International Magnetic Measurement Workshop 21 ESRF ... · • Mechanical centre can be found by...

A stretched wire system for the measurement of accelerator lattice and

insertion device magnets

Cheng Ying Kuo, J-C Jan, F-Y Lin, C-K Yang, T-Y Chung, Ching Shiang Hwang

National Synchrotron Radiation Research Center (NSRRC)Hsinchu, Taiwan

International Magnetic Measurement Workshop 21

ESRF, Grenoble, FR, June 2019

1

Contents Motivation

Analysis Method and Simulation Results

Stretched wire measurement system

Experimental results

Conclusions

• Circular path• Elliptical path

International Magnetic Measurement Workshop 21 National Synchrotron Radiation Research Center (NSRRC) Stretched Wire System

• A Quadrupole Magnet• In-vacuum Undulator

2

Introduction

TPS 3 GeV

TLS 1.5 GeV

TLS: Taiwan Light Source (1993-now)TPS: Taiwan Photon Source (2015-now)


2014 Aug.Booster ring and storage ring accelerators installed

Dec.The first TPS light at the 3-GeV design beam energy delivered.

2015 Jan. Taiwan Photon Source Inauguration Ceremony.

Dec. TPS exceeds its design beam current 500 mA

2016 Sep. TPS Opening Ceremony.Four TPS phase-I beamlines available to users worldwide.

2017 May.Flagship Project initiated – construction of 5 TPS phase-II beamlines begins

Dec.Construction of TPS phase-I beamlines completed

3

Motivation

• Small bore measurement for ultimate storage ring.

• Elliptical measurement for closed aperture of dipole and insertion device.


IU EPU4

Analytic Methods

n

nnxy iyxiabiBB ))((

The magnetic field By+iBx is expressed in polynomial expansions as

...)(2),( 22

22110 yxbxyaxbyabyxBy

...)(2),( 22

22110 yxaxybybxaayxBx

The equation is divided into real part By and imaginary part Bx

(1)

(2)

(3)

b0:normal dipole termb1:normal quadrupole term

a0:skew dipole terma1:skew quadrupole term


5

Polynomial fitX1, Y1, By1

X2, Y2, By2

X3, Y3, By3

.

.

.Xj, Yj, Byj

b0, a0

b1, a1

b2, a2

b3, a3

.

.

.bn, an

...)(2),( 22

22110 yxbxyaxbyabyxBy

Choose fitting number n

A circle path divided to j points


DataFormat

X1, Y1, Bx1

X2, Y2, Bx2

X3, Y3, Bx3

.

.

.Xj, Yj, Bxj

b0, a0

b1, a1

b2, a2

b3, a3

.

.

.bn, an

...)(2),( 22

22110 yxaxybybxaayxBx

6

FFT

By()=Σrn[bncos(n)-ansin(n)]

By+iBx=Σ(bn+ian)rnein1, By1

2, By2

3, By3

.

.

.j, Byj

b0, a0

b1, a1

b2, a2

b3, a3

.

.

.bn, an

A circle path divided to j points

j points can define n number

0 30 60 90 120 150 180 210 240 270 300 330 360

0.800

0.805

0.810

0.815

0.820

0.825

0.830

0.835

0.840

0.845B

y (T

)

Theta (degree)

Raw Data

Fast Fourier transfer

DataFormat


7

Pierre Schnizer

Elliptical multipoles

Circular multipoles


P.Schnizer et al. "Theory and Applicationof Plane Elliptic multipoles for Static Magnetic Fields",NIMA 607(3):505-516, 2009

8

3 2 1 0 1 2 3

0.79

0.80

0.81

0.82

0.83

0.84

0.85

By() Ra=20mmRb=8mmr=15mm


-

m=odd: tkm=

m=even: tkm=

semi-major axissemi-minor axisradius of circular multipoles expansion

9


10

Simulation Case

Circular path data of a combined dipole

11

Simulation of Multipoles in a circleCombined Dipole

Main components Normalize to b0(x10-4) @10mm

b0 0.823 T 10000

b1 -1.79 T/m -216.8

b2 -3.38 T/m2 -4.1

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] @

10

mm

Harmonic Order n

Polynomial Fit

FFT

Circle R=10mm, Normalize at 10mm

• The multipole results of polynomial fit and FFT are the same in a circular pathat a combined dipole.

