SPS impedance
transverse impedance described by broadband resonator (many geometric transitions, shielded pumping ports) with frequency 1.3 GHz, Q~1, Rsh~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~-0.6
0.5 1.0 GHz 0.5 1.0 GHz 0.5 1.0 GHz
2/1
revV
inst
Q )(/1 instZ
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/cdata muchcleaner than26-GeV/cdata(unfortunatelynot availablein 2004)
impedanceconcentratedin a few locations – MKP & MKEkickers, ~ rf,and oneother
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)impedancefrom LHCDesign Report
individualcomponents
total w/o collimators
collimators
beamscreen
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 impedancecalculations 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~1000negligible energy exchange of <2 eV with the proton beam
longit. wake envelope
1s0
0.2 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 45o collimator (F. Ruggiero)
)1(
0
)1(
0
)1(
0
4
1
2
4
3
2
4
3
2
ZRZ
NrjQ
ZRZ
NrjQ
ZRZ
NrjQ
yxpxy
ypy
xpx
complex tune shift=75% of that forx or y collimator
complex xy couplingdue 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 chamberlongitudinal 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-2001-044-HRF E. Haebel et al., SL-98-008-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 transitionlongitudinal 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 BPMwe obtained MAFIA output files from B. Spataro (Frascati)
second type of BPMs: hybrid monitorsD. Brandt et al. in LHC Project Note 315: Impedance of the LHC Hybrid Beam Position Monitors BPMCwe obtained MAFIA output files from B. Spataro (Frascati)
pure stripline monitorsL. Vos and A. Wagner, LHC Project Report 126 (1997) [longitudinal impedance only].
LHC BPMs
~ complete
Type Number in MAD
Total Number in Both
Rings [R. Jones]
BPMC 8 16 OK
BPMSW 16 8 OK?
BPMS 16 8 OK?
BPMSY 8 4 OK?
BPMSX 8 4 OK?
BPMW 18 36 OK
BPMWA 4 8 OK
BPMWB 8 16 OK
BPMR 18 36 OK
BPMYA 12 24 OK
BPMYB 6 12 OK
BPM 430 720(arc)+140(DS+Q7)=860 OK
LHCBPMnumbers
MADcomparedwithR. Jones’table
LHC BPMs cont’d: numbers, types (& functions)
Orbit System BPMs
BPM type Number
BPM (Arc) 720
BPM (DS+Q7) 140BPMR 36BPMYA 24BPMYB 12BPMW 36BPMWA 8BPMWB 16BPMC 16BPMS 8BPMSW 8BPMSX 4BPMSY 4
Orbit Total 1032
Other Special BPMsBPRS 8BPLS 4BPQS(H/V) 4BPQS 2Mobile BPM 8BPTX 8BQMS 4CNGS target 1BPMWC? 8BPMWD? 2BPMWE? 2BPMWF? 2BPMRF 2
elements which are not accountedfor in the database(from where theMADX input is generated)
ok
tables from R. Jones
warm
warm
warm
striplines
striplines
striplines
striplines
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 beta Injection Top
Horizontal, vertical beta 109.9 m, 115.1 m 328.0 m, 306.5 m
BPM length = 285 mm, inner bore radius b~30 mm, thickness d~10 mm (st.st.with conductivity of =1.4x106 -1m-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)
0.00038 (injection)0.00025 (top)
0.183-0.220 i (injection)0.517-0.621 I (top energy)
0.004-0.004 i (injection)0.013-0.013 i (top)
(Zlong/n)eff () Zeff [8 kHz] (M/m) Zeff [20 MHz] (M/m)
0.0700.076
45-22 i (injection)91-24 i (top energy)
3- 9 i (injection)5-5 i (top)
(Zlong/n)eff ()
Zeff [8 kHz] (M/m)
Zeff [20 MHz] (M/m)
0.000034 (injection)0.000028 (top)
0.258+0.288 i (injection)0.728+0.813 i (top energy)
0.001-0.001 i (injection)0.002-0.002 i (top)
for comparison: total LHC impedance from design report
for 100-m Cu coating (=5.9x107 -1m-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 impedanceReferences: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-2003-002 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 2002-156Bench Measurements of Low Frequency Transverse Impedance, CERN-AB-2003-051-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. 1.0.
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.41:221-248
quadrupolar impedance
electron cloud
k
Ncrf
z
beres
1
22
2
2
12
2
Ck
rH
Q
cR
b
ecemp
s2/12/33
2/1
SPSinjection
LHCinjection
LHCtop
xy 2.5 mm 1 mm 0.3 mm
z 0.25 m 0.175 m 0.075 m
k 2 2 2
Hemp 4 4 4
C 6.9 km 27 km 27 km
N 1.15x1011 1.15x1011 1.15x1011
e 5x1011 m-3 5x1011 m-3 5x1011 m-3
fres 0.31 GHz 0.91 GHz 4.66 GHz
R/Q 45 M/m 372 M/m 812 M/m
single-bunch e- cloud effectcan be approximated bybroadband resonatorwith resonant frequency
R/Q value
and Q~1-5
References:K.Ohmi et al., PRE65:016502,2002 E. Benedetto et al., ECLOUD’04
fres and R/Q depend on bunch intensity and beam size,R/Q also varies linearly with cloud density
LHC impedance larger than SPS impedancedue to smaller beam size & larger circumference