1. Sergey Antipov, Nicolo Biancacci, and david amorim
Study of the destabilizing effect of the resistive transverse damper with NHTVS
Sergey Antipov, Nicolo Biancacci, and david amorim

2. Ring model – Broadband resonator impedance
Using only Z for single bunch
Energy: E0 = 26 GeV
Rev. frequency: f0 = kHz
Tunes: Qx = 26.13, Qy = 26.18, Qs = 7.3*10-3
Resonator: Q = 1, fr = 1 GHz, Rs = 10 MΩ/m
Data taken from D. Amorim’s slides
3/27/2017
S. Antipov

3. Single bunch model No of nested rings: 5
Azimuthal modes: l = -10 … +10
Total no. of modes: 105
Chromaticity: Q’ = -20 … 0 … +20
Bunch length: τb = 0.8, 2.8 ns
Norm. intensity: x = 0 … 2
SC tune shift: ΔQSC ~ 0.1 (!)
Couple-bunch modes can be easily added
Distribution of the nested rings
3/27/2017
S. Antipov

4. “Flat” damper
Goal – to see how a damper leads to an instability through the coupling of the azimuthal modes
Checked resistive and reactive damper
Varying strength: 1/g = 0 … 1/(50 turns)
Can add a frequency cut-off
From E. Metral’s slides,
3/27/2017
S. Antipov

5. Coupling between modes 0 and 1
Low intensity: Resistive damper couples the modes, making l = 1 unstable
High intensity: resistive damper helps
3/27/2017
S. Antipov

6. Resistive damper Blue NHTVS Red E. Metral’s approximate solution:
Black DELPHI (data from David)
Double the damper strength!
3/27/2017
S. Antipov

7. Reactive damper Blue NHTVS Red E. Metral’s approximate solution
Black DELPHI (data from David)
3/27/2017
S. Antipov

8. Adding couple-bunch modes does not change the picture
Intensity parameter 0.25, resistive damper
The picture may change for a higher Z at low f
Single-bunch only
With couple-bunch
3/27/2017
S. Antipov

9. Resistive damper, τb = 2.8 ns
Blue NHTVS
Black DELPHI
3/27/2017
S. Antipov

10. Reactive damper, τb = 2.8 ns Blue NHTVS Black DELPHI 3/27/2017
S. Antipov

11. Conclusion
We see a good agreement between the simulation results in NHT and DELPHI for the case of ns bunch length
There is a noticeable discrepancy for the case of 2.8 ns bunch length
Simulation confirms the analytic estimates
Up to a factor of 2 in the damper strength
Resistive damper leads to mode coupling and causes an instability at Q’ = 0.
Would be interesting to look for a similar effect for the LHC beam parameters and impedance model
3/27/2017
S. Antipov

12. Bonus slides: LHC
Ongoing work
3/27/2017
S. Antipov

13. LHC model Intensity: Nb = 1.0x1011 Bunch length: τb = 1.2 ns
Damper: Resistive
Chromaticity: ξ = -6, -4,…, +6
Emittance: εn = 2 μm
Octupole sign: Positive
LHC Impedance model from Nicolo
3/27/2017
S. Antipov

14. LHC: Preliminary results
Single-bunch only
Adding couple-bunch modes
3/27/2017
S. Antipov

15. LHC: Preliminary results
From E. Metral’s slides,
3/27/2017
S. Antipov