• Shows two analysis methods are consistence in a circular path.

Combined Dipole

Circle Polynomial FFT

b0 0.8234427 T 0.823443 T

b1 -1.785341 T/m -1.785342 T/m

b2 -3.376005 T/m2 -3.375895 T/m2

12

10000

-216

bn、an intoBy()=Σrn[bncos(n)-ansin(n)]orBy(x,y)=b0+a1y+b1x+2a2xy+b2(x2-y2)+...

Combined Dipole Magnet

Circular PathR=10mm

0 30 60 90 120 150 180 210 240 270 300 330 360-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

Err

or(

1E

-4)

Theta (degree)

(Polynomial Fit - Raw)/Raw

(FFT - Raw)/Raw

0 30 60 90 120 150 180 210 240 270 300 330 3600.800

0.805

0.810

0.815

0.820

0.825

0.830

0.835

0.840

0.845

By (

T)

Theta (degree)

Raw Data

Polynomial Fit

FFT

• The errors of these two methods are within 5x10-6.


13

Simulation Case

Elliptical path data of a combined dipole

14

Elliptical Path Analysis

Ellipse Polynomial FFT P. Schnizer

b0 0.8234423 T 0.822633 T 0.823442 T

b1 -1.785267 T/m -1.784512 T/m -1.78526 T/m

b2 -3.341436 T/m2 -3.359222 T/m2 -3.34125 T/m2

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] @

10

mm

Harmonic Order n

polynomial Fit

FFT

P. Schnizer

Elliptical Path Ra=20mm,Rb=8mm Normalize at 10mm

-5

-4

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] @

10

mm

Harmonic Order n

Polynomial Fit

FFT


Circle Polynomial FFT

b0 0.8234427 T 0.823443 T

b1 -1.785341 T/m -1.785342 T/m

b2 -3.376005 T/m2 -3.375895 T/m2

15

Combined Dipole

0 30 60 90 120 150 180 210 240 270 300 330 360

0.78

0.79

0.80

0.81

0.82

0.83

0.84

0.85

0.86

By (

T)

Theta (degree)

Raw

Polynomial Fit

FFT

P. Schnizer

0 30 60 90 120 150 180 210 240 270 300 330 360

-20

-15

-10

-5

0

5

10

15

20

Err

or

(1E

-4)

Theta (degree)

Orthogonal Fit

FFT

P. Schnizer

120 150 180 210 2400.83

0.84

0.85

0.86

By (

T)

Theta (degree)

Raw

Polynomial Fit

FFT

P. Schnizer

0 30 60 90 120 150 180 210 240 270 300 330 360-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Err

or

(1E

-4)

Theta (degree)

Orthogonal Fit

FFT

P. Schnizer

Elliptical path bn、an intoBy(x,y)=b0+a1y+b1x+2a2xy+b2(x2-y2)+...

16

Combined Dipole

Analysis Conclusion

• The multipole results of polynomial fit and FFT are the same in a circular path at a combined dipole. The errors of these two methods are within 5x10-6.

• Polynomial fit, FFT and P. Schnizer in an ellipse are compared, polynomial fit result is the same as P. Schnizer, FFT multipole got a large errors. So we can chose polynomial fit or P. Schnizer anaylsis method for multipoles in an ellipse.

• The fitting errors of polynomial fit and P. Schnizer of elliptical path are within 5x10-5.


17

Stretched wire system

18

Stretched Wire System Setup

Parameter Value Units

Wire length 1100 mm

Wire diameter 0.3 mm

Wire mass density 0.4 g/m

Wire sag 0.25 mm

Parameters of 8 turns copper wires.

• Integrator and voltmeter (Keithley2182) testing results are very close.

• The movement of transverse and vertical direction are moving by stepping motors.

• The wires are stretched by moving the stage longitudinal manually.

• Mechanical centre can be found by level meter and theodolite.

• 8 turns copper wires are in series.


