Optics analysis of BEPCII using orbit response matrix
Transcript of Optics analysis of BEPCII using orbit response matrix
Institute of High Energy Physics Chinese Academy of Science
Optics analysis of BEPCII using Optics analysis of BEPCII using orbit response matrixorbit response matrix
Y.Y.Wei, Q.Qin, G. Xu, W.B. Liu, D.M. Zhou, Y. Chen
IHEP, Beijing 100049, P.R. China
Institute of High Energy Physics Chinese Academy of Science
OutlineOutline
BEPCII latticeBER and BPR
CommissioningOptics analysisOptics correctionProblemStudies on parasitic synchrotron radiation mode
BSR Optics analysisUnderstanding the fudge factorSlow orbit feedbackApplication of response matrix
Summary
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Limited space, for both collision and SR useThe geometric and optics design are relatively complex.
In the IR,The superconducting quadrupole SCQs not only squeeze the vertical beta but also bend the beam further.
4 warm bore quadrupoles connecting the arc and IPDual aperture quadrupoles Q1A and Q1B
In the arcs,6 quasi-FODO cells with the 5th and11th dipoles missingNo special region for dispersion suppressionNarrow space between quadrupoles and sextupoles
Lattice of collision modeLattice of collision mode
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3 kinds of lattice used at the beginning of commissioningβx*/βy* = 2m/5cm (inj. )βx*/βy* = 2m/3cm (inj. )βx*/βy* = 1m/1.5cm (inj. & col.)
Features of 3 latticesDifferent beta functions @ IPSimilar Twiss function distributionsSame tunes, νx/νy = 6.54/5.58Same sextupole families (4 families)
Optics of collision modeOptics of collision mode
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Circumference(m) 237.53Beam energy(GeV) 1.89RF voltage(MV) 1.5Tune(x/y/s) 6.54/5.59/0.035Momentum compaction factor 0.0237Nature chromaticity(x/y) -10.8/-20.8Nature horizontal emittance(nm⋅rad) 132Nature energy spread 5.16×10-4
Nature bunch length(cm) 1.36βx,y @ IP(m)(x/y) 1/0.015βx,y, max @ IR(m)(x/y) 70.2/91.4βx,y, max @ arc(m)(x/y) 24.2/23.5Dx,max(m) 2.28
Main parameters of the BEPCII storage rings in collision
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Lattice at the beginning: βx
* /βy*= 2m/5cm
Fitting νx/νy=6.58/5.59Quadrupole fudge factors of the last run appliedMeasured tunes: νx /νy=6.546/5.6189The beam accumulated smoothly
Optimize the lattice step by step:βx*/βy* = 2m/3cm, νx/νy=6.58/5.59
Optic correction based on the lattice:βx*/βy* = 1m/1.5cm, nominal tunes:νx/νy=6.58/5.59
BER commissioningBER commissioning
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BER orbit correctionBER orbit correction
Determine all the BPM offsets by BBA system.Correct the orbit to the center of quadrupoles based on measured response matrix.After correction, the average orbit is 0.11/-0.064 mm, and rms orbit is 1.087/0.744 mm.
Institute of High Energy Physics Chinese Academy of Science
Optics analysis using orbit response matrixOptics analysis using orbit response matrix
Using LOCO (Linear Optics from Closed Orbits) to adjust the parameters of a computer model until the model response matrix best fits the measured response matrix.
Determining the errors by,
ΔK q — error of quadrupole strengthΔGi — error of BPM gainΔθj — error of corrector strengthΔδj — energy shift when horizontal corrector strength change
∑ ∑≡−
=ji ji
iji
ijmeasij VMM
, ,
22
2,mod,2 )(
σχ
∑ ∑ ∑∑ +Δ∂
∂+Δ
∂
∂+Δ
∂
∂+Δ
∂
∂=Δ ......j
j
ijj
j
iji
i
ijq
q
ijij
VVG
GV
KKV
V δδ
θθ
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BER optics analysisBER optics analysis
Measure response matrix with sextupoles turning on
The parameters varied in fitting :
BPM gains
corrector kicks
Strengths of quadrupoles, except forSCQs are not included.
Q1A and Q1B, Q2 and Q3 are adjacent with same polarity.Their strength errors are shown very large and fight eachother if varied dependently. Only Q1B and Q2 in the couplesare fitted.
