SPS impedance transverse impedance described by broadband resonator (many geometric transitions, shielded pumping ports) with frequency 1.3 GHz, Q~1, R sh ~10 M  /m, plus contribution from MKE kickers Z~1.25 M  /m per unit longitudinal impedance dominated by 200-MHz rf, some contribution from HOM at 629 MHz, 800-MHz rf, MKE kickers in 2002 one attempt to measure frequency spectrum of transverse impedance by debunching, with transverse wideband monitor (rf group & then SL/AP) in 2003 two attempts to localize the transverse impedance around the ring from current-dependent phase beating

 v ~-0.4  v ~-0.5  v ~ GHz GHz GHz unstable frequency (frequency where Landau damping is lost) growth rate at this frequency measuring frequency-dependent impedance! transverse SPS impedance spectrum via debunching T. Bohl et al., 2002

impedance inferred from iterative SVD fit localized SPS impedance from  beating vs. intensity 14-GeV/c data much cleaner than 26-GeV/c data (unfortunately not available in 2004) impedance concentrated in a few locations – MKP & MKE kickers, ~ rf, and one other G. Arduini, C. Carli, F. Zimmermann, EPAC 2004

LHC impedance contributions resistive wall impedance of beam-screen (cold+warm), collimators, TDI absorbers, MQW, MBW, and septa geometric impedance of collimators, bellows and interconnects resonator impedances (due to HOM's of RF-cavities & trapped modes in experimental chambers & transverse damper): narrow-band and broad-band. kickers, BPM's, and cold-warm transitions quadrupolar impedance causing s-dependent incoherent tune shifts pumping slots, high-frequency resistive impedance of the beam screen diagnostics & instrumentation unconventional impedances: electron cloud, (long-range) beam-beam

transverse resistive wall (low frequency) impedance from LHC Design Report individual components total w/o collimators beam screen collimators

broadband impedance from LHC Design Report pumping slots, BPMs bellows collimators not much discussed in LHC Design Report: narrow-band resonances & trapped modes

collimator impedance calculations by A. Grudiev with HFSS & GdfidL longitudinal wave guide mode trapped between the graphite jaws: in open position the frequency is ~3 GHz and Q~1000 negligible energy exchange of <2 eV with the proton beam longit. wake envelope 1  s V/nC

LHC collimator impedance measured in the SPS tune shift with gap ~1e-4, similar as, and slightly smaller than expected; dependence on gap size differs from theory even taking into account nonlinear wake and beam loss (‘Piwinski enhancement’) orbit deflection by single jaw below resolution limit (~1  rad; expected < 0.2  rad) head-tail growth rates with collimator open or closed below resolution limit (SPS impedance dominant as expected) multi-batch beam (in)stability cycle-to-cycle variation larger than effect of closing the gap; in principle sensitive resistive-wall model (Burov-Lebedev vs. Zotter) some uncertainties

collimator impedance cont’d tensor impedance for 45 o collimator (F. Ruggiero) complex tune shift =75% of that for x or y collimator complex xy coupling due to tilted impedance

HOM data for resonators following data sheets were obtained from D. Angal-Kalinin (Daresbury); they are based on MAFIA calculations by J. Tuckmantel, rf group + rf-group visitors, Y. Luo, and D. Brandt longitudinal HOM data for transverse damper (damped & undamped) longitudinal HOM data of CMS chamber longitudinal HOM data for 200-MHz cavities (undamped, damped w. 2 couplers, & damped w. 4 couplers) longitudinal HOM data for 400-MHz s.c. cavities (undamped & damped) transverse HOM data for 400-MHz s.c. cavities (undamped & damped) transverse HOM data for 200-MHz cavities (undamped only) Notes: 200-MHz damped data only approximate 400-MHz: for HOMs module with 4 single cell cavities = 4-cell supercavity; non-negligible fabrication scatter, so that field-profile - excitation of the different single cavities - can be anything for the 4 modes (J. Tuckmantel) References: D. Angal-Kalinin, LHC Project Report 595 D. Boussard et al., LHC Project Report 368 T. Linnecar et al., SL-Note HRF E. Haebel et al., SL RF ~ complete

IR recombination (“Y”) chamber following MAFIA outputs were obtained from B. Spataro (INFN Frascati); they were obtained partially in collaboration with D. Li, LBNL real and imaginary parts of longitudinal impedance up to 8 GHz for the IN and OUT transitions scaled longitudinal wake for IN and OUT transition longitudinal and transverse loss parameters as a function of vertical coordinate D. Brandt et al., LHC Project Report 604: On Trapped Modes in the LHC Recombination Chambers: Numerical and Experimental Results horizontal impedance?

