ANALYSIS OF BEPCII OPTICS AND CORRECTION

Yuanyuan Wei

2007.05.10

OutlineOutline

For BSR 、 BPR 、 BER respectively,

Beam based alignment of BPM offsets Orbit correction Optics analysis to determine quadruple strength errors, BP

M gains and couplings, corrector kicks Optics measurement after correction Conclusion and problems

Use the method of beam based alignment to determine all the BPM- to-quadrupole offsets

Horizontal offset of R3IBPM03 is 0.16m Vertical offset of R2IBPM11 is -0.41m

BSR BPM offsetsBSR BPM offsets

用响应矩阵方法进行轨道校正

BSR (2.5GeV with all wigglers on) orbit correction before (yellow) and after (blue) BPM offsets are applied

Optics analysis and correction using orbit response matrixOptics analysis and correction 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 strength ΔGi — error of BPM gain Δθj — error of corrector strength Δδj — energy shift when horizontal corrector strength change

ji ji

iji

ijmeasij VMM

, ,

22

2,mod,2

)(

......j

j

ijj

j

iji

i

ijq

q

ijij

VVG

G

VK

K

VV

BSR optics analysis and correctionBSR optics analysis and correction

Measure the response matrix with sextupoles off and determine the quadrupole strength errors using LOCO.

The change of quadrupole strengths to restore the optics is described by using the amplitude fudge factor.

Q3 and Q2, Q15 and Q16 , two Q17 are adjacent with same polarity. Furthermore, there is no BPM between Q15 and Q16, two Q17. Their strength errors are shown very large and fight each other. It seems that LOCO can not fit their errors accurately in this case.

- 0. 08

0

0. 08

0. 16

R3OQ1A

R3OQ02

R3OQ04

R3OQ06

R3OQ08

R3OQ10

R3OQ12

R3OQ14

R3OQ16

R2OQ17

R2OQ15

R2OQ13

R2OQ11

R2OQ09

R2OQ07

R2OQ05

R2OQ03

R1OQ02

R1OQ04

R1OQ06

R1OQ08

R1OQ10

R1OQ12

R1OQ14

R1OQ16

R4OQ17

R4OQ15

R4OQ13

R4OQ11

R4OQ09

R4OQ07

R4OQ05

R4OQ03

AF- 1

AFKK 11 1 AFAF

0

5

10

15

20

25

30

35

R3OQ1A

R3OQ04

R3OQ06

R3OQ08

R3OQ10

R3OQ12

R3OQ14

R3OQ16

R2OQ17

R2OQ15

R2OQ13

R2OQ11

R2OQ09

R2OQ07

R2OQ05

R2OQ03

BetaX (m)

Measured LOCO modelDesi gn model

0

5

10

15

20

25

30

R3OQ1A

R3OQ04

R3OQ06

R3OQ08

R3OQ10

R3OQ12

R3OQ14

R3OQ16

R2OQ17

R2OQ15

R2OQ13

R2OQ11

R2OQ09

R2OQ07

R2OQ05

R2OQ03

BetaY (m)

Measured

LOCO model

Desi gn model

The fit model predicts the measured horizontal and vertical Beta function. The Beta function is measured when sextupoles on.

The comparison of measured Beta function and design model after quadrupole strength errors from LOCO are corrected.

0

5

10

15

20

25

30

R3OQ1A

R3OQ04

R3OQ06

R3OQ08

R3OQ10

R3OQ12

R3OQ14

R3OQ16

R2OQ17

R2OQ15

R2OQ13

R2OQ11

R2OQ09

R2OQ07

R2OQ05

R2OQ03

BetaX (m)

Measured bef orecorrect i onMeasured af tercor rect i onDesi gn model

0

5

10

15

20

25

30

R3OQ1A

R3OQ04

R3OQ06

R3OQ08

R3OQ10

R3OQ12

R3OQ14

R3OQ16

R2OQ17

R2OQ15

R2OQ13

R2OQ11

R2OQ09

R2OQ07

R2OQ05

R2OQ03

BetaY (m)

Measured bef orecor rect i onMeasured af tercor rect i onDesi gn model

Measured dispersion of BSR before correction

Design chromaticity ζx =4.935 ζy =4.803

Measured chromaticity ζx =4.67 ζy =5.78

Design chromaticity ζx =2.961 ζy =2.88

Measured chromaticity ζx =3.42 ζy =3.83

Distribution of BPR BPM offsets

-6 -5 -4 -3 -2 -1 0 1 2 3 40

2

4

6

8

10

12

14

offsetx

Num

ber

of B

PM

Distribution of BPR BPM Horizontal OFFSET

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

14

16

18

20

offsety

Num

ber

of B

PM

Distribution of BPR BPM Vertical OFFSET

BPR optics analysis and correctionBPR optics analysis and correction

BPR orbit correction before (yellow) and after (blue) BPM offsets are applied

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 response matrix after fitting with LOCO

