LHC crab cavity impedance - 1 st and 2 nd thoughts. Frank Zimmermann 3 rd LHC-ILC crab synergy meeting 5 April 2008 thanks to: Rama Calaga, Zenghai Li, Andrei Seryi. longitudinal impedance requirements – 1 st thoughts:
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3rd LHC-ILC crab synergy meeting
5 April 2008
thanks to: Rama Calaga, Zenghai Li, Andrei Seryi
Andrei, 3 April 2008:
“In Deepa's paper ZAP code was used which performed an analytical evaluation of all the modes or sources of impedance, sort the more dangerous modes, etc. The question is -- how accurate is the ZAP calculation?For quick evaluation of particular modes we could use simple analytical estimation (should be just couple tens of lines of Matlab code). “
Zenghai, 2 & 4 April 2008:
“In the 800MHz design, one of the monopole modes has a R/Q of around 200 Ohm (for point charge), the Q would be lower than 10 to satisfy the 1-2kOhm requirement, which would be difficult…”
“Here are the R/Q numbers for the LOM, SOM, and the operating modes (→ next slide). These numbers are based on the first preliminary design. They will change some as design evolves. Should be a good starting point for impedance studies. We need the Qext requirement for the LOM and SOM modes for the damping coupler design. Let me know if you need more info. (If needed, the frequencies of the LOM and SOM can also be adjusted to avoid resonances).”
slide from Zenghai
should units of dipole R/Q not be Ohm/meter?
*(Based on Liling-1/20/08 talk. R/Q will change slightly as design evolves)
- “2nd thoughts”
1. narrow-band impedance – threshold of coupled-bunch instability [5,6]
→ Rsh,L< 137 kW (inj.)
Rsh,L <196 kW (top)
→ Q < 100-200 should be fine for SLAC 800-MHz cavity
2. broad-band impedance – loss of Landau damping [5,6,7]
→ Im(Z/n) < 0.24 W (inj.)
Im(Z/n) < 0.15 W (top)
stability limit from Landau octupoles at 7 TeV
(Berg-Ruggiero , Resta-Lopez )
for m=0 modes
the two lines refer to
opposite or equal polarity
of octupole families
roughly speaking: stability if Re (DQ)< 3x10-4, Im (DQ)<10-4;
on the next page we will estimate DQ and deduce the resulting
limit on the transverse shunt impedance
F. Sacherer, Transverse Bunched Beam Instabilities, 9th HEACC, Stanford, Springfield 1975, 347
A. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators, Wiley, 1993
conservatively assume hm~1 and that sampling frequency falls onto resonance;
note that sampling interval is ~40 MHz (25 ns spacing) so that for Q~100
mainly one single line contributes to a multibunch mode (~1GHz/(40MHz)~25);
consider the rigid dipole mode m=0 and, slightly pessimistically, b~5 km
→ Rsh,T<< 2 MW/m (top)
Rsh,L< 100 kW/#cavities
(Q < 100-200 OK)
Im(Z/n) << 0.10 W/#cavities
Rsh,T<< 2 MW/m/#cavities
 F. Ruggiero, “Single-Beam Collective Effects in the LHC,” CERN SL/95-09 (AP) 1995.
 D. Angal-Kalinin, “Review of Coupled-Bunch Instabilities in the LHC,” LHC Project-Report 595, http://doc.cern.ch/archive/electronic/cern/preprints/lhc/lhc-project-report-595.pdf
 LHC Design Report, Vol. 1, Chapter 5, CERN-2004-003-V-1 (2004).
 R. Tomas, “Optics for Crab Cavities in the LHC,” LHC-CC08, BNL, March 2008
 E. Shaposhnikova, “Longitudinal Beam Parameters During Acceleration in the LHC,” LHC Project Note 242 (2000).
 F.J. Sacherer, “A Longitudinal Stability Criterion for Bunched Beams”, IEEE Tr. Nucl.Sci. NS-20 , 825 (1973).
 V.I.Balbekov,S.V.Ivanov, “Thresholds of Longitudinal Instability of Bunched Beam in the Presence of Dominant Inductive Impedance,” IHEP Preprint 91-14, Protvino (1991).
 J.S. Berg, F. Ruggiero, “Landau Damping with Two-Dimensional Betatron Tune Spread,” CERN-SL-AP-96-071-AP (1996).
 J. Resta Lopez, “Design and Performance Evaluation of Nonlinear Collimation Systems for CLIC and LHC,” PhD Thesis, U. Valencia (2007).