Evaluation of synchrotron radiation bucking coil locations ...tnweb.jlab.org/tn/2008/08-027.pdf · Evaluation of synchrotron radiation bucking coil locations in 4m arc dipole Jay

Evaluation of synchrotron radiation bucking coil locations in 4m arc dipole

Jay Benesch

Abstract

Five cases of a detailed model of the XP 4m arc dipole were solved in TOSCA and the results

compared. The five cases included four bucking coil locations and no coil (base). No significant

effect on field quality was found for any of the four locations. The bucking coil B/B modeled

was 8E-4, 10% above the requirement for arc 10.

Model

The figure below shows the basic model looking from -Z. Green is steel. Grey is air. The large

red squares are the main racetrack coils also seen on the right of the figure. The small red

squares are the four bucking coils. Steel and air are reflected about X=0 by symmetry conditions

in the software to create the H magnet. Only half the Z extent was modeled, again by defining a

symmetry condition. The model was run with all bucking coils off and then each of the four

coils turned on individually. The first is designated hereafter "basic". The four cases with

bucking coil are designated bottom-inboard (close to pole), bottom-outboard, midplane-inboard

and midplane-outboard. I abbreviate these bot_in, bot_out, mid_in and mid_out. Bottom

bucking coils are racetracks. Midplane coils are bedsteads, rising above the beam pipe at the

ends as seen on the right side below. Mesh is 2mm between the poles and 3mm where the

bucking coils reside.

I compared the models in two ways. First I used the post-processor table function to compute By

and Bmod on a 2.5mm grid in the midplane encompassing x=[0,3] and z= [0,225]. The steel is

200 cm long so the grid extends 25 cm beyond the steel. Half-sagitta is 2.455cm so 3cm x extent

covers the region in which 3 of the electrons may be found including a 3mm steering

allowance. Pole half-width is 6.51cm. Second, I used the post-processor to compute multipoles

on 901 circles, 2cm diameter, arrayed at 2.5mm intervals along the arc of the 34.65m radius

circle which is the nominal beam path inside the magnet. The small circles are normal to the

large one which is the nominal beam path. The 25cm of this arc which is beyond the steel is

within a few mm of the expected beam path at its end, The field is low at the end so the error in

integrated multipoles from this approximation is negligible.

I would be happy to provide the spreadsheets to any reader who wishes to draw his/her own

conclusions. I would also be happy to run any other post-processing jobs requested. Below I use

Kaleidagraph (2D graphing package) and JMP (stat analysis) to plot some of the data to begin to

back up the conclusion stated in the abstract. Full confidence can only be obtained by looking at

the spreadsheets in detail.

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

2500 7500

Count

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

0.0041

0.00081

0.0008

0.0008

0.00079

0.00079

0.00079

0.00079

0.00079

0.00078

-0.0049

Quantiles

Mean

Std Dev

Std Err Mean

upper 95% Mean

lower 95% Mean

N

0.0007907

0.0001294

0.0000013

0.0007932

0.0007882

10413

Moments

bot_in/basic-1

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

2500 7500

Count

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

0.0041

0.00081

0.0008

0.0008

0.00079

0.00079

0.00079

0.00079

0.00079

0.00078

-0.0049

Quantiles

Mean

Std Dev

Std Err Mean

upper 95% Mean

lower 95% Mean

N

0.0007895

0.0001294

0.0000013

0.000792

0.0007871

10413

Moments

bot_out/basic-1

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

2500 7500

Count

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

0.0041

0.00081

0.0008

0.0008

0.00079

0.00079

0.00079

0.00079

0.00079

0.00078

-0.0049

Quantiles

Mean

Std Dev

Std Err Mean

upper 95% Mean

lower 95% Mean

N

0.0007909

0.0001298

0.0000013

0.0007934

0.0007884

10413

Moments

mid_in/basic-1

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

0.003

0.004

2500 7500

Count

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

0.0041

0.00081

0.0008

0.0008

0.00079

0.00079

0.00079

0.00079

0.00079

0.00078

-0.0049

Quantiles

Mean

Std Dev

Std Err Mean

upper 95% Mean

lower 95% Mean

N

0.0007895

0.0001298

0.0000013

0.000792

0.000787

10413

Moments

mid_out/basic-1

Distributions

Distributions of ratios of Bmod values from tables for z=[0,200]cm to basic case without

bucking coil. For all cases 99% of the values lie within [0.00078,0.00081]. One can see from

the histogram that ~10000 of the 10413 points graphed are in the central peak. Below I graph

the absolute difference in field for the full grid. All of the points outside the central peaks are

also outside the steel. These values were evaluated for the 4m dipole. Each model took four

days of computation time. The multipole amplitudes will change if the dipole is shortened but

the conclusions won't.

