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


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


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


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



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


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


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.


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


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.


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



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.




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=


△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



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


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


-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


The wrong polarity of corrector R3IBV02 and R4IBV02 revealed according to the kicks derived from LOCO



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


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


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

30

40

50

60

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


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


-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)


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


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


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


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


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)


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


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.


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


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


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


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)


Orbit shift before (upper) and after (bottom) SOFB system applied (Jun.07, 100~180mA)


Orbit shift at 3B1 before (upper) and after (bottom) SOFB system applied( Jun. 07, 100~180mA)


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


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


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.


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


Thanks for your attention!

Documents

Optics analysis of BEPCII using orbit response matrix