Coupling analysis
Analysis is based on the high statistics measurements in the last night
of the first MD :
• For each plane, kicks of +- 40 mrad were applied to 2 correctors 90˚ out of
phase in the first part of TI8 (~ 1 hour at each setting).
• The analysis is based on autosave data from steering program.
• Each data sample is averaged and then re-converted into new steering
program file using UNIX shell and gawk scripts.
• The difference orbits are analysed with the steering program to get a first idea
of the possible source of coupling (if any).
• The data is then converted to LOCO input and fitted with LOCO in a version
that handles the coupled response.
02.12.2004
TI8 analysis / J. Wenninger
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Coupling – steering test / V1
Coupling from 80 mrad kick @ MCIAV.813
Correction with a single kick in H plane … MICADO picks QIF.824 : 1.4 mrad
Before
Difference
After
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TI8 analysis / J. Wenninger
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Coupling – steering test / V2
Coupling from 80 mrad kick @ MCIAV.815
Correction with a single kick in H plane … MICADO picks again QIF.824 : 1.4 mrad
Before
Difference
After
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TI8 analysis / J. Wenninger
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Coupling – steering test / H1
Coupling from 80 mrad kick @ MCIAH.816
Correction with a single kick in V plane … MICADO picks now QID.821 : -1.1 mrad
Before
Difference
After
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TI8 analysis / J. Wenninger
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Coupling – steering test / H2
Coupling from 80 mrad kick @ MCIAH.818
Correction with a single kick in V plane … MICADO picks again QIF.824 : -3.3 mrad
Before
Difference
After
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‘Graphical’ analysis : V  H
Have a look at the trajectories associated to the V correctors…
A kick at 821 should appear for one corrector
– does not fit with simple analysis of the
trajectories…
From a naïve point of view the result from
the steering prgram analysis can be
explained : same kick because the trajectory
phase & amplitude is the same !
813 814 815 816 817 818 819 820 821 822 823 824 825 826
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TI8 analysis / J. Wenninger
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Graphical analysis : H  V
Have a look at the trajectories associated to the H correctors…
A kick at 821 should appear for both
correctors – does not fit with simple analysis
of the trajectories…
Also it does not fit with the V  H !
From 824 there can only be a kick for corr.
818 – trajectory goes through 0 for 816.
This is consistent with the steering program
results…
813 814 815 816 817 818 819 820 821 822 823 824 825 826
 the situation may be more complex : more than 1 or 2 sources !
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TI8 analysis / J. Wenninger
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Coupling fit
The fit is done with the LOCO – full analysis of the response including
cross-plane response. The fit includes BPM and corrector gains.
• To handle the coupling, short (1 cm) skew quads are installed in the MADX
sequence file in front of suspicious quadrupoles.
• A full fit is performed, including skews. Very small skews are removed and the
fit is iterated…
• The skew strength Ks is converted into a quadrupole tilt f using :
f
1 K s Ls 1 a2

2 K n Ln 2 b2
• The fit is redone with the tilts and skew strengths until the Ks  0. Two
iterations are sufficient.
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TI8 analysis / J. Wenninger
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Fit results
Coupling :
• QIF.824 is ‘outstanding’ with a tilt of 5 mrad
corresponding to a2/b2 = 0.01.
• The values for the tilts can be plugged
directly into the TI8 sequence.
• Coupling is at the level of 2% (defined as
amplitude ratio).
Other fit results :
• The spread of the BPM calibrations is 1.5%.
This better than before – better statistics…
• The average BPM gain is consisted with
previous fits :
G = 0.898
G = 0.880
Quadrupole
f (mrad)
QID.819
1.2
QIF.822
2.6
QIF.824
5.0
QID.855
-1.2
QID.859
-1.2
H plane
V plane
• The residual fit-measurement is ~ 250 mm for the in-plane data. This is a factor ~
10 higher than the statistical error on the data of ~ 30 mm :
• Local errors ?
• BPM effects ? non-linearities…
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TI8 analysis / J. Wenninger
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Fit results - plots
Fit residual are slightly larger than errors (~ 30 mm)
HV 816
HV 818
VH 813
VH 815
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TI8 analysis / J. Wenninger
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Stability analysis / 1
The BPMs are high correlated in a line/ring, and one can profit from this property
through a Singular Value Decomposition (SVD) of the BPM data. This
decomposition is a powerful way of extracting modes out of the data.
The BPM data is put in the form of a matrix B. The reading of BPM i for
measurement j represented by bij . Each trajectory corresponds to a line of B :
b1N 


