1. update on SPS impedance localization
Frank Zimmermann
Accelerator Performance Committee
13. April 2006
Thanks to G. Arduini & E. Shaposhnikova

2. introduction reminder of results presented to the APC on 26. 05. 2005

3. Optics Perturbation APC 26.05.2005
considering only vertical plane, impedance acts
like a current-dependent quadrupole of effective
gradient
bunch
population
effective
impedance
beam energy
note that vertical impedance is defocusing

4. + APC 26.05.2005 impedance will introduce beta & phase beating
(C. Carli); explains oscillations in 2003 analysis
APC
response matrix was derived in 1st order perturbation theory:
rewritten as
adding
87x237 matrix
cut-off of singular
values in SVD
inversion is another
free parameter +
SVD solution is stabilized
by introducing additional
equations with weights l
M computed from MAD optics
solution obtained by matrix
pseudo-inversion, e.g., SVD

5. APC 26.05.2005 take data at different beam intensities Nb
for each BPM & data set, determine the phase of
oscillation with respect to the start of the line;
constrain f to lie within +/-p from MAD model
then for each BPM fit f vs. Nb to a straight line
APC
→ apply previous
equations to obtain
DK/DNb from Df/DNb
optics phase error
at 0 current (?)
effect of impedance

6. determine impedance sources at positions of 237 quadrupoles
quads # 11, 24, 88, 102, 139, 164
(QD111, QDA119, QD307, QD319,
QF420 and QD507) w. large impedance
quads # 24, 80, 136, 140, 157, 164, 236
(QDA119, QD301, QDA417, QD421,
QD501, QD507, and QD635)
with large impedance
SVD minimization recipe:
singular-value cut-off = 5
initial weight l = 1 for all quadrupoles; increased by factors of 10 for DK values of the wrong sign in 10 iterations, to make impedance defocusing
APC

7. fair agreement “perfect” agreement APC 26.05.2005
current-dependent phase change predicted by biased SVD fit compared with the measurements
fair agreement
“perfect” agreement
APC
based on impedance distribution from previous slide

8. Robustness checks APC 26.05.2005 (1) selection of quadrupoles
could impedance located near QD301 in reality be due
to rf cavities (at quadrupoles )? [G. Arduini]
re-processed only 14 GeV/c data which have higher quality
successively eliminated quadrupoles in the 300s region with
large fitted impedance from subsequent fits until rf cavity
location is found
QD301
QF300
QD305, QD309
QE302, QF308, QD313
QD317
QF304, QECD306, QF316,
QD317, QD319
APC

9. APC 26.05.2005 fit quality only slightly degrades as more
and more quadrupoles are added
APC

10. APC 26.05.2005 fit with all quadrupoles fit without 9 quadrupoles
in the 3rd arc
APC

11. APC 26.05.2005 difference between the two fits is much smaller than
results from full fit & from fit w/o 9 quads compared with data
difference between the two fits is much smaller than
the remaining discrepancy to the measurement
APC

12. APC 26.05.2005 (2) dependence on quadrupole weight
effect on fit quality of varying initial quadrupole weight
APC

13. APC 26.05.2005 impedances fitted for different initial values of l

14. fits for different initial l values and the measurement
APC

15. two outstanding actions
(APC 26/05/2005, reminder GA ):
the available information on the transverse impedance from rf cavities (or others?) should be included in the model
explore possibility that the impedance source in Sextant 5 is compatible with a localized source in 517 (instrumentation - IPM in particular)

16. (1) include rf ‘broadband’ impedance?

17. rf impedance - knowledge
meeting with Elena Shaposhnikova on , providing two papers:
T. Bohl/U. Wehrle, ‘RF Installations in the SPS’ updated
T.P.R. Linnecar, E.N. Shaposhnikova, ‘Resonant Impedances in the SPS,’ SL-Note RF
TW 200 MHz, fr=938.5 MHz (V), R/Q=16.4 W, Q=1500, Ztotal=2.49 MW/m, 4 cavities, at locations m, m, m, m
TW 800 MHz, fr=1146 MHz, R/Q=335 W, Q=1000, Ztotal=4.0 MW/m, 2 cavities at locations m, m

18. Form of the transverse resonator impedance:
RF Group seems to use
following formula for
the transverse
broadband impedance:
where Rs is in
units of W
[also Oliver Bruning, LHC-PN-36]
Alex Chao’s
textbook
[also Francesco
Ruggiero, CERN-
SL-95-09; Bruno Zotter,
LEP-TH/87-34]
where Rs is in
units of W/m2
SL Note RF:
travelling wave cavity
standing wave cavity
if I use these last relations which is the functional form of the impedance?