19

Standard deviation at one position

STDEV VoltmeterKEITHLEY 2182

IntegratorFDI 2056

Be-Cu wire dx=2mm 3.0 G-cm 2.9 G-cm

Be-Cu wire dx=4mm 2.0 G-cm -

8 Cu wires dx=2mm 1.0 G-cm 1.0 G-cm

8 Cu wires dx=4mm 0.5 G-cm 0.5 G-cm

Move step dx (mm)

STDEV (G-cm)

1 2

2 1

4 0.5

6 0.2

8 0.3

8Cu wiresWith FDI2056v=25 mm/s

Ref. NdFeB BlockBy(x=0mm)=3300 G-cm


20

Poor space resolution

Integral multipoles of a quadrupole magnet

by stretched wire system

21

QM R25mm HPS & SW Experimental Results

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] a

t 2

5m

m

Harmonic Order n

Normal bn harmonics

HPS R25

SW R25

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

Ske

w a

nh

arm

on

ics[

un

its]

at

25

mm

Harmonic Order n

Skew an harmonics

HPS R25

SW R25


System Gdz (T)

HPS 5.178

SW 5.179


22

• Normal sextupole(b2) and octupole (b3) are particular multipole.

• The difference of all multipole are within 1 units between HPS and SW.

0 60 120 180 240 300 360

-150000

-100000

-50000

0

50000

100000

150000

Iy(G

-cm

)

Theta (degree)

HPS Iy(Raw)

HPS Iy(BnAn)

0 60 120 180 240 300 360-100

-80

-60

-40

-20

0

20

40

60

80

100

Iy

(G-c

m)

Theta (degree)

HPS Iy(Raw-BnAn)

SW Iy(Raw-BnAn)

0 60 120 180 240 300 360

-150000

-100000

-50000

0

50000

100000

150000

Iy(G

-cm

)

Theta(degree)

SW Iy Raw

SW Iy(BnAn)

R25mm HPS vs SW


23

QM

R5mm HPS vs SW

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] a

t 5

mm

Harmonic Order n

Normal bn harmonics

HPS R5

SW R5

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

Ske

w a

nh

arm

on

ics[

un

its]

at

5m

m

Harmonic Order n

Skew an harmonics

HPS R5

SW R5


System Gdz (T)

HPS 5.177

SW 5.178


24

QM

• The deviation of R5 data is larger than R25.

• The difference is within 2 units between HPS and SW.

Elliptical Path HPS vs SW

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] @

15

mm

Harmonic Order n

Normal bn harmonics

HPS Ra25 Rb15

SW Ra25 Rb15

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

Ske

w a

nh

arm

on

ics[

un

its]

@1

5m

m

Harmonic Order n

Skew an harmonics

HPS Ra25 Rb15

SW Ra25 Rb15

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] @

5m

m

Harmonic Order n

HPS Ra25 Rb5

SW Ra25 Rb5

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

Ske

w a

nh

arm

on

ics[

un

its]

@5

mm

Harmonic Order n

HPS Ra25 Rb5

SW Ra25 Rb5

Normalize at short axis radius


HPS/SWPath

Gdz (T)

HPS Ellipse Ra25 Rb15

5.177

HPS Ellipse Ra25 Rb5

5.176

SW Ellipse Ra25 Rb15

5.174

SW Ellipse Ra25 Rb5

5.176

25

QM

25mm

15mm

5mm

25mm

Integral multipoles of in-vacuum undulator

by stretched wire system

26

Fit n=12

To check skew quadrupole value which is out of spec. -15 < x < 15 (mm) Linear MeasurementGap(mm) Dipole(n=0) Quadrupole(n=1) Sextupole(n=2)

Spec. 100 G-cm 50 G 100 G/cm

6.8 Normal(Iy) -3.9 34.1 14.1

Skew(Ix) 62.2 -79.8 -8.1

7 Normal(Iy) -11.7 38.5 15.4

Skew(Ix) 50.5 -82.3 16.7

8 Normal(Iy) -28.9 26.3 14.6

Skew(Ix) 48.8 -60.2 18.5

9 Normal(Iy) -38.8 29.6 16.2

Skew(Ix) 52.4 -41.2 3.6

Linear

-15 -10 -5 0 5 10 15

-100

-50

0

50

100

150

Ix(G

-cm

)