Strengths of R4OQ1B and R3IQ1B can only be adjusted independently in a small region , so they are served as one parameter.
Institute of High Energy Physics Chinese Academy of Science
2 14 26 38 51 2 14 26 38 51
18
1522
292
916
2330
-3
-2
-1
0
1
2
3
HBPM# and VBPM#
Measured Response Matrix
HCM# and VCM#
[mm
]
2 14 26 38 51 2 14 26 38 51
18
1522
292
916
2330
-0.04
-0.02
0
0.02
0.04
HBPM# and VBPM#
Model - Measured Response Matrix
HCM# and VCM#
Err
or [
mm
]
Measured response matrix Difference between the measured response matrix and the model after
fitting with LOCO
BER optics analysisBER optics analysis
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Distribution of residual differences between measured and fitted response matrix, normalized to the noise level of the respective BPMs
Width of the distribution ~1
The fitting in LOCO converged to the noise level of BPMs.
BER optics analysisBER optics analysis
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BER optics analysisBER optics analysis
The change of quadrupole strengths to restore the optics is described by using the amplitude fudge factor.
K0 : design strength K : optimized strength
60% fudge factor errors are within 1%
R1OQ16: △AF ~ 15%
On Dec.25, 2007, the shortcut between R1OQ16 magnet poles was confirmed.
Response matrix was measured and fitted again.
AFKK *0=
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△AF of R1OQ16 : 15% -> 1%Measured tunes after correction: (6.5474,5.6377)
nominal tunes: (6.5434, 5.6396 )
-0. 15
-0. 1
-0. 05
0
0. 05
0. 1
0. 15
R3IQ
1B
R3IQ
05R3
IQ07
R3IQ
09R3
IQ11
R3IQ
13R3
IQ15
R3IQ
17R2
IQ16
R2IQ
14R2
IQ12
R2IQ
10R2
IQ08
R2IQ
06R2
IQ04
R2IQ
02
R1OQ
02R1
OQ04
R1OQ
06R1
OQ08
R1OQ
10R1
OQ12
R1OQ
14R1
OQ16
R4OQ
17R4
OQ15
R4OQ
13R4
OQ11
R4OQ
09R4
OQ07
R4OQ
05
AF-1bef ore R1OQ16 probl em resol ved
af t er R1OQ16 probl em resol ved
BER optics analysisBER optics analysis
Institute of High Energy Physics Chinese Academy of Science
0
10
20
30
40
50
60
70
R4OQ
1AR4
OQ02
R4OQ
04R4
OQ06
R4OQ
08R4
OQ10
R4OQ
12R4
OQ14
R4OQ
16R1
OQ17
R1OQ
15R1
OQ13
R1OQ
11R1
OQ09
R1OQ
07R1
OQ05
R1OQ
03R2
IQ01
R2IQ
03R2
IQ05
R2IQ
07R2
IQ09
R2IQ
11R2
IQ13
R2IQ
15R2
IQ17
R3IQ
16R3
IQ14
R3IQ
12R3
IQ10
R3IQ
08R3
IQ06
R3IQ
04R3
IQ02
R3IQ
1A
BetaY_measured
BetaY_desi gn
01020304050607080
R4OQ
1AR4
OQ02
R4OQ
04R4
OQ06
R4OQ
08R4
OQ10
R4OQ
12R4
OQ14
R4OQ
16R1
OQ17
R1OQ
15R1
OQ13
R1OQ
11R1
OQ09
R1OQ
07R1
OQ05
R1OQ
03R2
IQ01
R2IQ
03R2
IQ05
R2IQ
07R2
IQ09
R2IQ
11R2
IQ13
R2IQ
15R2
IQ17
R3IQ
16R3
IQ14
R3IQ
12R3
IQ10
R3IQ
08R3
IQ06
R3IQ
04R3
IQ02
R3IQ
1A
BetaX_measuredBetaX_desi gn
The comparison of measured and design Beta function before optics correction
