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

Ring model – Broadband resonator impedance Using only Z for single bunch Energy: E0 = 26 GeV Rev. frequency: f0 = 43.29 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

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

“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, 20.02.17 3/27/2017 S. Antipov

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

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

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

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

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

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

Conclusion We see a good agreement between the simulation results in NHT and DELPHI for the case of 0.8 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

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

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

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

LHC: Preliminary results From E. Metral’s slides, 20.02.17 3/27/2017 S. Antipov