1. On The Geometry of the HEC Readout Channels Local HEC coordinate system Readout families Readout channels Volumes and geometrical centers Neighbors Michel Lefebvre University of Victoria Physics and Astronomy 15 August 2003

2. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels2 The ideal (pointing) ATLAS coordinate system The , ,  and  quantities for a point in the ideal (pointing) ATLAS coordinate system are defined in the usual way.  Using a cylindrical coordinate system, we obtain the following relations: z y x

3. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels3 HEC module geometry in  -z plane at middle  this drawing is in the plane of the middle  of a HEC module and shows the 7 readout families and the  boundaries passing through the pad  boundaries at the middle z of readout families z

4. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels4 HEC readout families 1 234567 not to scale!

5. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels5 HEC readout layers (or depths) 1 234 not to scale!

6. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels6 HEC readout channel geometry parameters For the beam test analysis, the HEC readout channel geometry parameters are kept in a file, available from http://particle.phys.uvic.ca/~web-atlas/atlas/hec-emec/geometry/ http://particle.phys.uvic.ca/~web-atlas/atlas/hec-emec/geometry/ It contains HEC readout channel “median” coordinates in the ideal (pointing) ATLAS coordinate system: These quantities do not in general denote the geometrical center of a readout channel. Rather, we have

7. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels7 Readout families and readout channels A readout channel is composed of either one or two readout families (denoted a and b in order of increasing z) The z position of the middle of a family (z F ) and the z width of a family (  z F ) are related to the readout channel parameters:

8. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels8 Pseudorapidity limits In the HEC, the pseudorapidity limits of a readout family refer to the middle  of a module and to the middle z (z F ) of a family  there are seven HEC readout families in ATLAS, 5 only in the 2002 combined beam test.  Consider the following schematic (not to scale!) of a HEC family in the  -  plane; middle  of module

9. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels9 Readout family  limits The  limits of a readout family refer to the middle  of a module middle  of module 11 22

10. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels10 Readout family volume and geometrical center First consider the  = 2  /64 readout channels (   2.5)  From elementary geometry we obtain geometrical center of this channel where The ± depends on which side of the module middle  plane the channel is

11. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels11 Readout family volume and geometrical center Second consider the  = 2  /32 readout channels (   2.5)  From the previous results we obtain where

12. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels12 Readout channel volume and geometrical center In the case of readout channels with one family, we use the results obtained for that family In the case of readout channels with two families, we weigh each family by their volume  From the previous results we obtain where

13. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels13 Readout channel volume The following readout channel volumes are obtained 2002 HEC-EMEC beam test configuration. The numbers refer to the channel numbers for this beam test

14. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels14 Readout channel geometrical center  The median center can be a few cm away from the geometrical center, the difference is (almost completely) in z 2002 HEC-EMEC beam test configuration. The numbers refer to the channel numbers for this beam test No difference in z for layer 1 since all the channels are composed of only one family. This is also the case for the lowest eta channels in layer 3

15. M. Lefebvre, 15 August 2003On the geometry of the HEC readout channels15 Readout channel neighbors The pseudo-pointing nature of the HEC channels lead to peculiarities in the list of neighbors for a channel  Consider three target channels (blue) and their touching neighbors (red) 2002 HEC-EMEC beam test configuration. The numbers refer to the channel numbers for this beam test Notice these are not touching neighbors, as would be obtained if only eta indices were considered