Institute of High Energy Physics Chinese Academy of Science
01020304050607080
R4OQ
1A
R4OQ
03
R4OQ
06
R4OQ
09
R4OQ
12
R4OQ
15
R1OQ
17
R1OQ
14
R1OQ
11
R1OQ
08
R1OQ
05
R1OQ
02
R2IQ
03
R2IQ
06
R2IQ
09
R2IQ
12
R2IQ
15
R3IQ
17
R3IQ
14
R3IQ
11
R3IQ
08
R3IQ
05
R3IQ
02
m
Bet aX_measured
Bet aX_desi gn
0
10
20
30
40
50
60
70
R4OQ
1A
R4OQ
03
R4OQ
06
R4OQ
09
R4OQ
12
R4OQ
15
R1OQ
17
R1OQ
14
R1OQ
11
R1OQ
08
R1OQ
05
R1OQ
02
R2IQ
03
R2IQ
06
R2IQ
09
R2IQ
12
R2IQ
15
R3IQ
17
R3IQ
14
R3IQ
11
R3IQ
08
R3IQ
05
R3IQ
02
m
Bet aY_measured
Bet aY_desi gn
The comparison of measured and design Beta function after optics correction
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-0. 6
-0. 4
-0. 2
01
0. 2
0. 4
0. 6
4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67
del ta_betaXdel ta_betaY
The relative errors of Beta function after correction
BER optics correctionBER optics correction
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The wrong polarity of corrector R3IBV02 and R4IBV02 revealed according to the kicks derived from LOCO
BER optics analysisBER optics analysis
Institute of High Energy Physics Chinese Academy of Science
Lattice at the beginning: βx
* /βy*= 2m/5cm
Fitting νx/νy=6.58/5.59Quadrupole fudge factors of last run appliedMeasured tunes: νx /νy=6.542/5.628The beam accumulated successfully
Optimize the lattice step by step:βx*/βy* = 2m/3cm, νx/νy=6.58/5.59
Optic correction based on the lattice:βx*/βy* = 1m/1.5cm, nominal tunes:νx/νy=6.62/5.55measured tunes:νx/νy=6.58/5.65
BPR commissioningBPR commissioning
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BPR orbit correctionBPR orbit correction
Determine all the BPM offsets by BBA system.Correct the orbit to the center of quadrupoles based on measured response matrix.After correction, the average orbit is 0.188/−0.065 mm
Institute of High Energy Physics Chinese Academy of Science
0
10
20
30
40
50
60
70
80
R3OQ
1A
R3OQ
1B
R3OQ
02
R3OQ
03
R3OQ
04
R3OQ
05
R3OQ
06
R3OQ
07
R3OQ
08
R3OQ
09
R3OQ
10
R3OQ
11
R3OQ
12
R3OQ
13
R3OQ
14
R3OQ
15
R3OQ
16
R3OQ
17
R2OQ
17
R2OQ
16
R2OQ
15
R2OQ
14
R2OQ
13
R2OQ
12
R2OQ
11
R2OQ
09
R2OQ
08
R2OQ
07
R2OQ
06
R2OQ
05
R2OQ
04
R2OQ
03
R2OQ
02
m
BetaX_measured
BetaX_desi gn
0
10
20
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70
R3OQ
1A
R3OQ
1B
R3OQ
02
R3OQ
03
R3OQ
04
R3OQ
05
R3OQ
06
R3OQ
07
R3OQ
08
R3OQ
09
R3OQ
10
R3OQ
11
R3OQ
12
R3OQ
13
R3OQ
14
R3OQ
15
R3OQ
16
R3OQ
17
R2OQ
17
R2OQ
16
R2OQ
15
R2OQ
14
R2OQ
13
R2OQ
12
R2OQ
11
R2OQ
09
R2OQ
08
R2OQ
07
R2OQ
06
R2OQ
05
R2OQ
04
R2OQ
03
R2OQ
02
m
BetaY_Measured
BetaY_desi gn
Comparison of measured and design beta function before optics correction
Institute of High Energy Physics Chinese Academy of Science
0
10
20
30
40
50