X (mm)

Lower Limit

Upper Limit

Gap 6.8mm Ix

Elliptical MeasurementGap(mm) Dipole(n=0) Quadrupole(n=1) Sextupole(n=2)

Spec. 100 G-cm 50 G 100 G/cm

6.8 Normal 0.4 47.1 43.1

Skew - -105.7 29.8

7 Normal -6.0 36.0 33.2

Skew - -78.7 21.3

8 Normal -21.8 48.5 68.0

Skew - -73.4 16.1

9 Normal -34.3 49.6 61.4

Skew - -44.8 35.8

4m-IU24

IU24 Linear & Elliptical measurement

Be-Cu wire

27

Ix(x)

IU24 Gap 6.8mmLinear

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-100

-50

0

50

100

150

Ix (

G-c

m)

X(cm)

Gap 6.8mm Ix

Polynomial Fit of Ix

Model Polynomial

Adj. R-Square 0.77937

Value Standard Error

Ix Intercept 52.9155 8.39504

Ix B1 -82.82405 22.05547

Ix B2 14.34021 22.0543

Ix B3 93.30193 36.45274

Ix B4 -11.86304 10.3169

Ix B5 -40.65097 13.42113

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-60

-40

-20

0

20

40

60

Ix

(G-c

m)

X(cm)

Ix(Raw-Linear Polynomial fit n=5)

4 5 6 7 8 9-100

-80

-60

-40

-20

0

20

40

60

80

a1(G

)

Linear Fit n

a1 (skew quadrupole)

• It is hard to confirm skew quadrupole value.

• Different linear polynomial fit number get different results.

28

IU24

0 60 120 180 240 300 360-150

-100

-50

0

50

100

150

Iy(G

-cm

)

Theta(degree)

Iy(Raw-1)

Iy(BnAn-1)

Iy(Raw-2)

Iy(BnAn-2)

Gap 6.8mm Ra15mm Rb 3mm

0 60 120 180 240 300 360-50

-40

-30

-20

-10

0

10

20

30

40Gap 6.8mm Ra15mm Rb 3mm

Iy

(G-c

m)

Theta(degree)

Iy(Raw-BnAn)-1

Iy(Raw-BnAn)-2

IU24 Gap 6.8mmElliptical path polynomial fit

29

IU24

3mm

15mm

Raw data Iy(x,y) still was looked like unusually but elliptical path polynomial fit well.

0 60 120 180 240 300 360-100

-80

-60

-40

-20

0

20

40

60

80

100

Iy(Raw-BnAn, n=6)

Iy(Raw-BnAn, n=8)

Iy(Raw-BnAn, n=10)

Iy(Raw-BnAn, n=12)

Iy(Raw-BnAn, n=14)

dIy

(G-c

m)

Theta (degree)

0 60 120 180 240 300 360-200

-150

-100

-50

0

50

100

150

200

Iy (

G-c

m)

Theta (degree)

Iy(Raw)

Iy(BnAn, n=6)

Iy(BnAn, n=8)

Iy(BnAn, n=10)

Iy(BnAn, n=12)

Iy(BnAn, n=14)

0 60 120 180 240 300 360-200

-100

0

100

200

Iy (

G-c

m)

Theta (degree)

Iy(Raw)

Iy(BnAn, n=14)

Iy(BnAn, n=16)

Iy(BnAn, n=18)

0 60 120 180 240 300 360-100

-80

-60

-40

-20

0

20

40

60

80

100

dIy

(G-c

m)

Theta (degree)

Iy(Raw-BnAn, n=14)

Iy(Raw-BnAn, n=16)

Iy(Raw-BnAn, n=18)N=14~18

N=6~14

Elliptical path Fitting number

30

IU24

Normal Terms

Skew Terms

6 8 10 12 14 16 18-7

-6

-5

-4

-3

-2

-1

0

1

b0 (

G-c

m)

Elliptical Fit n

b0(G-cm)

6 8 10 12 14 16 18

-60

-50

-40

-30

-20

-10

0

b1 (

G)