bNM 
time
 b11

B
 b1M

N = no. of BPMs
M = no. measurements
assume M > N !
space
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Stability analysis / 2
The matrix B is decomposed by SVD into :
 w1 0

0
T
B  UWV  U 


0
0 

 VT
0 

0 wN 
where :
• U is a matrix of normalized and orthogonal time patterns.
• V is a matrix of normalized and orthogonal space patterns.
• W is a diagonal matrix with the eigenvalues of the space patterns.
Each ‘mode’ / spacial pattern has an associated weight / eigenvalue that
characterizes its amplitude and an associated time pattern.
This method is often referred to as MIA (Model Independent Analysis).
It is an interesting and (sometimes) powerfull way to extract characteristic
‘behaviours’ from the data.
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TI8 analysis / J. Wenninger
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Stability data
The analysis is based on the stability measurement from the first night
(SatSun) of the first MD (pilots).
• For each plane, the trajectories are combined into a file suitable to be read in by
the SPS multi-turn acquisition program where the MIA method is implemented.
• SVD is applied and the eigenvectors are scanned for ‘meaningful’ information.
• Except for the ‘static’ trajectory (one mode), there is nothing of interest (just noise
and BPM junk) except for one mode in the horizontal plane.
• The ‘meager’ outcome is probably due to the fact that the noise of 200-300 mm
and bad BPM readings tend to dominate.
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TI8 analysis / J. Wenninger
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Eigenvalues
When the analysis is applied to TI8 data (H and V) there is only one interesting signal :
the 5th horizontal eigenvalue shows a clean betatron oscillation starting at the beginning
of the line…
time structure
spacial structure (BPMs)
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TI8 analysis / J. Wenninger
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MSE candidate
The spacial vector is fed back into steering program for analysis :
• Search for most efficient corrector with MICADO.
• MICADO picks MSE (or MDMH.4001 that is ~ at the same phase) as possible
source of the perturbation !
Before corr.
Difference
After corr.
with MSE
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Cross-check
Pick 2 extreme trajectories (large MSE contribution according to MIA) :
• Compute trajectory difference to get largest possible signal.
• Search for most efficient corrector with MICADO.
• MICADO picks MSE – OK !
H traj difference
Before corr.
Difference
After corr.
RMS is ~ consistent with noise…
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TI8 analysis / J. Wenninger
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MSE contribution to (in)stability
• Largest kicks : ± 4.5 mrad

± 3.8×10-4 relative error.
1.4 mrad

± 1.2×10-4 relative error.
• RMS kick :
• The oscillation amplitude corresonding to the RMS kick is ~ 100 mm
which corresponds to ~ s/8 for a nominal emittance.
• The expected RMS stability at the location of the TCS (Dm = 158˚) is ~ 40 mm.
• BUT : I cannot see a correlation with the logged MSE currents !! ??
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Long term average
Trajectory difference (average) after 5 hours :
• RMS ~ 50 mm – practicaly consistent with the noise.
• No significant coherent oscillation visible.
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Further work…
One could search for coherent oscillations by fitting betatron oscillations to the
BPM data :
xˆi 
xi
i
  fit to : f ( mi )  A sin( mi )  B cos( mi )
A fit to the entire line should find the signal observed with MIA and find/set a
limit of the signal that is 90˚ out of phase  sensitive to ‘incoming’ signals.
A fit to the end of the line (last 4-5 BPMs ?) may give and indication on
contributions coming from the line itself (+ incoming).
Could resurect / adapt my LEP fit program…
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TI8 analysis / J. Wenninger
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