LiCAS Simulation Based on: Simulation of the LiCAS survey system for the ILC by G. Grzelak¤, A. Reichold+, J. Dale+, M. Dawson+, J. Green+, Y. Han+, M. Jones+, G. Moss+, B. Ottewell+, R. Wastie+, D. Kamptner#, J. Prenting#, M. Schlosser# ¤University of Warsaw, +University of Oxford, #DESY, Hamburg Presented at the 9th INTERNATIONAL WORKSHOP ON ACCELERATOR ALIGNMENT, IWAA-2006 Stanford Linear Accelerator Center, September 25-29, Catherine LeCocq SLAC 04/05/07

LiCAS Overview LiCAS Instrumentation One laser line per train: 4 CCD cameras per car Internal FSI: 6 laser lines per train, 6 retro-reflectors per car One clinometer per car External FSI: 6 laser lines per car shooting to wall marker

Methodology Start with the 3 graphs shown in Figure 4 of the paper TH007 presented at IWAA06 Build a geometrical model Compare to the SIMULGEO results for the wall markers, presented in Figure 3 Compare to the “Random Walk Model” presented in paragraph 3.1

Single Train – Cars Sigma Train Coordinate System –Z axis Internal FSI with Car 0 as origin Internal FSI gives Z of following cars The clinometer on the car gives R Z The 4 CCDs in the car give X and Y of the car as well as R X and R Y

Single Train – Markers Sigma Train Coordinate System to Car Coordinate System: (u,v,w) are the coordinates of the marker in the car coordinate system. They can been obtained from the 6 external FSI measurements of the car.

Single Train – Markers Sigma Because car 0 is the origin of the train coordinate system, the coordinates of marker 0 are simply the derived observations (u,v,w). Using the appropriate graph gives: First approach, no correlation between (u,v,w). The sigma on the v measurement is very close to the value obtained by calculating the average of 6 FSI measurements at 1µm (0.41 vs 0.45)

25 Markers MATLAB Simulation

135 Markers MATLAB Simulation

Where To Go From Here Confirm the internal geometry of the train and the derived a-priori standard deviations. Obtain a detailed description of the external FSI system to complete the error model for the derived observations (u,v,w). Introduce systematic errors in the external FSI system for each car of the train.

IWAA Paper Extracts

Schematic layout of the LSM CCDs