60
70
80
R34I
Q1A
R4IQ
02R4
IQ04
R4IQ
06R4
IQ08
R4IQ
10R4
IQ12
R4IQ
14R4
IQ16
R1IQ
17R1
IQ15
R1IQ
13R1
IQ11
R1IQ
09R1
IQ07
R1IQ
05R1
IQ03
R1IQ
01R2
OQ03
R2OQ
05R2
OQ07
R2OQ
09R2
OQ11
R2OQ
13R2
OQ15
R2OQ
17R3
OQ16
R3OQ
14R3
OQ12
R3OQ
10R3
OQ08
R3OQ
06R3
OQ04
R3OQ
02
mBetaX_measuredBetaX_desi gnDi f f . Rat i o
0
10
20
30
40
50
60
70
80
90
R34I
Q1A
R4IQ
02R4
IQ04
R4IQ
06R4
IQ08
R4IQ
10R4
IQ12
R4IQ
14R4
IQ16
R1IQ
17R1
IQ15
R1IQ
13R1
IQ11
R1IQ
09R1
IQ07
R1IQ
05R1
IQ03
R1IQ
01R2
OQ03
R2OQ
05R2
OQ07
R2OQ
09R2
OQ11
R2OQ
13R2
OQ15
R2OQ
17R3
OQ16
R3OQ
14R3
OQ12
R3OQ
10R3
OQ08
R3OQ
06R3
OQ04
R3OQ
02
m
Bet aY_measuredBet aY_desi gnDi f f . Rat i o
Comparison of measured and design beta function after optics correction
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-0. 50
0. 00
0. 50
1. 00
1. 50
2. 00
2. 50
3. 00
1 6 21 29 41 49 68 78 87 96 107 122 135 144 154 163 181 194 203 213 225 234 237
m
m
di spy_measureddi spx_desi gndi spx_measured
-0. 50
-0. 30
-0. 10
0. 10
0. 30
0. 50
1 6 21 29 41 49 68 78 87 96 107 122 135 144 154 163 181 194 203 213 225 234 237
m
m
di spx_measured - di spx_desi gn
di spy_measured - di spy_desi gn
Comparison of measured and design dispersion(several data from bad BPM removed)
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Q2s’ △AF >10% for both BPR and BERQ2s have the same polarity as SCQsIs Q2s’ AF compensate the SCQs’ gradient errors ?Decrease the strength of SCQs’ by 0.2% measured the response matrix and fitted at BPR Q2s’ △AF ~7%For SR mode (shown later) no SCQsQ2s’ △AF <1%Simulations at BPR and BER :
Increase the SCQs’ strengths by 1% in model lattice to assume the SCQs’ strengths of real machine higher by 1%Q2s’ △AF <1% for BPR and BER
Problem on Q2 fudge factors Problem on Q2 fudge factors
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BER AF errors
-0. 15
-0. 1
-0. 05
0
0. 05
R3IQ
1AR3
IQ02
R3IQ
04R3
IQ06
R3IQ
08R3
IQ10
R3IQ
12R3
IQ14
R3IQ
16R2
IQ17
R2IQ
15R2
IQ13
R2IQ
11R2
IQ09
R2IQ
07R2
IQ05
R2IQ
03R2
IQ01
R1OQ
03R1
OQ05
R1OQ
07R1
OQ09
R1OQ
11R1
OQ13
R1OQ
15R1
OQ17
R4OQ
16R4
OQ14
R4OQ
12R4
OQ10
R4OQ
08R4
OQ06
R4OQ
04
AF-1
SCQ: AF=1
SCQ: AF=1. 01
BPR AF errors
-0. 15
-0. 1
-0. 05
0
0. 05
0. 1
R4IQ
1B
R4IQ
04
R4IQ
07
R4IQ
10
R4IQ
13
R4IQ
16
R1IQ
16
R1IQ
13
R1IQ
10
R1IQ
07
R1IQ
04
R1IQ
01
R2OQ
04
R2OQ
07
R2OQ
10
R2OQ
13
R2OQ
16
R3OQ
16
R3OQ
13
R3OQ
10
R3OQ
07
R3OQ
04
R3OQ
1B
AF-1
SCQ: AF=1
SCQ: AF=1. 01
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Coupling
Coupling measurement:Δνmin2/(Δνmin
2+2Δν2)
Coupling adjustment by changing the bump height at R2IS5 of BER,R1IS5 of BPR, the results of BER listed as follow:
It is planned to fit the coupling at sextupoles with response matrix.
