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

Index FCC Layout Coordinates and Alignment Simulations Tools Error Sources Case A: 10.5 km Case B: 5 km Comments Nerea Ibarrola | 07.12.2016 | 1

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 2499731 1108403 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 Nerea Ibarrola | 07.12.2016 | 2

Coordinates and Alignment Surface Network Surface-Tunnel transfer Alignment X-Y Z Underground Network X Y 214.755 m 53.7 m Nerea Ibarrola | 07.12.2016 | 3

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 - 10.5 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, 0.015mm + 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 10 + 1 stations GYRO 3+1 stations ANGL 10+1 stations DIST 6 stations 5+1 stations Nerea Ibarrola | 07.12.2016 | 4

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. Nerea Ibarrola | 07.12.2016 | 5

Error Sources Non considered in the simulations… Inhomogeneous field of atmospheric air temperature gradients Humidity and air currents Fumes Dust rock Darkness Shocks Vibrations Nerea Ibarrola | 07.12.2016 | 6

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 + 214.8 m between stations Gyro station every 4 points 1074 m L R Gyro 5 m 5+1 stations 6 stations Station every 2 points + 107.4 m between stations Gyro station every 6 points + 322.2 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 + 322.2 m between stations 1074 m L R 6 stations 4 stations Nerea Ibarrola | 07.12.2016 | 7

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 6 stations ANGL 11 stations DIST 11 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 + 558 stations ANGL +1024 stations DIST +1024 stations * Fixed orientation Nerea Ibarrola | 07.12.2016 | 8

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 | 07.12.2016 | 9

Case A: 10.5 km Max & min differences + error ellipse MAX & MIN X differences Point NetR134 Dxmax = 8.94 mm Dxmin = -7.73 mm Dymax = 11.66 mm Dymin = -11.9 mm Dxmean = -0.01 mm Dymean = 0.20 mm Sx = 2.59 mm Sy = 3.08 mm MAX & MIN Y differences Max & min differences + error ellipse Standard deviation If 100 simulations -- Max diff= 22.72 (DYmax= 10.14mm, DYmin= -12.58 ), same SX SY, same relative error If ANGL 1.5cc – SAME SHAPE- MAX DIFF Net134- 21.57mm (10.27, -11.3 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 Nerea Ibarrola | 07.12.2016 | 10

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 2499731 1108403 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 Nerea Ibarrola | 07.12.2016 | 11

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 | 07.12.2016 | 12

Case B: 5 km Max & min differences + error ellipse Standard deviation MAX & MIN X differences Point NetR52 Dxmax = 4.88 mm Dxmin = -5.79 mm Dymax = 7.86 mm Dymin = -8.02mm Dxmean = 0.03 mm Dymean = 0.15 mm Sx = 1.63 mm Sy = 2.29 mm MAX & MIN Y differences Max & min differences + error ellipse Standard deviation NetR52 Nerea Ibarrola | 07.12.2016 | 13

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 = 8.94 mm Dxmin = -7.73 mm Dymax = 11.66 mm Dymin = -11.9 mm Dxmean = -0.01 mm Dymean = 0.20 mm Sx = 2.59 mm Sy = 3.08 mm Point NetR52 Dxmax = 4.88 mm Dxmin = -5.79 mm Dymax = 7.86 mm Dymin = -8.02mm Dxmean = 0.03 mm Dymean = 0.15 mm Sx = 1.63 mm Sy = 2.29 mm Nerea Ibarrola | 07.12.2016 | 13

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 Nerea Ibarrola | 07.12.2016 | 14