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Beam pipe impedance vs. Frequency
21 April 2023 | 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
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Growth rates vs. Energy
21 April 2023 | 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 tolarger energies
1
30
bN
SE b
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Resistive wall Impedance with thick Cu
21 April 2023 | TU Darmstadt | Fachbereich 18 | Fachgebiet Beschleunigerphysik | Oliver Boine-Frankenheim | 3
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Comparison with round pipe impedance Vertical
21 April 2023 | 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)
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Coupled bunch resistive instability
21 April 2023 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 5
Pipe only, solid Cu 50KE=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 umcoating
Required thickness for “thick wall“150 um for 50K450 um for 140K
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Scenario Data
21 April 2023 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 6
▪ E=3TeV
▪ Qs=0.0028
▪ M=13344 (25ns)▪ rms bunch length 8 cm
▪ Nb=1.0e11
▪ Qx=120.31
▪ Qy=120.32
▪ Chroma=0
▪ E=50TeV
▪ Qs=0.0078