kai Papke and Alexej Grudiev HOM couplers were modified, leading to stronger damping of the 1. 276 GHz dipole mode, but sacrificing the damping of a monopole mode Old HOMs (August 2017)* Frequency New HOMs (July 2018)* Q Frequency Q 0. 667 GHz 6. 95 48000 0. 667 GHz 6. 95 49000 0. 827 GHz 12. 55 4800 0. 827 GHz 12. 55 14000 Q Frequency Q 0. 4 GHz 171. 4 1 (fundamental) 0. 4 GHz 171. 9 1 (fundamental) 0. 638 GHz 7. 85 35 0. 644 GHz 0. 04 40 0. 643 GHz 0. 04 40 1. 276 GHz 0. 15 23000 1. 276 GHz 0. 15 1100 5

Impedance updates: laser treated beamscreen for e-cloud Data from M. Arzeo, S. Aull or AC Theoretical model: Making grooves parallel to the beam decreases transverse impedance, despite some currents flowing perpendicular to the beam Recent measurements show a big difference in impedance depending on the current direction For the moment, AC coating is assumed in the impedance budget, but can be changed to laser treatment if FRESCA experiments show moderate impedance increase Planned in 2019 -2020 6

Total FCC impedance as of Oct 2018 Total FCC-hh impedances at injection / flat top Impedance is higher at top energy due to • Squeezed collimators • Magnetoresistance of the beamscreen Effective impedances Injection HOM resonance peaks from crab cavities (may have to be damped) Flat top HOM resonance peaks are welldamped 7

Distribution of dipolar impedance by elements Frequencies important to coupled bunch instabilities Frequencies important to single bunch instabilities Coupled bunch instability is always dominated by the resistive wall impedance of the beamscreen Single bunch instabilities are dominated by • Res wall BS, BS coating, collimators, interconnects (injection) • Collimators (flat top) 8

Part 2: stability simulations 9

Simulated stabilization scheme Landau octupoles Transverse feedback (damper) Necessary at nominal settings Stabilizing effect: Specification Safety factor of 3 10

Simulation procedure with Vlasov solvers Nested-Head-Tail – NHT - Author: Doctor A. Burov Discrete Expansion over Laguerre Polynomials and Headta. Il modes - DELPHI - Author: Doctor N. Mounet Only the most unstable is kept Longitudinal phase space distribution divided in equipopulated rings (NHT) 11

Typical agreement between the two solvers The two independent Vlasov solvers typically are in good agreement Only DELPHI results are shown in the next slides (unless otherwise stated) 12

Stability diagram with damper (injection) Octupole stability region from Claudia Tambasco m zoo assuming negative octupole polarity 13

Stability diagram with damper (flat top) Octupole stability region from Claudia Tambasco m zoo assuming negative octupole polarity 14

Mode coupling (injection, single bunch) Nominal bunch intensity Destabilizing effect of a resistive damper 15

Mode coupling (flat top, single bunch) Nominal bunch intensity Destabilizing effect of a resistive damper 16

Mode coupling (injection, multi-bunch) Nominal bunch intensity No distortion here Residual growth rate even after damper is applied New scale! 17

Mode coupling (flat top, multi-bunch) Nominal bunch intensity No distortion here Residual growth rate even after damper is applied New scale! 18

Effect of the HOMs on beam stability With the HOM with Q=23000 (old impedance model from Mar 2018) No matter how high the damper gain, the growth rate is not reduced to single-bunch level Without the HOM with Q=23000 (old impedance model from Mar 2018) Growth rate is reduced to single-bunch level (CB motion is killed off by the damper) 19

Destabilizing effect of a resistive damper Prediction of a simple model is surprisingly accurate: Regime 2 Regime 1 20

Conclusions Impedance: • Increase in impedance due to 12. 22 mm beamscreen aperture is accepted • HOWs in crab cavities are better damped • Laser treatment of beamscreen is not yet accepted due to unknown impedance, but active research is going on Transverse beam stability: • Number of octupoles is sufficient with a safety margin of more than 3 • Feedback damping rate 20 turns / 150 turns is sufficient at injection / flat top with a safety factor of 3 • Single bunch mode coupling instability threshold is more than 3 times higher than the bunch intensity • Multi-bunch mode coupling instability is slow enough, but more investigation is required 21