Elliptical Fit n

b1(G)

6 8 10 12 14 16 18-60

-40

-20

0

20

40

60

80

100

b2 (

G/c

m)

Elliptical Fit n

b2(G/cm)

6 8 10 12 14 16 18

-50

0

50

100

150

200

250

300

350

b3 (

G/c

m2)

Elliptical Fit n

b3(G/cm2)

6 8 10 12 14 16 18-120

-100

-80

-60

-40

-20

0

a1 (

G)

Elliptical Fit n

a1(G)

6 8 10 12 14 16 18-70

-60

-50

-40

-30

-20

-10

0

a2 (

G/c

m)

Elliptical Fit n

a2(G/cm)

6 8 10 12 14 16 18-100

0

100

200

300

400

500

600

700

a3 (

G/c

m2)

Elliptical Fit n

a3(G/cm2)

Normal Dipole

Normal QuadrupoleNormal Sextupole

Skew Quadrupole

Skew Sextupole

Elliptical path Fitting number

31

IU24

b0, b1, b2, a1, a2 are convergent.

IU24 Gap 40mm Circle & Ellipse

0 60 120 180 240 300 360

-20

-10

0

10

20

30

40

50Gap 40mm Ra15mm Rb 3mm

Iy (

G-c

m)

Theta (degree)

Ellipse Iy(Raw)

Ellipse Iy(BnAn)

0 60 120 180 240 300 360-10

-8

-6

-4

-2

0

2

4

6

8

10

Iy

(G

-cm

)

Theta (degree)

Ellipse Iy(Raw-BnAn)

0 60 120 180 240 300 360

-100

-50

0

50

100

Gap 40mm R15mm

Iy (

G-c

m)

Theta (degree)

Circle Iy(Raw)

Circle Iy(BnAn)

0 60 120 180 240 300 360-10

-8

-6

-4

-2

0

2

4

6

8

10

Iy

(G

-cm

)

Theta (degree)

Circle Iy(Raw-BnAn)

CircleGap

(mm)Dipole(n=0)

Quadrupole(n=1)

Sextupole(n=2)

Spec. 100 G-cm 50 G 100 G/cm

40 Normal 3.59 7.40 4.95

Skew - -52.42 -6.94

EllipseGap

(mm)Dipole(n=0)

Quadrupole(n=1)

Sextupole(n=2)

Spec. 100 G-cm 50 G 100 G/cm

40 Normal 3.74 5.69 1.59

Skew - -53.85 -16.1

32

3mm

15mm

15mm

The multipole results are similar in a circle and ellipse.

Conclusions• A quadrupole magnet was measured by Hall probe system and stretched

wire system and results were compared. Hall probe system can be more precise but stretched wire system can save lot of time.

• The difference of multipoles are within 2x10-4 between Hall probe system and stretched wire system.

• Circular and elliptical measurement of a quadrupole magnet multipoles are showed. If elliptical path multipoles normalized at short radius, the result is similar to circular path multipoles.

• Compare to linear measurement of in-vacuum undulator, elliptical path result shows more easy to confirm the main multipoles(n=0, 1, 2).

• Stretched wire system not only can measure 1st and 2nd integral fields but also can measure multipoles.


33

Many Thanks for Your Attention!


34

Circle R=10 Fitting Number

0 2 4 6 8 10 12 14 16 18 20 22 24

0.8234425

0.8234426

0.8234427

0.8234428

b0

(T

)

N

polynomial Fit

FFT

0 2 4 6 8 10 12 14 16 18 20 22 24

-1.78538

-1.78537

-1.78536

-1.78535

-1.78534

-1.78533

-1.78532

-1.78531

-1.78530

b1

(T

/m)

N

polynomial Fit

FFT

0 2 4 6 8 10 12 14 16 18 20 22 24

-3.379

-3.378

-3.377

-3.376

-3.375

b2

(T

/m2)

N

polynomial Fit

FFT

0 2 4 6 8 10 12 14 16 18 20 22 24

10.0

10.1

10.2

10.3

10.4

10.5

b3

(T

/m3)

