1. S. M. Gibson, IWAA7 November 2002 1 ATLAS Group, University of Oxford, UK S. M. Gibson, P. A. Coe, A. Mitra, D. F. Howell, R. B. Nickerson Geodetic Grids for the continuous, quasi real time alignment of the ATLAS Semiconductor Tracker

2. S. M. Gibson, IWAA7 November 2002 2 Overview Motivation – the alignment of ATLAS The ATLAS SCT alignment system Demonstration system Square Grid Tetrahedral Grid Large grids for ATLAS Grid simulations Check with FEA

3. S. M. Gibson, IWAA7 November 2002 3 Motivation – the alignment of ATLAS Inner detector: Physics requires shape variations to be measured to <10  m 7m

4. S. M. Gibson, IWAA7 November 2002 4 Solution – FSI geodetic grids Barrel SCT grid Forward SCT grid SemiConductor Tracker monitored using a geodetic grid of 800 length measurements.

5. S. M. Gibson, IWAA7 November 2002 5 The ATLAS SCT alignment system Frequency Scanning Interferometry (as shown earlier) will be used to simultaneously measure all lines of sight in the geodetic grids. Benefits:  Continuous alignment during ATLAS operation.  An understanding of the detector shape on day one of physics.  Corrections of short time scale motions that degrade track-based alignment.  Corrections of complex distortions, that cannot be corrected with tracks alone.

6. S. M. Gibson, IWAA7 November 2002 6 Alignment system layout Surface building ground level ATLAS cavern Fibre Splitter Tree Crate APD read out crate Detector Cavern ATLAS SCT grid of 800 grid-line- interferometers Equipment Cavern Lasers Reference Interferometer System Surface building fibre coupling optics

7. S. M. Gibson, IWAA7 November 2002 7 Demonstration System ‘equipment cavern’ ‘detector cavern’ Splitter Tree and APD readout box 250mm Fibres Power Square Grid

8. S. M. Gibson, IWAA7 November 2002 8 Demonstration system: Square Grid 6 simultaneous length measurements made between four corners of the square. +7th interferometer to measure stage position. Displacements of one corner of the square can then be reconstructed.

9. S. M. Gibson, IWAA7 November 2002 9 Square Grid

10. S. M. Gibson, IWAA7 November 2002 10 Model Degrees of Freedom Node A defines the origin Node B defines the X axis Node C is free in X and Y Node D is free in X and Y

11. S. M. Gibson, IWAA7 November 2002 11 Node Reconstruction A B C D 1m1m 1m1m 50  m 1m1m Node A Node B Node D Node C

12. S. M. Gibson, IWAA7 November 2002 12 Reconstruction of Jewel C Translation (Square Grid) Std Dev = 400 nm

13. S. M. Gibson, IWAA7 November 2002 13 Square Grid Tetrahedral Grid Jewel C raised up by 100mm Now sensitive to Z coordinate, allowing three dimensional coordinate reconstruction

14. S. M. Gibson, IWAA7 November 2002 14 Node C Three Dimensional Coordinate Reconstruction (Stationary Stage) RMS scatter = 640nm

15. S. M. Gibson, IWAA7 November 2002 15 Node C Three Dimensional Coordinate Reconstruction (Stage translated in X)

16. S. M. Gibson, IWAA7 November 2002 16 Reconstruction of Jewel C Translation (Tetra Grid)

17. S. M. Gibson, IWAA7 November 2002 17 Grids for ATLAS The grid for ATLAS will contain eight hundred lines of sight in a complex geometry. A quarter of the Barrel grid: One of the two Endcap grids: The error propagation through these grids has been simulated.

18. S. M. Gibson, IWAA7 November 2002 18 Barrel Grid Simulations Lines of sight for one quadrant of Alignment Grid FEA model of carbon fibre support structure 70 35  m0m0m Simulgeo ref1 model of Alignment Grid nodes (jewels) ASSUME: end flanges are rigid rings & central jewels constrained in rotation Z X Y

19. S. M. Gibson, IWAA7 November 2002 19 Single Barrel Grid Simulation Results NB: rigid end flanges assumed – currently repeating with increased number of degrees of freedom. 1 micron precision assumed throughout. Fixed inner barrel. Central jewels constrained in rotation Result without radial lines

20. S. M. Gibson, IWAA7 November 2002 20 FEA model of SCT structure Barrel SCT is normally supported at four points

21. S. M. Gibson, IWAA7 November 2002 21 Torsional behaviour: 4 point to 3 point support Loss of contact with this point

22. S. M. Gibson, IWAA7 November 2002 22 Future work: Cross-check of Grid Simulations Take FEA model of perfect barrel  Extract lengths from geodetic grid  (add random errors to lengths)  Pass to reconstruction software for calibration of model Distort FEA model eg, twist and/or multipole distortions  Extract new lengths  (add random errors to lengths)  Pass to reconstruction software  Reconstruct nodes co-ordinates and compare with those in FEA model Compare with predicted errors

23. S. M. Gibson, IWAA7 November 2002 23 Conclusions A novel alignment system, based on FSI, is under construction for the ATLAS SCT. Prototype geodetic grid nodes can be reconstructed to well within the ATLAS requirements (<1ppm). Error propagation through the final SCT grid has been simulated. Future work: cross-check simulations using distorted FEA models. References ref1 used with kind permission of the author: L. Brunel, ‘SIMULGEO: Simulation and reconstruction software for opto- geometrical systems’, CERN CMS Note 1998/079.