1. Beam pipe impedance vs. Frequency 22 July 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 1 An artifact, due to numerical cancelation at high gamma Coating with Copper at 50K, k=6e9 S/m x2.0 Skindepth=coating thickness 80um

2. Growth rates vs. Energy 22 July 2015 | TU Darmstadt | Fachbereich 18 | Fachgebiet Beschleunigerphysik | Fedor Petrov | 2 *N. Mounet, 3 TeV, 20 K Realistic half-gap ∈ [12 mm, 18 mm] Multi-bunch and single bunch growth rates: - Growth rates for bunch trains (empty buckets) using detailed (2D) impedance results. - Landau damping by octupoles (coupled bunch) -> thresholds with octupoles and feedback vs. energy Beam becomes more stable, but feedback is weaker. Needed if possible: 1. Resistance data for 20-50 K ( factor 2-3 uncertainty) 2. Feedback rates vs. Energy Scaling to larger energies

3. Resistive wall Impedance with thick Cu 22 July 2015 | TU Darmstadt | Fachbereich 18 | Fachgebiet Beschleunigerphysik | Oliver Boine-Frankenheim | 3

4. Comparison with round pipe impedance  Vertical 22 July 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 4 An artifact, due to numerical cancelation at high gamma X1.4 Skindepth=coating thickness 80 um (1 meter pipe)

5. Coupled bunch resistive instability 22 July 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 5 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

6. Scenario Data 22 July 2015 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 6 ▪E=3TeV ▪Q s =0.0028 ▪M=13344 (25ns) ▪rms bunch length 8 cm ▪N b =1.0e11 ▪Q x =120.31 ▪Q y =120.32 ▪Chroma=0 ▪E=50TeV ▪Q s =0.0078