N

polynomial Fit

FFT

2 4 6 8 10 12 14 16 18 20 22 24

930

940

950

960

970

980

b4

(T

/m4)

N

polynomial Fit

FFT

4 6 8 10 12 14 16 18 20 22 24

-32000

-31500

-31000

-30500

-30000

-29500

-29000

-28500

b5

(T

/m5)

N

polynomial Fit

FFT

4 6 8 10 12 14 16 18 20 22 24

-9950000

-9900000

-9850000

-9800000

-9750000

-9700000

b6

(T

/m6)

N

polynomial Fit

FFT

6 8 10 12 14 16 18 20 22 24

350000000

355000000

360000000

365000000

370000000

b7

(T

/m7)

N

polynomial Fit

FFT

6 8 10 12 14 16 18 20 22 24

2.25E+010

2.30E+010

2.35E+010

2.40E+010

2.45E+010

2.50E+010

b8

(T

/m8)

N

polynomial Fit

FFT

8 10 12 14 16 18 20 22 24

-4.22E+012

-4.20E+012

-4.18E+012

-4.16E+012

-4.14E+012

-4.12E+012

-4.10E+012

-4.08E+012

b9

(T

/m9)

N

polynomial Fit

FFT

Simulation of a Combined Dipole

35

Ellipse Ra=20 Rb8 Fitting Number

6 8 10 12 14 16 18 20 22 24

0.82343

0.82344

0.82345

0.82346

b0

(T

)

N

polynomial Fit

P. Schnizer

2 4 6 8 10 12 14 16 18 20 22 24

-1.786

-1.785

-1.784

-1.783

-1.782

b1

(T

/m)

N

polynomial Fit

P. Schnizer

4 6 8 10 12 14 16 18 20 22 24

-3.40

-3.35

-3.30

-3.25

-3.20

-3.15

-3.10

-3.05

-3.00

b2

(T

/m2)

N

polynomial Fit

P. Schnizer

2 4 6 8 10 12 14 16 18 20 22 24

-20

-10

0

10

20

30

b3

(T

/m3)

N

polynomial Fit

P. Schnizer

0 2 4 6 8 10 12 14 16 18 20 22 24

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

b4

(T

/m4)

N

polynomial Fit

P. Schnizer

4 6 8 10 12 14 16 18 20 22 24

-100000

-80000

-60000

-40000

-20000

0

20000

40000

60000b

5 (

T/m

5)

N

polynomial Fit

P. Schnizer

4 6 8 10 12 14 16 18 20 22 24

-8.00E+007

-6.00E+007

-4.00E+007

-2.00E+007

0.00E+000

2.00E+007

4.00E+007

6.00E+007

b6

(T

/m6)

N

polynomial Fit

P. Schnizer

6 8 10 12 14 16 18 20 22 24 26

-4.00E+008

-2.00E+008

0.00E+000

2.00E+008

4.00E+008

6.00E+008

b7

(T

/m7)

N

polynomial Fit

P. Schnizer

6 8 10 12 14 16 18 20 22 24 26

-2.00E+011

-1.50E+011

-1.00E+011

-5.00E+010

0.00E+000

5.00E+010

1.00E+011

1.50E+011

2.00E+011

b8

(T

/m8)

N

polynomial Fit

P. Schnizer

8 10 12 14 16 18 20 22 24 26

-6.00E+012

-4.00E+012

-2.00E+012

0.00E+000

2.00E+012

4.00E+012

b9

(T

/m9)

N

polynomial Fit

P. Schnizer

Simulation of a Combined Dipole

36

X(mm) Mean Iy(G-cm) STDEV (G-cm) %2182 VR=0.1V

0 124.9331 2.02206 1.618514 v=25mm/s5 26095.99 2.7032 0.010359

10 52052.82 3.89971 0.00749215 78037.31 7.30075 0.00935520 103991.3 4.60909 0.00443225 129934.9 10.92665 0.00840930 155890.3 8.40531 0.00539235 181813.7 10.61701 0.005839

2182 VR=0.01V0 132.9866 2.36717 1.780006 v=15mm/s5 26003.88 1.66275 0.006394

10 51875.94 2.98905 0.00576215 77733.24 5.94341 0.00764620 103612.1 3.71975 0.0035925 129462.5 2.62688 0.00202930 155297.1 6.77026 0.0043635 OVER