several types of BPMs most arc BPMs: buttons D. Brandt et al. in LHC Project Note 284: Impedance of the LHC Arc Beam Position Monitors BPM we obtained MAFIA output files from B. Spataro (Frascati) second type of BPMs: hybrid monitors D. Brandt et al. in LHC Project Note 315: Impedance of the LHC Hybrid Beam Position Monitors BPMC we obtained MAFIA output files from B. Spataro (Frascati) pure stripline monitors L. Vos and A. Wagner, LHC Project Report 126 (1997) [longitudinal impedance only]. LHC BPMs ~ complete

TypeNumber in MAD Total Number in Both Rings [ R. Jones ] BPMC816 OK BPMSW168 OK? BPMS168 OK? BPMSY84 OK? BPMSX84 OK? BPMW1836 OK BPMWA48 OK BPMWB816 OK BPMR1836 OK BPMYA1224 OK BPMYB612 OK BPM (arc)+140(DS+Q7)=860 OK LHC BPM numbers MAD compared with R. Jones’ table LHC BPMs cont’d: numbers, types (&  functions)

elements which are not accounted for in the database (from where the MADX input is generated) ok tables from R. Jones warm striplines hybrid stripline impedances 3-7 times larger than button impedances, BPM sum ~ % of total LHC BPMs cont’d

46 BPMs per beam (16 BPMSW, 18 BPMW, 4 BPMWA, 8 BPMWB) Average betaInjectionTop Horizontal, vertical beta109.9 m, m328.0 m, m BPM length = 285 mm, inner bore radius b~30 mm, thickness d~10 mm (st.st. with conductivity of  =1.4x10 6  -1 m -1 at room temperature), skin depth of copper is 0.7 mm at 8 kHz, and 15  m at 20 MHz. warm BPMs in LHC with or w/o Cu coating (Zlong/n)eff (  ) Zeff [8 kHz] (M  /m) Zeff [20 MHz] (M  /m) (injection) (top) i (injection) I (top energy) i (injection) i (top) (Zlong/n)eff (  )Zeff [8 kHz] (M  /m)Zeff [20 MHz] (M  /m) i (injection) i (top energy) 3- 9 i (injection) 5-5 i (top) (Zlong/n)eff (  ) Zeff [8 kHz] (M  /m) Zeff [20 MHz] (M  /m) (injection) (top) i (injection) i (top energy) i (injection) i (top) for comparison: total LHC impedance from design report for 100-  m Cu coating (  =5.9x10 7  -1 m -1 ) uncoated BPMs [using Burov/Lebedev formula] even in the worst case the total impedance for the uncoated warm BPMs is 1% or less of the total LHC impedance

Narrow-band and broad-band impedance References: G. Lambertson, Calculation of the LHC Kicker Impedance, PAC99, [analytical calculation for combined contribution of ceramic, metallic stripes and kicker magnet; estimate of longitudinal and transverse impedance for the injection kickers] Impedance of coated ceramic: D. Brandt et al., Penetration of Electro-Magnetic Fields through a Thin Resistive Layer, AB-Note MD (2003) [measurements with coating and second shield] D. Brandt et al., EPAC 2000 Vienna [results without second shield] F. Caspers et al., Bench Measurements of the LHC Injection Kicker Low-Frequency Impedance Properties, PS/RF/ Note Bench Measurements of Low Frequency Transverse Impedance, CERN-AB RF [describes novel measurement procedure] H. Tsutsui: Simulation of the LHC Injection Kicker Impedance Test Bench, LHC Project Note 327 A. Burov, Transverse Impedance of Ferrite Kickers, LHC Project Note 353 dump & injection kickers some uncertainties

Narrow-band and broad-band Info from L. Vos: Vacuum chamber made of 1 m stainless steel + 5-  m Cu layer which Luc proposed to compromise between heat conduction & power deposition, 100 units. Ref. LHC-VST-ES-0001 rev Length per unit about 0.3 m. Inner diameter ~63 mm. Impedance calculation by Luc. Inductive bypass important. Geometric impedance sources: shape transition taper angle <10 degree, rf junctions? cold-warm transitions

deflection depends on displacement of test particle e.g., for collimators References: G. Stupakov, Impedance of Small Angle Collimators in High Frequency Limit, SLAC-PUB-8857 (2001). Kaoru Yokoya, Resistive Wall Impedance of Beam Pipes of General Cross Section. Part.Accel.41: quadrupolar impedance

electron cloud SPS injection LHC injection LHC top  xy 2.5 mm1 mm0.3 mm zz 0.25 m0.175 m0.075 m k222 H emp 444 C6.9 km27 km N 1.15x10 11 ee 5x10 11 m -3 f res 0.31 GHz0.91 GHz4.66 GHz R/Q 45 M  /m372 M  /m812 M  /m single-bunch e- cloud effect can be approximated by broadband resonator with resonant frequency R/Q value and Q~1-5 References: K.Ohmi et al., PRE65:016502,2002 E. Benedetto et al., ECLOUD’04 f res and R/Q depend on bunch intensity and beam size, R/Q also varies linearly with cloud density LHC impedance larger than SPS impedance due to smaller beam size & larger circumference