Bump height (mm) Coupling (%)
0 0.477
-4 5.44
-2 2.15
-1.5 1.53
-1 1.08
-0.5 0.723
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Optics correction of parasitical SR mode
Meet the requirements of HEP and SR simultaneously
Optics correction to compensate the optics distortion caused by wiggler Close the 1W2, measured response matrix of BER
Fitted global quadrupole strengths
After correction, the luminosity shown by zero degree luminosity detector: 1W2 closed,6.93mA*7.85mA, Spec.L = 564 (number of photon/mA2) 1W2 open, 6.87mA*7.79mA, Spec.L = 540 (number of photon/mA2)
More studies are under way
1W2 closed 1W2 open
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BSR orbit correctionBSR orbit correction
Correct the orbit in the injection mode without wigglers and the one with wigglers After correction the rms orbit is about 1/0.6 mm.
BSR orbit before (red) and after (blue) correction, @2.3GeV, wigglers on (except wiggler 4W2)
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BSR optics analysisBSR optics analysis
BSR consists of two outer half-rings of the BPR and BER. Superconducting dipole coils beside the IP and the QSR at the north crossing point are used.SCQ , Q1B,Q03 are off.
5 wigglers are installed, the tune shifts induced by wigglers are:
Measured the response matrix with sextupoles and all wigglers.
Fitted quadruple strengths, BPM gains and corrector kicks in LOCO.
The changes of quadrupole strength compensate the optics distortion caused by:
Quadrupole strength errors
Wigglers used for synchrotron radiation operation
Sextupoles and other components
1W1 1W2 3W1 4W1 4W2Δνy 0.016 0.0125 0.0116 0.0289 0.0125
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BSR optics analysisBSR optics analysis
BSR AF errors
-0. 2
-0. 15
-0. 1
-0. 05
0
0. 05
0. 1
QSR
R3OQ
02
R3OQ
05
R3OQ
07
R3OQ
09
R3OQ
11
R3OQ
13
R3OQ
15
R3OQ
17
R2OQ
16
R2OQ
14
R2OQ
12
R2OQ
10
R2OQ
08
R2OQ
06
R2OQ
04
R2OQ
02
R1OQ
03
R1OQ
05
R1OQ
07
R1OQ
09
R1OQ
11
R1OQ
13
R1OQ
15
R1OQ
17
R4OQ
16
R4OQ
14
R4OQ
12
R4OQ
10
R4OQ
08
R4OQ
06
R4OQ
04
R4OQ
02
AF-1
The quadrupole strengths where wigglers located change intensively.
The discrepancy between measured and design beta function are also large in the wiggler regions.
Institute of High Energy Physics Chinese Academy of Science
Comparison of measured and design beta functions after optics correction ( with all wigglers)
0
5
10
15
20
25
R34Q
1AR4
OQ04
R4OQ
06R4
OQ08
R4OQ
10R4
OQ12
R4OQ
14R4
OQ16
R1OQ
17R1
OQ15
R1OQ
13R1
OQ11
R1OQ
09R1
OQ07
R1OQ
05R1
OQ03
R2OQ
02R2
OQ04
R2OQ
06R2
OQ08
R2OQ
10R2
OQ12
R2OQ
14R2
OQ16
R3OQ
17R3
OQ15
R3OQ
13R3
OQ11
R3OQ
09R3
OQ07
R3OQ
05R3
OQ02
m
Bet aX_measuredBet aX_desi gn
0
5
10
15
20
25
30
35
R34Q
1A
R4OQ
04
R4OQ
06
R4OQ
08
R4OQ
10
R4OQ
12
R4OQ
14
R4OQ
16
R1OQ
17
R1OQ
15
R1OQ
13
R1OQ
11
R1OQ
09
R1OQ
07
R1OQ
05
R1OQ
03
R2OQ
02
R2OQ
04
R2OQ
06
R2OQ
08
R2OQ
10
R2OQ
12
R2OQ
14
R2OQ
16
R3OQ
17
R3OQ
15
R3OQ
13
R3OQ
11
R3OQ
09
R3OQ
07
R3OQ
05
R3OQ
02
m
BetaY_measuredBetaY_desi gn
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40% fudge factor errors are more than 1%. What is the reason?
Interaction of quadrupole and its adjacent sexupoles due to their short distance.
Fringe filed effect of dipoles and qudrupoles.
Experiment was performed at BSR, no wiggler and no optics correction, nominal tunes are (7.28,5.38)
Vertical tune restored to the design,but horizontal tune still had the discrepancy of 0.055
Other origin is still under the study.