0 124.5182 2.43309 1.954004 v=25mm/s5 26061.29 1.88915 0.007249

10 51998.96 1.92215 0.00369715 77928.96 3.39732 0.0043620 103863.8 5.58763 0.0053825 129772.1 9.35304 0.00720730 OVER

FDI2056 G100

x Mean Iy(G-cm) STDEV (G-cm) %

0 134.3428 1.80489 1.343496 v=25mm/s

5 26157.84 1.59773 0.006108

10 52182.57 4.02849 0.00772

15 78209.52 4.50289 0.005757

20 104234.9 3.18839 0.003059

25 130247.2 2.85603 0.002193

30 156256.7 2.78412 0.001782

35 182254.6 5.04362 0.002767

dx=2mm

Stretched wire measure QM 180A

37

Circle vs Ellipse

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] a

t 2

5m

m

Harmonic Order n

Normal bn harmonicsHPS R25

HPS Ra25 Rb15

HPS Ra25 Rb5

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

Ske

w a

nh

arm

on

ics[

un

its]

at

25

mm

Harmonic Order n

Skew an harmonics

HPS R25

HPS Ra25 Rb15

HPS Ra25 Rb5

HPS Path B1 (T)

Circle R25 5.178

Ellipse Ra25 Rb15

5.177

Ellipse Ra25 Rb5

5.176

Normalize at long axis radius

38

QM

Circle vs Ellipse

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

No

rmal

bn

har

mo

nic

s[u

nit

s] a

t 2

5m

m

Harmonic Order n

Normal bn harmonicsSW R25

SW Ra25 Rb15

SW Ra25 Rb5

-5

-4

-3

-2

-1

0

1

2

3

4

5

2 3 4 5 6 7 8 9 10 11 12 13

Ske

w a

nh

arm

on

ics[

un

its]

at

25

mm

Harmonic Order n

Skew an harmonics

SW R25

SW Ra25 Rb15

SW Ra25 Rb5

SW Path B1 (T)

Circle R25 5.179

Ellipse Ra25 Rb15

5.174

Ellipse Ra25 Rb5

5.176

Normalize at long axis radius

39

QM

IU24 Gap 7mm

0 60 120 180 240 300 360-200

-150

-100

-50

0

50

100

150

200Gap 7mm Ra15mm Rb 3mm

Iy (

G-c

m)

Theta (degree)

Iy(Raw)

Iy(BnAn)

0 60 120 180 240 300 360-100

-80

-60

-40

-20

0

20

40

60

Iy(Raw-BnAn)

dIy

(G-c

m)

Theta (degree)

Fit n=12 40

IU24 Gap 8mm

0 60 120 180 240 300 360-100

-80

-60

-40

-20

0

20

40

60

80

Iy (

G-c

m)

Theta (degree)

Iy(Raw)

Iy(BnAn)

Gap 8mm Ra15mm Rb 3mm

0 60 120 180 240 300 360

-40

-30

-20

-10

0

10

20

30

40

Iy

(G

-cm

)

Theta (degree)

Iy(Raw-BnAn)

Fit n=12 41

IU24 Gap 9mm

0 60 120 180 240 300 360

-100

-80

-60

-40

-20

0

20

40

60


Iy (

G-c

m)

Theta (degree)

Iy(Raw)

Iy(BnAn)

0 60 120 180 240 300 360

-30

-20

-10

0

10

20

30

Iy

(G

-cm

)

Theta (degree)

Iy(Raw-BnAn)

Fit n=12 42

IU24 Gap 10mm

0 60 120 180 240 300 360-120

-100

-80

-60

-40

-20

0

20

40


Iy (

G-c

m)

Theta (degree)

Iy(Raw)

Iy(BnAn)

0 60 120 180 240 300 360

-30

-20

-10

0

10

20

30

Iy

(G

-cm

)

Theta (degree)

Iy(Raw-BnAn)

Fit n=12 43

International Magnetic Measurement Workshop 21 ESRF ... · • Mechanical centre can be found by...

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