Evaluation of synchrotron radiation bucking coil locations ...tnweb.jlab.org/tn/2008/08-027.pdf ·...
Transcript of 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 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