16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 1 Single Beam Collective Effects Impedances and Collective Effects for FCC-hh Uwe Niedermayer Institut für Theorie Elektromagnetischer Felder Technische Universität Darmstadt, Germany

Contents ▪Beam pipe impedance ▪Other impedance sources ▪Coupled bunch instability ▪Transverse Mode Coupling Instability (TMCI) threshold ▪Electron clouds (briefly)  More details in the talk by K. Ohmi 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 2

The beam pipe 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 3 Design by R. Kersevan, CERN So far only this design considered D. Schulte

Discretization 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 4 GMSH (Geuzaine et al.) triangular mesh Thilo Egenolf, TU Darmstadt Meshing the whole structure is required only for extremely low frequency! Otherwise: Surface Impedance Boundary Condition (SIBC)

2D Simulations in the Frequency Domain 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 5 f=100Hz f=1MHz Horizontal Vertical ▪BeamImpedance2D, PYTHON code using FEniCS finite element toolbox (U. Niedermayer et al., to appear in PRSTAB)

Materials ▪Beam Screen: Titanium ▪Coating: Copper (80um or maybe higher) ▪Outer pipe, synchr. rad. reflector: Stainless Steel ▪Conductivities k at room temperature T=293K -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=4K)/ k(293K) usually RRR ~ 300 ▪Temperatures for the FCC pipe: -Scenario 1: K (roughly… k =100 k 0 ) -Scenario 2: K (roughly… k =10 k 0 ) ▪Magnetoresistance at 16T ? 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 6

Penetration depth ▪Surface impedance for coated surface 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 7 CopperTitaniumVacuum 6.4kHz

Comparison with round pipe impedance  Horizontal 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 8 An artifact, due to numerical cancelation at high gamma Coating with Copper at 50K, k=6e9 S/m X2.0 Skindepth=coating thickness 80um (1 meter pipe)

Comparison with round pipe impedance  Vertical 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 9 An artifact, due to numerical cancelation at high gamma X1.4 Skindepth=coating thickness 80 um (1 meter pipe)

Pumping Holes, Collimators, … 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 10 B. Salvant and X. Buffat, CERN Collimators scaled from LHC, see also talk by M. Fiascaris (this morning) Maybe LHC-like carbon collimators are not the best choice… Collimators closed only at top energy! Pumping holes with resonator model,... f res =f cutoff ~6GHz Q=1 (Broadband) S. Kurennoy, Part. Accel., 1995, Vol. 50, pp

Scenario Data 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 11 ▪E=3TeV ▪Q s = ▪M=13344 (25ns) ▪rms bunch length 8 cm ▪N b =1.0e11 ▪Q x = ▪Q y = ▪Chroma=0 ▪E=50TeV ▪Q s =0.0078

Coupled bunch resistive instability 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 12 Pipe only, solid Cu 50K E=3TeV N. Mounet, EPFL Lausanne, formerly CERN most unstable coupled-bunch mode at lowest frequency=2kHz Most critical at injection due to less stiff beam! Growth rate by factor 1.6 higher for 80 um coating Required thickness for “thick wall“ 150 um for 50K 450 um for 140K

TMCI intensity threshold 3TeV 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 13 B. Salvant and X. Buffat, CERN coherent tune shift of the mode Pipe +holes Pipe only

TMCI intensity threshold 50TeV 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 14 B. Salvant and X. Buffat, CERN More stiff beam, but higher impedance due to closed collimators Pipe + holes + collimators

Electron Cloud effects 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 15 Electron clouds lead to Tune shift / spread Synchronous phase shift Instabilities 3D and 2D particle in cell codes for electron cloud simulations community supported beam tracking codes (e.g. PyOrbit) working on coupling the electron cloud simulations to the beam tracking including impedances. Difference to LHC Syncr. Rad. Asymmetry Small aperture Pic. by F. Petrov TU-Darmstadt

Computing Resources at TEMF, TU-Darmstadt 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 16 Pic. by W.F.O Müller

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 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 17

Outlook ▪A lot of work to do! ▪Pumping hole impedance to be studied in more detail ▪Asymmetry  Quadrupolar impedance ▪Combination of impedance and electron cloud ▪Finally impedance check of all components in the ring 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 18

The End 16 April 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 19 Thank you for your attention!