19. tentatively I now take transverse impedance Zt from SL note,
but then I identify it with Zt in the expression derived from Alex’
textbook, and employ this latter formula for computing an
effective impedance
doing so I obtain:
Zeff ~ -i 1685 W/m for 200-MHz system
Zeff ~ -i 4040 W/m for 800-MHz system
these numbers are much smaller than total SPS transverse
system Zeff ~ -i 20 MW/m
lowest mode is not sufficient to estimate effective impedance
for a single bunch

20. summary 1: rf impedance two problems:
do not have any reasonable estimate for the broadband impedance, only data for 1 HOM
formula for transverse HOMs does not seem to comply with standard theory (Chao, Ruggiero,…)
I cannot pursue this action further until these problems are resolved

21. (2) repeat previous analysis using different weights etc
(2) repeat previous analysis using different weights etc., in particular w.r.t. impedance of sector 5

22. = normalize data differently to allow for direct comparison
with result of coherent tune shift measurement
current-dependent quadrupole strength is converted
into effective impedance: =
for 14 GeV/c
& sz=0.3 m

23. potential impedance locations:
MKQ:
MKD:
MKP:
MKE:
RF:
IPM: 4169?
instrumentation: 517 …

24. all quadrupoles initial weight=1, SVD cutoff=5, l=10
fit quality: ((Df/DN)fit-(Df/DN)meas)r,s= (2p/1011)
rms impedance strength: 4.86x10-5 [m-1/1011]
total impedance S b/<b> Im (Z) = 30.9 MW/m
QDA MW/m
QD MW/m
QD MW/m
QD MW/m
QD MW/m
QDA MW/m
QD MW/m
QD MW/m
QD MW/m
QD MW/m …

25. fit with all quadrupoles

26. ImZeff [W/m] fit with all quadrupoles
impedance weighted with b function
QDA119
MKP?
QD635,??
QD301,
RF??
QD421,
MKE?
QD507, ??
QD105
QDA417,
MKE?
QD501, ??
QD115, MKQ?
QD525,
diagnostics
QD133, ??

27. without 11 quadrupoles (w/o QD301, QF300, QD305, QD309, QE302, QF308, QD313, QF304, QECD306, QD501, QD507), initial weight=1, SVD cutoff=5, l=10
fit quality: ((Df/DN)fit-(Df/DN)meas)r,s= (2p/1011)
rms impedance strength: 4.63x10-5 [m-1/1011]
total impedance S b/<b> Im (Z) = 29.5 MW/m
QDA MW/m
QD MW/m
QD MW/m
QD MW/m
QDA MW/m
QD MW/m
QD MW/m …

28. fit without 11 quadrupoles: QD301, QF300, QD305, QD309, QE302,
QF308, QD313, QF304, QECD306, QD501, QD507

29. ImZeff
[W/m]
fit without 11 quadrupoles: QD301, QF300, QD305, QD309, QE302,
QF308, QD313, QF304, QECD306, QD501, QD507
QDA119
MKP?
QD317, RF?
QD421, MKE?
QD103
QDA417, MKE?
QD115, MKQ?
QD525,
diagnostics

30. another fitting attempt
consider all ‘H/V kicker’ and ‘rf cavity’
elements as potential impedance sources
instead of the quadrupoles; there are 308
such elements in the SPS MAD model

31. with kickers and rf cavities initial weight=1, SVD cutoff=5, l=10
fit quality: ((Df/DN)fit-(Df/DN)meas)r,s= (2p/1011)
rms impedance strength: 3.95x10-5 [m-1/1011]
total impedance S b/<b> Im (Z) = 29.4 MW/m
MDV MW/m
MDV MW/m
MDV MW/m
MDVA MW/m
MKP MW/m
MDV MW/m

32. fit with all kickers and rf cavities (no quadrupoles)

33. ImZeff [W/m] fit with all kickers and rf cavities (no quadrupoles)
MDV509
MDV103
MDV301
MDVA119
MKP119
MDV423

34. summary 2: new fitting studies
large impedances are consistently found
at the following five locations (both when
fitting to quadrupoles and to kickers/rf):
119 (MKP?)
301 (→317(RF?) w 9 quads suppressed)
(MKE?)
(disappears if quads 501&507
are removed from the fit)
accurate optics model is essential!