Exploration of the Triplet Parameter Space
Leon van Riesen-Haupt (JAI Oxford)
on behalf of the
JAI FCC Team
7th November 2016
EuroCirCol WP3 JAI updates, 31 March 2016
2
Shortening Inner Triplet
• Minimise the size of
the inner triplet
–
–
–
–
Save space
Reduce chromaticity
Easier correction scheme
Cheaper
• Keep sufficient beam
stay clear
• Initial design (early
2016)
– ~ 𝟒𝟎 𝝈 beam stay clear
– ~140 m long
– 10 m gaps between
magnets
Exploration of the Triplet Parameter Space, 7th November 2016
3
Inner Triplet
𝒈𝟏
𝒈𝟐
𝒈𝟑
0
𝑥𝐼𝑃 ′
0
𝑥𝑒𝑥𝑖𝑡 ′
𝑚11
𝑚21
𝑚12
𝑚22
𝒍𝟐
𝒍𝟏
• Simplified approach:
𝒍𝟒
1.8
1.6
– Using thin lenses
– Point-to-point focusing
x
y
1.4
1.2
x and y / m
• 𝒎𝒙𝟏𝟐 = 𝒎𝒚𝟏𝟐 = 𝟎
– Two constraints
• Analytical solution
1
0.8
0.6
0.4
– Work out lens strength for
fixed spatial layout
– Iterate through many
configurations quickly
Exploration of the Triplet Parameter Space, 7th November 2016
𝒍𝟑
0.2
0
-0.2
0
200
400
800
600
S/m
4
1000
1200
1400
Figure of Merit
•
Figure of Merit (FOM):
–
•
𝒙𝒊
𝒍
𝒈𝒊 𝑸𝒊
Quadrupole Lengths
–
–
𝒍𝑸𝟏 = 𝒍𝑸𝟑 = 𝟐 × 𝒍𝟒 − 𝑳∗
𝒍𝑸𝟐 = 𝟐 × 𝒍𝟑 −
𝒍𝑸𝟑
𝟐
𝒅
−𝒅
𝒍𝟏
• Thick lens PyMadX
–
–
–
Scan smaller area determined by fast scan
Match accurately using MadX
Work out stay clear using aperture module
Exploration of the Triplet Parameter Space, 7th November 2016
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𝒍𝟐
𝒍𝟑
𝒍𝟒
𝑳∗
Python Script
Set total length and fix required beam stay clear, β*, L*, gaps and shielding
Use PyMadX for small scan of accurate beam stay clear using current
shielding (12 × 25 resolution)
Find setup with largest beam stay clear
If beam stay clear larger than required
Plot ideal setup and output lengths + strengths
Exploration of the Triplet Parameter Space, 7th November 2016
6
Increase total length
Determine sensible range 𝑔 ± 0.005, 𝑙4 −2% + 8%
If beam stay clear smaller than required
Use fast FOM to scan large range in parameter space
First attempt 70 m (12 𝝈, 𝜷∗ = 𝟎. 𝟑, 3 m gaps)
Exploration of the Triplet Parameter Space, 7th November 2016
7
Optimising shielding
Set required β*, L* and
use initial shielding
Integrate and match into
machine for further studies
Exploration of the Triplet Parameter Space, 7th November 2016
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Use code to
find shortest
setup with
good beam
stay clear
Use this
setup for
radiation
studies of
triplet
Change
shielding
accordingly
Work out
shielding
required for
this setup
Comparison to baseline
Ilaria. Dose in nominal
triplet (FCC week 2016)
Exploration of the Triplet Parameter Space, 7th November 2016
9
Constraints
Parameter
Baseline
Final Design
Space Between Magnets
10 m
2m
𝜷∗
0.3 m
0.3 m
𝑳∗
45 m
45 m
Peak dose profile, per 3000 fb-1
< 15 MGy
< 15 MGy
Beam Stay Clear
40 σ
15.5 σ
Exploration of the Triplet Parameter Space, 7th November 2016
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JAI Nov 2016 Triplet
Parameter
Baseline
Final Design
Space Between Magnets
10 m
2m
𝜷∗
0.3 m
0.3 m
𝑳∗
45 m
45 m
Peak dose profile, per 3000 fb-1
< 15 MGy
< 15 MGy
Beam Stay Clear
40 σ
15.5 σ
Shielding
15 mm
24.2 mm
Triplet Length
138.5 m
95 m
(of which is quadrupoles)
108.5 m
89 m
Exploration of the Triplet Parameter Space, 7th November 2016