BPR optics analysisBPR optics analysis

Measure response matrix with sextupoles off

The parameters varied in fitting the model to the measured response matrix were:

BPM gains and couplings

Corrector magnet kicks and couplings

Strengths of all quadrupoles

-30 -20 -10 0 10 20 300

20

40

60

80

100

120

140

160

180

Error in Units of Standard Deviations

Num

ber

of P

oint

s (8

109

tota

l poi

nts)

Histogram: (Mmeas

- Mmodel

) / bpm

BPR optics analysisBPR optics analysis

Distribution of residual differences between measured and fitted orbit response matrix ,normalized to the noise level of the respective BPMs

BPR quadrupole strength errors

- 0. 08

0

0. 08

0. 16

QSR

R4IQ1B

R4IQ03

R4IQ05

R4IQ07

R4IQ09

R4IQ11

R4IQ13

R4IQ15

R4IQ17

R1IQ16

R1IQ14

R1IQ12

R1IQ10

R1IQ08

R1IQ06

R1IQ04

R1IQ02

R2OQ02

R2OQ04

R2OQ06

R2OQ08

R2OQ10

R2OQ12

R2OQ14

R2OQ16

R3OQ17

R3OQ15

R3OQ13

R3OQ11

R3OQ09

R3OQ07

R3OQ05

R3OQ03

AF- 1

Measure the response matrix with sextupoles off and determine the quadrupole strength errors using LOCO.

There are still problems on the adjacent quadrupoles which have same polarity.

BPR optics analysisBPR optics analysis

0.7 0.75 0.8 0.85 0.9 0.95 1 1.050

2

4

6

8

10

12

14

Gain

VB

PM

s

-0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.060

2

4

6

8

10

12

14

16

Coupling

HB

PM

s

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.040

2

4

6

8

10

12

14

Coupling

VB

PM

s

0.7 0.8 0.9 1 1.1 1.2 1.30

2

4

6

8

10

12

14

16

18

Gain

HB

PM

s

BPR BPM gains and couplings fitted with LOCO

BPR optics analysisBPR optics analysis

BPR correctors kicks fitted with LOCO

5 10 15 20 25 30

-0.26

-0.25

-0.24

-0.23

-0.22

-0.21

-0.2

-0.19

Corrector Magnet Parameter Fits (34)

Hor

izon

tal K

ick

[mra

d]

Horizontal Corrector Number5 10 15 20 25 30

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

0.22

Corrector Magnet Parameter Fits (33)

Ver

tical

Kic

k [m

rad]

Vertical Corrector Number

BPR optics analysisBPR optics analysis

BPR optics correctionBPR optics correction

- 0. 08

0

0. 08

R4IQ02

R4IQ04

R4IQ06

R4IQ08

R4IQ10

R4IQ12

R4IQ14

R4IQ16

R1IQ17

R1IQ15

R1IQ13

R1IQ11

R1IQ09

R1IQ07

R1IQ05

R1IQ03

R1IQ01

R2OQ03

R2OQ05

R2OQ07

R2OQ09

R2OQ11

R2OQ13

R2OQ15

R2OQ17

R3OQ16

R3OQ14

R3OQ12

R3OQ10

R3OQ08

R3OQ06

R3OQ04

R3OQ02

AF- 1

Response matrix is measured with sextupoles on.

QIR and Q1A 、 Q1B are not fitted in LOCO.

Replace the strengths of two adjacent quadrupoles which have same polarity by one parameter fitted in LOCO. As a result their strength errors are averaged .

Design tune is 6.54/5.59, measured tune when measuring response matrix is 6.544/5.648, model tune after fitted with LOCO is 6.54485/5.64849, measured tune after correction is 6.539/5.589.

Quadrupole strength changes to restore design optics

0

10

20

30

40

50

60

70

R3OQ1A

R3OQ03

R3OQ06

R3OQ09

R3OQ12

R3OQ15

R2OQ17

R2OQ14

R2OQ11

R2OQ08

R2OQ05

R2OQ02

R1IQ03

R1IQ06

R1IQ09

R1IQ12

R1IQ15

R4IQ17

R4IQ14

R4IQ11

R4IQ08

R4IQ05

R4IQ02

BetaX (m) Measured

Desi gn

0

10

20

30

40

50

60

R3OQ1A

R3OQ03

R3OQ06

R3OQ0

9

R3OQ12

R3OQ15

R2OQ17

R2OQ14

R2OQ11

R2OQ08

R2OQ05

R2OQ02

R1IQ03

R1IQ06

R1IQ09

R1IQ12

R1IQ15

R4IQ17

R4IQ14

R4IQ11

R4IQ08

R4IQ05

R4IQ02

Beta

Y (m

) Measured

Desi gn

The comparison of measured Beta function and design model after quadrupole strength changes from LOCO are applied.

