1. FCC Underground Network Simulations
Nerea Ibarrola
EN/ACE-SU
CERN, 07 December 2016

2. Index FCC Layout Coordinates and Alignment Simulations Tools
Error Sources
Case A: 10.5 km
Case B: 5 km
Comments
Nerea Ibarrola | | 1

3. Slope Direction y-y (%)
FCC Layout
FCC intersecting 100 km layout
Option
Elevation (mASL)
Azimuth
Slope Angle x-x (%)
Slope Direction y-y (%)
Centroid X
Centroid Y
100km quasi-circular
261
-20
0.65
Accum. Dist. (m)
Shaft Depth (m) A
304 B
4900
266 C
14500
257 D
25000
272 E
35500
132 F
45100
392 G
50000
354 H
54900
268 I
64500
170 J
75000
315 K
85500
221 L
95100
260
100000
Distance (m)
A-B
4900
B-C
9600
C-D
10500
D-E
E-F
F-G
G-H
H-I
I-J
J-K
K-L
L-A
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4. Coordinates and Alignment
Surface Network
Surface-Tunnel
transfer
Alignment
X-Y Z
Underground Network X Y m
53.7 m
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5. Simulations Goal - alignment of the machine FCC-hh : 150 μm -> LHC
FCC-ee : 17 μm > CLIC
Alignment precision requirements
Simulations – Planimetry.
Radial– most critical parameter
Straight section km in length
196 reference points
Point spacing of 53.7 m
Design of the measurements configuration
station every 2, 3, 4 points, different combinations
Precision of the instrument-
Horizontal angles (1.5cc, 3cc, 5cc)
Distances (0.5mm, 1mm + 2ppm, mm + 6ppm)
Orientation (8cc)
All the points must be well control
checking of statistical parameters after calculation of the geodetic network
Distances & Horizontal angles
Horizontal angles
Gyro measurements
Distances
stations
GYRO stations
ANGL stations
DIST 6 stations
5+1 stations
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6. Tools LGC v2 - New version of LGC (Logiciel Général de Compensation).
LGC is an essential tool for processing geodetic networks at CERN. It can carry out calculations with all the different kind of measurements used at CERN.
New version:
Better maintainability an arbitrary stack of local Cartesian.
More instrument and target parameters into account.
Systematic and random errors of instruments and targets.
Better control of the error propagation.
Sophisticated setups using local frames.
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7. Error Sources Non considered in the simulations…
Inhomogeneous field of atmospheric air temperature gradients
Humidity and air currents
Fumes
Dust rock
Darkness
Shocks
Vibrations
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8. Error Sources
5 m
6 m
Effect of lateral refraction - The zig-zag traverses and reciprocal gyro-azimuths will ameliorate the refraction problem.
Even a very small lateral temperature gradient can produce a severe error if it prevails over the length of a line-of-sight.
Distances & horizontal angles
Station every 4 points
m between stations
Gyro station every 4 points
1074 m L R
Gyro
5 m
5+1 stations
6 stations
Station every 2 points
m between stations
Gyro station every 6 points
m between stations
1074 m L R
9+1 stations
4 stations
Station every 4 points
214.8 m between stations
Gyro station every 6 points
m between stations
1074 m L R
6 stations
4 stations
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9. Case A: 10.5 km In +1km … In 100 km… Station every 2 points
107.4 m between stations
Gyro station every 4 points
214.8 m between stations
GYRO stations
ANGL stations
DIST stations
1074 m
In 100 km…
Station every 2 points
4 observations from each station (2 forward, 2 backward)
Gyro station every 4 points
8 observations from each station (4 forward, 4 backward)
ANGL - station every 2 points – 3cc
DMES - station every 2 points – 0.5mm
ORIE - station every 4 points – 8cc
GYRO stations
ANGL stations
DIST stations
* Fixed orientation
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10. Case A: 10.5 km Y X MAX & MIN X differences - LONGITUDINAL
Number of Simulations: 1000
Number of points: 196
Fixed orientation (first to last point)
Number of observations: 1173
ANGL - station every 2 points – 3cc
DMES - station every 2 points – 0.5mm
ORIE - station every 4 points – 8cc
MAX & MIN Y differences - TRASVERSAL
Nerea Ibarrola | | 9

11. Case A: 10.5 km Max & min differences + error ellipse
MAX & MIN X differences
Point NetR134
Dxmax = mm
Dxmin = mm
Dymax = mm
Dymin = mm
Dxmean = mm
Dymean = mm
Sx = mm
Sy = mm
MAX & MIN Y differences
Max & min differences + error ellipse
Standard deviation
If 100 simulations Max diff= (DYmax= 10.14mm, DYmin= ), same SX SY, same relative error
If ANGL 1.5cc – SAME SHAPE- MAX DIFF Net mm (10.27, mm), SX =2.60 SY=3.05 (at NetR134) - relative error SIGMA R= 0.36mm
If GYRO station every 2 points - SIMILAR VALUES – Simulations with fixed orientation
NetR134
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12. Slope Direction y-y (%)
FCC layout
FCC intersecting 100 km layout
Option
Elevation (mASL)
Azimuth
Slope Angle x-x (%)
Slope Direction y-y (%)
Centroid X
Centroid Y
100km quasi-circular
261
-20
0.65
Accum. Dist. (m)
Shaft Depth (m) A
304 B
4900
266 C
14500
257 D
25000
272 E
35500
132 F
45100
392 G
50000
354 H
54900
268 I
64500
170 J
75000
315 K
85500
221 L
95100
260
100000
Distance (m)
A-B
4900
B-C
9600
C-D
10500
D-E
E-F
F-G
G-H
H-I
I-J
J-K
K-L
L-A
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13. Case B: 5 km Y X MAX & MIN X differences - LONGITUDINAL
Number of Simulations: 1000
Number of points: 95
Fixed orientation (first to last point)
Number of observations: 565
ANGL - station every 2 points – 3cc
DMES - station every 2 points – 0.5mm
ORIE - station every 4 points – 8cc
MAX & MIN Y differences - TRASVERSAL
Nerea Ibarrola | | 12

14. Case B: 5 km Max & min differences + error ellipse Standard deviation
MAX & MIN X differences
Point NetR52
Dxmax = mm
Dxmin = mm
Dymax = mm
Dymin = mm
Dxmean = mm
Dymean = mm
Sx = mm
Sy = mm
MAX & MIN Y differences
Max & min differences + error ellipse
Standard deviation
NetR52
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15. Case A vs Case B 10.5 km 5 km Max & min differences + error ellipse
MAX & MIN Y differences
Max & min differences + error ellipse
Point NetR134
Dxmax = mm
Dxmin = mm
Dymax = mm
Dymin = mm
Dxmean = mm
Dymean = mm
Sx = mm
Sy = mm
Point NetR52
Dxmax = mm
Dxmin = mm
Dymax = mm
Dymin = mm
Dxmean = mm
Dymean = mm
Sx = mm
Sy = mm
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16. Comments Goal - alignment of the machine FCC-hh : 150 μm -> LHC
FCC-ee : 17 μm > CLIC
All the points are well control
Angular and distance observations
Dmax and Dmin values change depending on the number of simulations
Results depend on the precision achieved by the instrument:
- kind of instrument
- distance from station to observed point
- conditions during the data collection
1 extra shaft in a 10.5 km in length section – minimize differences up to:
± 2.5 mm in X
± 4 mm in Y
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