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Comparison
Exploration of the Triplet Parameter Space, 7th November 2016
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Comparison
1600
1800
Wy 45
Wy 45 New
1400
1600
Wx 45
Wx 45 New
1400
1200
Wx
Wy
1200
1000
1000
800
800
600
600
400
200
400
0
0
20000
40000
60000
80000
100000
0
S (m)
Exploration of the Triplet Parameter Space, 7th November 2016
20000
40000
60000
S (m)
13
80000
100000
Comparison
Ilaria. Dose in
nominal triplet
(FCC week 2016)
Exploration of the Triplet Parameter Space, 7th November 2016
14
Conclusions
• Wrote up an algorithm that helps find
the optimum triplet layout for a set of
constraints
• Designed optics in collaboration with
radiation studies
• Used this to come up with an
alternative design
• In future we can use this to quickly
find new designs satisfying
requirements
Exploration of the Triplet Parameter Space, 7th November 2016
15
Thank you!
Different Shielding
12 σ
Exploration of the Triplet Parameter Space, 7th November 2016
16 σ
17
19 σ
Different Shielding
Exploration of the Triplet Parameter Space, 7th November 2016
18
Chromaticity
•
𝝏𝑸
𝝏𝜹
=
𝟏
𝟒𝝅
𝜷 𝒔 𝒌 𝒔 𝒅𝒔
– Larger 𝜷 and longer quads cause higher
chromaticity
– Larger L* forces 𝜷 to be larger and
needs stronger focusing
– Higher chromaticity requires more
correction and takes more space
– Try and keep triplet as short as possible
Exploration of the Triplet Parameter Space, 7th November 2016
19
W functions for different L*
2500
Wx 36
Wx 45
Wx 61
Wx
2000
1500
1000
500
0
0
20000
40000
60000
S (m)
Exploration of the Triplet Parameter Space, 7th November 2016
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80000
100000
Aperture as a function of strength
• So far assumed
constant
maximum
strength:
ap. R
(mm)
50
60
70
80
90
100
110
120
130
– 𝑟𝑎𝑝𝑒𝑟𝑡𝑢𝑟𝑒 =
𝐵𝑀𝐴𝑋
𝑔
=
11 T
𝑔
• Received an
email by Daniel
Schoerling
about the cold
bore
Exploration of the Triplet Parameter Space, 7th November 2016
21
w
(mm)
25
28
33
35
38
40
43
45
48
G
(T/m)
193
166
149
133
120
110
102
94
88
140
Accurate Aperture
B/g Aperture
Apperture (mm)
120
100
80
60
40
80
100
120
140
160
Gradient (T/m)
Exploration of the Triplet Parameter Space, 7th November 2016
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180
200
-2.0
Log(Aperture/m)
-2.2
Equation
y = a + b*x
Weight
Residual
Sum of
Squares
Pearson's r
No Weighting
Adj. R-Squar
5.6075E4
-0.99967
0.99924
Value
Log(Aperture Intercept
/m)
Slope
-2.4
Standard Err
3.40813
0.05738
-1.2152
0.01188
-2.6
-2.8
-3.0
4.4
4.6
4.8
5.0
Log(Gradient/T/m)
Exploration of the Triplet Parameter Space, 7th November 2016
23
5.2
5.4
Model
• In future uses of my code I can
update the aperture calculations
• 𝐴 = 𝑒 𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑔𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡 = 29.96𝑔−1.215 m
• Difference not significant to change
previous designs
• Previous designs probably discarded
when iterating with Jose
Exploration of the Triplet Parameter Space, 7th November 2016
24
140
Accurate Aperture
B/g Aperture
Model
Apperture (mm)
120
100
80
60
40
80
100
120
140
Gradient (T/m)
Exploration of the Triplet Parameter Space, 7th November 2016
25
160
180
200