The relative errors or Beta function after correction

-50

-40

-30

-20

-10

0

10

20

30

R3OQ1A

R3OQ03

R3OQ06

R3OQ09

R3OQ12

R3OQ15

R2OQ17

R2OQ14

R2OQ11

R2OQ08

R2OQ05

R2OQ02

R1IQ03

R1IQ06

R1IQ09

R1IQ12

R1IQ15

R4IQ17

R4IQ14

R4IQ11

R4IQ08

R4IQ05

R4IQ02

(BX_mea - BX_des)/ BX_des

(BY_mea - BY_des)/ BY_des

BPR optics correctionBPR optics correction

Comparison of measured dispersion before and after correction

BPR optics correctionBPR optics correction

-4 -3 -2 -1 0 1 2 3 4 50

1

2

3

4

5

6

7

8

9

10

offsetx

Num

ber

of B

PM

Distribution of BER BPM Horizontal OFFSET

-4 -3 -2 -1 0 1 2 3 40

5

10

15

20

25

offsety

Num

ber

of B

PM

Distribution of BER BPM Vertical OFFSET

BER optics analysis and correctionBER optics analysis and correction

Distribution of BER BPM offsets

BER orbit correction before (yellow) and after (blue) BPM offsets are applied

-0. 04

0

0. 04

0. 08

0. 12

0. 16

R3IQ1A

R3IQ03

R3IQ06

R3IQ09

R3IQ12

R3IQ15

R2IQ17

R2IQ14

R2IQ11

R2IQ08

R2IQ05

R2IQ02

R1OQ03

R1OQ06

R1OQ09

R1OQ12

R1OQ15

R4OQ17

R4OQ14

R4OQ11

R4OQ08

R4OQ05

R4OQ02

AF- 1

Response matrix is measured with sextupoles on

QIR and Q1A 、 Q1B are not fitted in LOCO

Replace the strengths of two adjacent quadrupoles that are the same polarity by one parameter fitted in LOCO (except for R1OQ15 and R1Q16).

Design tune is 6.54/5.59, measured tune when measuring response matrix is 6.57/5.61, model tune after fitted with LOCO is 6.5706/5.6085, measured tune after correction is 6.5380/5.5903

BER optics correctionBER optics correction

Quadrupole strength changes to restore design optics

0

10

20

30

40

50

60

R3IQ1A

R3IQ02

R3IQ04

R3IQ06

R3IQ08

R3IQ10

R3IQ12

R3IQ14

R3IQ16

R2IQ17

R2IQ15

R2IQ13

R2IQ11

R2IQ09

R2IQ07

R2IQ05

R2IQ03

R2IQ01

BetaX (m)

Measured BetaXDesi gn model

0

10

20

30

40

50

60

70

R3IQ1A

R3IQ02

R3IQ04

R3IQ06

R3IQ08

R3IQ10

R3IQ12

R3IQ14

R3IQ16

R2IQ17

R2IQ15

R2IQ13

R2IQ11

R2IQ09

R2IQ07

R2IQ05

R2IQ03

R2IQ01

BetaY (m)

Measured BetaYDesi gn model

The comparison of measured Beta function and design model after quadrupole strength changes from LOCO are applied.

0

0. 5

1

1. 5

2

2. 5

R3IBH02

R3IBT03

R3IBT05

R3IBT09

R2IBH17

R2IBT09

R2IBT05

R2IBT03

R2IABT

R1OBT01

R1OBT04

R1OBT07

R1OBT10

R4OBT10

R4OBT07

R4OBT04

R4OBH02

k/k0

BER horizontal correctors kicksBER horizontal correctors kicks

With the corrector kicks fitted by LOCO, we found the corrector strengths of inner ring are reduced a half by mistake.

ConclusionConclusion

All the BPM offsets are determined and orbit correction has been done successfully . After correction the average orbit is 0.2/0.08 mm, and rms orbit is 1/0.5 mm.

Analysis of the BEPCII measured orbit response matrix determined the quadrupole strength errors 、 BPM gains and couplings 、 correctors kicks and couplings.

The fudge factors of quadrupole are mostly within 1.01~1.02, that is means the real quadrupole strengths are lower than the design strengths. It can be explained by the effect of adjacent sextupole due to the short distance between them.

The fit model accurately predicted the tune 、 Beta function and dispersion .

The analysis also gave the best settings for quadrupoles to restore the design optics.

After correction, the measured Beta function at most BPMs can be restored within ±10% of design model, except for 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.

Problems Problems

The quadrupole errors are relatively large. The sources come from their construction tolerances, power supplies and effects of adjacent sextupole , are there any other systematic errors? Should longitudinal position of quadrupoles 、 BPMs or correctors be considered?

In injection and interaction regions, because of the same polarity problems, the discrepancies are also large. Is there any ideal method to resolve this problem?

In the futher, Do some experiments to correct coupling.

Add some constraint conditions in fitting , such as the phase advance in injection region.

Try to determine the sextupole strength errors or offsets .

Thanks a lot !Thanks a lot !