Design lattice Increase the strength of Q5~Q13 by 0.6%
Include fringe filed effect of Q and B in model Both considered
Measured tunes νx/νy 0.1685/0.2834 0.1917/0.3174 0.2005/0.3413 0.225/0.379
Δνx/Δνy 0/0 0.023/0.034 0.0315/0.058 0.054/0.096
Understanding the fudge factorUnderstanding the fudge factor
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To improve the performance of SR mode, an SOFB system is setup based on response matrix method.
The procedure:Measure the response matrix.
Measure the current orbit once a minute, and remove some unreliable data.
Calculate the orbit drift relative to the golden orbit.
Determine the effective correctors according to the predicted results.
Derive the change of corrector strengths by SVD from:
Ramp the correctors.
Slow orbit feedback system for BSRSlow orbit feedback system for BSR
ymeasRy θΔ=Δ
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SOFB system is for global orbit, and only applied on vertical plane currently.
The vertical beam size is about 100μm (extraction point of beam line).
The stability of orbit is within ±5~±10 μm (extraction point of beam line).
Slow orbit feedback systemSlow orbit feedback system
Position Stability
1W2 ±8μm
1W1 ±8μm
4W1 ±10μm
4B9 ±10μm
4B8 ±10μm
4B7 ±10μm
4W2 ±8μm
3B1 ±5μm
3W1 ±5μm
The stability of vertical orbit after SOFB system is applied (Jun.07, I<180mA)
Institute of High Energy Physics Chinese Academy of Science
Orbit shift before (upper) and after (bottom) SOFB system applied (Jun.07, 100~180mA)
Institute of High Energy Physics Chinese Academy of Science
Orbit shift at 3B1 before (upper) and after (bottom) SOFB system applied( Jun. 07, 100~180mA)
Institute of High Energy Physics Chinese Academy of Science
Abrupt changes of orbit were observed in Jun. 07 during the backup scheme commissiong.
Analyzed based on measured response matrix.
Problem of sextupole R2OS7 was revealed.
Application of response matrix methodApplication of response matrix method
Institute of High Energy Physics Chinese Academy of Science
The change of orbit
-0. 2-0. 15-0. 1
-0. 050
0. 050. 1
0. 150. 2
0. 25
R3CB
PM00
R3OB
PM05
R3OB
PM10
R3OB
PM15
R2OB
PM13
R2OB
PM08
R2OB
PM03
R1OB
PM05
R1OB
PM10
R1OB
PM15
R4OB
PM13
R4OB
PM08
R4OB
PM03
( mm)1 2007-6-24 4: 202 2007-6-23 22: 003 2007-6-17 16: 10
-0. 01
0. 00
0. 01
0. 01
0. 02
0. 02
0. 03
0. 03
R3OBV02
R3OBV05
R3OBV09
R3OBV13
R2OBV17
R2OBV13
R2OBV09
R2OBV05
R1OBV02
R1OBV07
R1OBV11
R1OBV16
R4OBV15
R4OBV11
R4OBV07
R4OBV04
mrad
Origin of the orbit change is equivalent to the change of R2OBV07 strength
Institute of High Energy Physics Chinese Academy of Science
SummarySummary
All the BPM offsets are determined and orbit correction has beendone successfully .After correction the average orbit is less than 0.2/0.08 mm, and rms orbit is 1/0.6 mm.
Analysis of the BEPCII measured orbit response matrix determined the quadrupole strength errors、BPM gains and correctors kicks, contributed to reveal some magnet problems.
The analysis also gave the best settings for quadrupoles to restore the design optics.
After correction, the measured Beta function at most Quadrupolescan be restored within ±10% design model (some places where the design Beta function are small have the relatively large discrepancies due to the measurement accuracy). The distortion of dispersion function is decreased.
The application of response matrix method on BSR SOFB system, global orbit analysis and correction are also successful.
Institute of High Energy Physics Chinese Academy of Science
Summary Summary
Studies to do:
Measure and correct coupling based on response matrix method.
Determine the strength errors of SCQs
Fit in LOCO with the model lattice considering the fringe filed effect to decrease the fudge factors.
More accurate optics correction for SR mode.
Further studies on optics correction of parasitical mode
Institute of High Energy Physics Chinese Academy of Science
Thanks for your attention!