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

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 2

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:

cossincot

xyz

z

y

x

2 2 2

2 2 2cos

tan

x yz

x y zyx

12ln tan

2arctansinh cotcosh cosectanh cos

e

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 3

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

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 4

HEC readout families

1 2 3 4 5 6 7

not to scale!

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 5

HEC readout layers (or depths)

1 2 3 4

not to scale!

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 6

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/

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

(in radians) (in cm), , , z z

1 12 2

1 12 2

1 12 2

,

,

,

z z z z z

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 7

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 (zF) and the z width of a family (zF) are related to the readout channel parameters:

14

14

z

z z z

z z

F

for channels with one family

family afor channels with two families

family b

12

zz

z

F

for channels with one family

for channels with two families

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 8

Pseudorapidity limits In the HEC, the pseudorapidity limits of a readout family refer to the middle of a module

and to the middle z (zF) 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;

z zst

F

corresponds to only

for the 1 HEC readout layer!

middle of module

12sinh

z

F

1

12sinh

z

F

2

F planez z

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 9

Readout family limits

The limits of a readout family refer to the middle of a module

1

F

12

cm family 1 at high boundary

cm families 1 at high boundary

other families

37.20

47.50

sinh

z

2 F

12

cm families at low boundary

other families

203.00

sinh

z

middle of module

12

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 10

Readout family volume and geometrical center First consider the = 2/64 readout channels ( 2.5)

From elementary geometry we obtain

2

64

c geometrical center of this channel

1

2c

c c c

c c c

c F

cossin

xyz z

where

2 21F 2 12 tanV z

2 21 1 2 2

c c1 2

1c c 2

2sec

3

1c 2

21c 4

tan tan

sec 1 tan

The ± depends on which side of the module middle plane the channel is

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 11

Readout family volume and geometrical center Second consider the = 2/32 readout channels ( 2.5)

From the previous results we obtain

c c c

c c c

c F

cossin

xyz z

where

2 2 1F 2 1 2tanV z

2 21 1 2 2

c1 2

c

2

3

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 12

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

a b

c a a b b

V V Vr r r

a ba b a 1V V

V V

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 13

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

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 14

Readout channel geometrical center

The median center can be a few cm away from the geometrical center, the difference is (almost completely) in z

c c c0.009 0.0015 3.7 cmz 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

M. Lefebvre, 15 August 2003 On the geometry of the HEC readout channels 15

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