Single Beam Collective Effects Impedances and Collective Effects

Single Beam Collective Effects Impedances and Collective Effects for FCC-hh Uwe Niedermayer Institut für Theorie Elektromagnetischer Felder Technische Universität Darmstadt, Germany niedermayer@temf. tu-darmstadt. de With a lot of input from: B. Salvant, X. Buffat, N. Nounet, D. Schulte, CERN T. Egenolf, F. Petrov, O. Boine-Frankenheim, TUD 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 1

Contents As discussed in Washington: ▪ Beam pipe impedance ▪ Other impedance sources ▪ Coupled bunch instability ▪ Transverse Mode Coupling Instability (TMCI) threshold Few new things and issues to be discussed: ▪ Which components? ▪ Details on the pipe… ▪ Plans, codes, outlines, timelines Collimators!!! Pipe aperture!!! 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 2

Discretization GMSH (Geuzaine et al. ) triangular mesh Meshing the whole structure is required only for extremely low frequency! Otherwise: Surface Impedance Boundary Condition (SIBC) Thilo Egenolf, TU Darmstadt 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 4

2 D Simulations in the Frequency Domain ▪ Beam. Impedance 2 D, PYTHON code using FEni. CS finite element toolbox (U. Niedermayer et al. , PRSTAB 18 032001, 2015) Horizontal Vertical f=100 Hz f=1 MHz 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 5

Materials ▪ Beam Screen: Titanium ▪ Coating: Copper (80 um or maybe higher) ▪ Outer pipe, synchr. rad. reflector: Stainless Steel ▪ Conductivities k at room temperature T=293 K -Titanium: k 0= 1. 8 MS/m -Copper: k 0 = 60. 0 MS/m -Stainless steel: k 0 = 1. 4 MS/m ▪ RRR= k(T=4 K)/ k(293 K) usually RRR ~ 300 ▪ Temperatures for the FCC pipe: -Scenario 1: 40 -60 K (roughly… k =100 k 0 ) -Scenario 2: 120 -160 K (roughly… k =10 k 0) ▪ Magnetoresistance at 16 T ? 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 6

Comparison with round pipe impedance Horizontal (1 meter pipe) Coating with Copper at 50 K, k=6 e 9 S/m X 2. 0 An artifact, due to numerical cancelation at high gamma Skindepth=coating thickness 80 um 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 8

Comparison with round pipe impedance Vertical (1 meter pipe) X 1. 4 An artifact, due to numerical cancelation at high gamma Skindepth=coating thickness 80 um 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 9

Pumping Holes, Collimators, … B. Salvant and X. Buffat, CERN Pumping holes with resonator model, . . . fres=fcutoff ~6 GHz Q=1 (Broadband) S. Kurennoy, Part. Accel. , 1995, Vol. 50, pp. 167 -175 Collimators scaled from LHC, see also talk by M. Fiascaris (this morning) Collimators closed only at top energy! Maybe LHC-like carbon collimators are not the best choice… 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 10

Scenario Data ▪ M=13344 (25 ns) ▪ rms bunch length 8 cm ▪ Nb=1. 0 e 11 ▪ Qx=120. 31 ▪ Qy=120. 32 ▪ Chroma=0 ▪ E=3 Te. V ▪ Qs=0. 0028 ▪ E=50 Te. V ▪ Qs=0. 0078 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 11

Coupled bunch resistive instability most unstable coupled-bunch mode at lowest frequency=2 k. Hz Most critical at injection due to less stiff beam! Pipe only, solid Cu 50 K E=3 Te. V Growth rate by factor 1. 6 higher for 80 um coating N. Mounet, EPFL Lausanne, formerly CERN Required thickness for “thick wall“ 150 um for 50 K 450 um for 140 K 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 12

TMCI intensity threshold 50 Te. V More stiff beam, but higher impedance due to closed collimators Pipe + holes + collimators B. Salvant and X. Buffat, CERN 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 14

Conclusion ▪ FCC-hh already on the edge of stability only with resistive pipe ▪ 50 turns feedback possible but maybe insufficient ▪ 10 turns feedback possible? ▪ Kickers not yet considered ▪ Landau damping and Octupoles not yet considered ▪ Impedance should play an important role in collimator design 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 15

Holes and rips 3 D simulations in the time domain by CST Particle Studio® Stabilization fins between beam pipe and reflector Vacuum pumping holes 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 16

Updates after Washington Meeting ▪ Holes under investigation: resonator model is justified but probably smaller bandwidth ▪ First simulations show no effect of stabilizing rips… --------------------------▪ Input from Collimation-Group has to be followed Proper design with few updates required. ▪ Material data: Vacuum group? ▪ We should avoid recalculating the impedance model for every screw that has changed! 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 18

Electron Cloud effects Electron clouds lead to • Tune shift / spread • Synchronous phase shift • Instabilities Pic. by F. Petrov TU-Darmstadt Difference to LHC • Syncr. Rad. • Asymmetry • Small aperture • 3 D and 2 D particle in cell codes for electron cloud simulations • community supported beam tracking codes (e. g. Py. Orbit) • working on coupling the electron cloud simulations to the beam tracking including impedances. 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 19

Scientific Outlook ▪ Asymmetry Quadrupolar impedance ▪ Combination of impedance and electron cloud ▪ Finally impedance check of all components in the ring? Nooo! Rather exclude some devices a priori and make a simplified model. This is a CDR not a TDR! 17 September 2020 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 20