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