Transcript Slide 1

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
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
transverse SPS impedance spectrum via debunching
xv~-0.4
0.5
inst
1.0 GHz
xV Q  rev

  1/  2
unstable frequency
(frequency where Landau
damping is lost)
xv~-0.5
0.5
1.0 GHz
xv~-0.6
0.5
1.0 GHz
1 /   Z (inst )
growth rate at this frequency
measuring frequency-dependent impedance!
T. Bohl et al., 2002
localized SPS impedance from f beating vs. intensity
14-GeV/c
data much
cleaner than
26-GeV/c
data
(unfortunately
not available
in 2004)
impedance inferred from iterative SVD fit
G. Arduini, C. Carli, F. Zimmermann, EPAC 2004
impedance
concentrated
in a few
locations –
MKP & MKE
kickers, ~ rf,
and one
other
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
beam
screen
individual
components
total w/o
collimators
collimators
collimators
transverse
resistive wall
(low frequency)
impedance
from LHC
Design Report
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
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
2 Z 0 R 4
complex tune shift
=75% of that for
x or y collimator
Nr p  y 3 (1)
Q y  j
Z
2 Z 0 R 4
Q xy  j
Nr p
x y 1
2
Z0R
4
Z (1)
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-2001-044-HRF
~ complete
E. Haebel et al., SL-98-008-RF
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?
LHC BPMs
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
BPM
numbers
MAD
compared
with
R. Jones’
table
Type
Number in
MAD
Total Number in Both
Rings [R. Jones]
BPMC
BPMSW
BPMS
BPMSY
BPMSX
BPMW
BPMWA
BPMWB
BPMR
BPMYA
BPMYB
BPM
8
16
16
8
8
18
4
8
18
12
6
430
16 OK
8 OK?
8 OK?
4 OK?
4 OK?
36 OK
8 OK
16 OK
36 OK
24 OK
12 OK
720(arc)+140(DS+Q7)=860
OK
LHC BPMs cont’d
tables from
R. Jones
ok
warm
hybrid
warm
elements which
are not accounted
for in the database
(from where the
MADX input is
generated)
striplines
striplines
striplines
warm
striplines
striplines
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
(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)
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
(Zlong/n)eff (W)
Zeff [8 kHz] (MW/m)
Zeff [20 MHz] (MW/m)
0.070
0.076
45-22 i (injection)
91-24 i (top energy)
3- 9 i (injection)
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
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-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
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
electron cloud
single-bunch e- cloud effect
can be approximated by
broadband resonator
with resonant frequency
SPS
injection
LHC
injection
LHC
top
sxy
2.5 mm
1 mm
0.3 mm
sz
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
cRs
c re1/ 2
 H emp 3 3 / 2 1/ 2 C
Q
s k b
re
5x1011 m-3 5x1011 m-3
5x1011 m-3
and Q~1-5
fres
0.31 GHz
4.66 GHz
R/Q
45 MW/m 372 MW/m 812 MW/m
0.91 GHz
LHC impedance larger than SPS impedance
due to smaller beam size & larger circumference
f res
1

2
2re c 2
2s 2
Nb
1
2 s z
k
R/Q value
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