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

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

Resistive wall Impedance with thick Cu

21 April 2023 | TU Darmstadt | Fachbereich 18 | Fachgebiet Beschleunigerphysik | Oliver Boine-Frankenheim | 3

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)

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

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