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									SPS impedance

transverse impedance described by broadband resonator
(many geometric transitions, shielded pumping ports)
with frequency 1.3 GHz, Q~1, Rsh~10 MW/m, plus
contribution from MKE kickers Z~1.25 MW/m per unit

longitudinal impedance dominated by 200-MHz rf, some
contribution from HOM at 629 MHz, 800-MHz rf , MKE

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
transverse SPS impedance spectrum via debunching
     xv~-0.4                   xv~-0.5                       xv~-0.6

   0.5     1.0 GHz           0.5   1.0 GHz                   0.5   1.0 GHz

              xV Q  rev           1 /   Z (inst )
   inst   
                1/  2            growth rate at this frequency
   unstable frequency              measuring frequency-dependent impedance!
   (frequency where Landau                               T. Bohl et al., 2002
   damping is lost)
localized SPS impedance from f beating vs. intensity
                                                 data much
                                                 cleaner than
                                                 not available
                                                 in 2004)

     impedance inferred from iterative SVD fit    impedance
                                                  in a few
                                                  locations –
                                                  MKP & MKE
                                                  kickers, ~ rf,
                                                  and one

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
• 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)
                                    resistive wall
                                    (low frequency)
beam                 components
                                    from LHC
screen                              Design Report

                      total w/o

collimators   collimators
broadband impedance from LHC Design Report




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

                                                0.2 V/nC

                                                  longit. wake envelope

                                           0                          1 ms
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 mrad; expected < 0.2 mrad)
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)

             Nr p  x 3 (1)
    Q x  j             Z               complex tune shift
             2 Z 0 R 4                 =75% of that for
             Nr p  y 3 (1)              x or y collimator
    Q y  j             Z
             2 Z 0 R 4
                       x y 1           complex xy coupling
                Nr p
    Q xy  j                    Z (1)   due to tilted impedance
                2    Z0R   4
  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)
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 transition
longitudinal and transverse loss parameters as a function of vertical

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].                  ~ complete
LHC BPMs cont’d: numbers, types (&  functions)
LHC         Type      Number in   Total Number in Both
BPM                   MAD         Rings [R. Jones]
numbers     BPMC      8           16 OK
            BPMSW     16          8 OK?
compared    BPMS      16          8 OK?
with        BPMSY     8           4 OK?
R. Jones’   BPMSX     8           4 OK?
table       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
LHC BPMs cont’d
                                                             tables from
                                                             R. Jones

                                                                warm       striplines

  elements which
  are not accounted
  for in the database
  (from where the                                                           striplines
  MADX input is
  generated)                                                    warm

stripline impedances 3-7 times larger than button impedances, BPM sum ~ % of total
     warm BPMs in LHC with or w/o Cu coating
        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 s=1.4x106 W-1m-1 at room temperature), skin depth of
     copper is 0.7 mm at 8 kHz, and 15 mm at 20 MHz.
    uncoated BPMs [using Burov/Lebedev formula]   for 100-mm Cu coating (s=5.9x107 W-1m-1)
(Zlong/n)eff   Zeff [8 kHz]    Zeff [20 MHz]  (Zlong/n)eff   Zeff [8 kHz]    Zeff [20 MHz]
(W)            (MW/m)          (MW/m)         (W)            (MW/m)          (MW/m)
0.00038           0.183-0.220 i     0.004-0.004 i        0.000034             0.258+0.288 i     0.001-0.001 i
(injection)       (injection)       (injection)          (injection)          (injection)       (injection)
0.00025 (top)     0.517-0.621 I     0.013-0.013 i        0.000028 (top)       0.728+0.813 i     0.002-0.002 i
                  (top energy)      (top)                                     (top energy)      (top)
                     for comparison: total LHC impedance from design report
                           (Zlong/n)eff (W)      Zeff [8 kHz] (MW/m)       Zeff [20 MHz] (MW/m)

                           0.070                 45-22 i (injection)       3- 9 i (injection)
                           0.076                 91-24 i (top energy)      5-5 i (top)

even in the worst case the total impedance for the uncoated warm
BPMs is 1% or less of the total LHC impedance
dump & injection kickers
Narrow-band and broad-band impedance
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 2002-156
         Bench 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

                                                               some uncertainties
cold-warm transitions
Narrow-band and broad-band

Info from L. Vos:
Vacuum chamber made of 1 m stainless steel + 5-mm 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?
quadrupolar impedance

deflection depends on displacement of test particle

e.g., for collimators

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
       electron cloud                             single-bunch e- cloud effect
                                                  can be approximated by
         SPS         LHC         LHC              broadband resonator
         injection   injection   top              with resonant frequency
sxy      2.5 mm      1 mm        0.3 mm                      1   2re c 2   Nb       1
sz                                                f res   
         0.25 m      0.175 m     0.075 m
                                                            2   2s 2      2 s z   k
k        2           2           2
                                                  R/Q value
Hemp     4           4           4
                                                  cRs          c re1/ 2
C        6.9 km      27 km       27 km                 H emp 3 3 / 2 1/ 2 C
N        1.15x1011   1.15x1011   1.15x1011         Q         s k b
re       5x1011 m-3 5x1011 m-3   5x1011 m-3       and Q~1-5
fres     0.31 GHz    0.91 GHz    4.66 GHz         References:
R/Q      45 MW/m 372 MW/m 812 MW/m                K.Ohmi et al., PRE65:016502,2002
LHC impedance larger than SPS impedance           E. Benedetto et al., ECLOUD’04
due to smaller beam size & larger circumference

     fres and R/Q depend on bunch intensity and beam size,
     R/Q also varies linearly with cloud density

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