-90

-70

-50

-30

-10

10

30

50

70

2500 7500

Count

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

76.35

9.85

7.12

7.11

7.09

7.08

7.07

1.87

-0.64

-16.45

-94.54

Quantiles

Mean

Std Dev

Std Err Mean

upper 95% Mean

lower 95% Mean

N

6.2284552

4.3392985

0.0400997

6.3070572

6.1498531

11710

Moments

bot_in-basic

-90

-70

-50

-30

-10

10

30

50

70

2500 7500

Count

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

76.34

9.84

7.11

7.10

7.08

7.07

7.06

1.86

-0.64

-16.46

-94.55

Quantiles

Mean

Std Dev

Std Err Mean

upper 95% Mean

lower 95% Mean

N

6.218695

4.3381998

0.0400895

6.2972772

6.1401128

11710

Moments

bot_out-basic

-90

-70

-50

-30

-10

10

30

50

70

2500 7500

Count

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

76.78

9.94

7.12

7.11

7.09

7.08

7.07

1.90

-0.60

-16.22

-94.09

Quantiles

Mean

Std Dev

Std Err Mean

upper 95% Mean

lower 95% Mean

N

6.2381883

4.3200842

0.0399238

6.3164456

6.1599309

11709

Moments

mid_in-basic

-90

-70

-50

-30

-10

10

30

50

70

2500 7500

Count

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

76.76

9.92

7.11

7.10

7.08

7.07

7.06

1.90

-0.61

-16.23

-94.10

Quantiles

Mean

Std Dev

Std Err Mean

upper 95% Mean

lower 95% Mean

N

6.226614

4.3185677

0.0399098

6.3048439

6.1483841

11709

Moments

mid_out-basic

Distributions

Absolute differences from basic model. Below I show the 11713 values for the basic model.

The values as the field falls off outside the steel are seen only in the outlier box plot above the

histogram.

2500

5000

7500

10000

Coun

t

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

100.0%

99.5%

97.5%

90.0%

75.0%

50.0%

25.0%

10.0%

2.5%

0.5%

0.0%

maximum

quartile

median

quartile

minimum

8930.1

8930.0

8930.0

8929.9

8929.8

8929.3

8927.5

2735.3

8.1

4.4

0.17385

Quantiles

Bmod(basic)

Distributions

-200

-150

-100

-50

0

50

-50 0 50 100 150 200 250

xp_multipoles

Cos1basicCos1bot_inCos1bot_outCos1mid_inCos1mid_out

Gau

ss (

quad

rupo

le)

z cm

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-50 0 50 100 150 200 250

xp_multipoles

Cos1basicCos1bot_inCos1bot_outCos1mid_inCos1mid_out

Ga

uss

(q

ua

dru

po

le)

z cm

Normal quadrupole terms as a function of Z along arc of circle for five models. Lower graph is

same data as upper with altered Y axis. No differences except near the bucking coil ends.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

195 200 205 210

xp_multipoles

Cos1basicCos1bot_inCos1bot_outCos1mid_inCos1mid_out

Gau

ss (

quad

rupo

le)

z cm

Note that each of the four models with bucking coils have the same values while all differ to a

small extent from the basic model.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

190 195 200 205 210 215 220

xp_multipoles

Sin1basicSin1bot_inSin1bot_outSin1mid_inSin1mid_out

Gu

ass

(sk

ew

qu

adru

po

le)

z cm

Skew quadrupole terms. Here there are three groupings, basic, bottom bucking coil racetracks

and midplane bucking coil bedsteads. Still, differences are modest.

-500

0

500

1000

0 50 100 150 200 250

xp_multipoles

Cos2basicCos2bot_inCos2bot_outCos2mid_inCos2mid_out

Ga

uss (

se

xtu

po

le)

z cm

-1

-0.5

0

0.5

1

0 50 100 150 200 250

xp_multipoles

Cos2basicCos2bot_inCos2bot_outCos2mid_inCos2mid_out

Ga

uss (

se

xtu

po

le)

z cmSextupole for five models on two vertical scales. Nothing of interest here except a few mesh

problems in the basic model.

-25

-20

-15

-10

-5

0

5

10

0 50 100 150 200 250

xp_multipoles

Sin2basicSin2bot_inSin2bot_outSin2mid_inSin2mid_out

Ga

uss (

ske

w s

extu

po

le)

z cm

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 50 100 150 200 250

xp_multipoles

Sin2basicSin2bot_inSin2bot_outSin2mid_inSin2mid_out

Ga

uss (

ske

w s

extu

po

le)

z cm

Skew sextupole for five models on two vertical scales. Again, nothing to worry about. With

2mm mesh, numerical noise in skew multipoles is of order 10mG.

In the figure above, Mike Tiefenback took the large spreadsheet of table output I provided and

plotted the differences between the basic XP model and the four models with bucking coils as a

function of X and Z. The thirteen vertical "stripes" correspond to x= 0, 0.25, 0.5, …, 3.0 cm

(0.25cm intervals). The horizontal axis is Z=[0,225]cm repeated thirteen times. The number on

the horizontal axis is the row number in the spreadsheet, there are 13*901=11713 rows of data.

He found that the two outboard locations (bottom traces) are slightly less variable than the

inboard ones (upper pair). He also sees an increase in the width of the trace as x increases from

0 (midpole) to 3 cm, left to right in the figure. This is likely due to mesh size and saturation at

the edge of the pole, even though the pole half-width is 6.5cm and the mesh is 2mm. See figure

4d of TN-08-024 for a picture of the pole mesh. The trace width at the right is about 1ppm of the

bending field.

Conclusions

I conclude that any location of the bucking coil will do. Mike Tiefenback prefers the outboard

locations or another location in which the bucking coil is not "seen" by the beam pipe. YMMV