**APPENDIX**

# **APPENDIX** {#appendix .unnumbered}

**Construction Of The Idealized COCOA Simulation Model**

The choice in labeling conventions used to specify objects and
parameters throughout this document is generally consistent with
commonly accepted naming conventions within CMS. However, as COCOA is a
geometrical simulation, the complexity of the fitting routines and
modeling of complex geometries require that multiple local coordinate
systems be devised for many of the components used in the simulation.
Additionally, the EMU Alignment consists of several unique objects and
structures that are not found elsewhere in the CMS detector. This
appendix describes the labeling scheme used throughout this document as
well as the construction of the Idealized EMU simulation within COCOA.
It offers a very detailed examination of all components in the system as
well as the precise placement of the objects in the simulation.

## Definition of Chamber Labeling Scheme in CMS

As discussed previously, the Endcap Muon System is comprised of 4 Muon
Endcap (ME) discs of Cathode Strip Chambers (CSCs) separated by the YE()
Return Field (RF) Iron disks. The RF iron acts as the principle
mechanical support for the CSCs, absorber for incident particle showers,
and a return for the large magnetic flux leaving the central solenoid.
The CSCs on each of the ME 2, 3, and 4 disks are placed into an inner
ring of 18 20-degree and outer ring of 36 10-degree chambers. The ME 1
rings 1,2, and 3 are composed of 36 10 degree chambers.

The location of a particular CSC in CMS is specified by a three digit
number denoting the ME disc, whether it is in the inner or outer ring of
chambers, and the chamber position on the ring. By convention, the ME
discs are label in order of their placement from the interaction point,
with the nearest disc in the + Endcap designated as ME +1 and the
nearest disc to the interaction point in the - Endcap designated as ME
-1. The two rings of chambers comprising a ME 2, 3, or 4 disc are
labeled 1 for the inner ring and 2 for the outer ring. The final number
specifying the ring position of a particular chamber is determined by
simply counting the number of chambers from the X(global CMS) = 0 axis
as viewed from the interaction point. Counting is done in a clockwise
fashion for rings in the + Endcap and in a counter-clockwise fashion for
the - Endcap. The chamber intersecting the X (global CMS) = 0 axis is
counted as the first chamber in the ring. References to specific CSCs in
CMS might look like this: ME +2/2/1, ME -1/1/17, or ME 4/2/30. Figure
A.1 illustrates how this labeling scheme is employed for a particular ME
disc.

> ![](media/image1.jpeg){width="4.038888888888889in"
> height="4.113888888888889in"}

Figure A.1: Typical ME Layout. Drawing of ME2, as viewed from
interaction point, with proper labeling of CSC chambers. \[A.1\]

### Local Definition of Cathode Strip and Anode Wire Planes

The naming and numbering convention used to describe the location of
cathode strips and anode wires and has been described in CMS Internal
Note 2000/004. This convention has been adopted for the present
simulation/reconstruction scheme.

The Cathode Strip Chambers are composed of seven trapezoidal honeycombed
panels separated by small gaps. All panels except the middle panel are
milled with cathode strips running the length of the panel on their
inner faces while the gaps between the panels are spanned by anode wires
which transverse the panel width (See Figure A.2, below).

![](media/image2.jpeg){width="3.9340277777777777in"
height="2.3520833333333333in"}

Figure A.2: Cross Section of Six Layer Cathode Strip Chamber. Dimensions
in mm. \[A.2\]

The design of the CSC chambers calls for all cathode strip readout
electronics to be mounted on the outside surface of one of the chamber
faces. For a single chamber, the labeling scheme designates the chamber
face on which these electronics are mounted as the top layer and the
nearest cathode strip plane to this face as the first strip plane.
Individual strips in the planes are number are numbered from left to
right (1 to *n*) when the top of the chamber is viewed from the smaller
to larger end of the trapezoid. Anode wire planes are designated in a
manner identical to that of the cathode strip planes, while the
numbering of individual anode wires in a plane increases as from the
smaller to larger end of the trapezoid (1 to n). Figure A.3 illustrates
the labeling scheme.

![](media/image3.jpeg){width="5.595833333333333in" height="4.3in"}

Figure A.3: Single Cathode Strip Chamber Labeling Scheme

### Global Orientation of Cathode Strip and Anode Wire Planes

Chambers placed in the + Endcap are mounted on the YE iron planes such
that the first plane of cathode strips is nearest the interaction point
for ME1 and ME2 chambers and furthest from the interaction point for ME3
and ME4 chambers. This arrangement means the numbering of cathode strips
in the +Endcap increases with for ME1 and ME 2 while decreasing with for
ME3 and ME4. In the - Endcap, the positioning of the first plane of
cathode strips for all chambers is identical to the + Endcap. However,
since the chambers are positioned on the opposite side of the
interaction point, the numbering of cathode strips in the -Endcap
decreases with in ME-1 and ME-2 while increasing with for ME-3 and ME-4.

## Development of COCOA Simulation and Definition of Simulated Objects

To optimize the development of Endcap simulations in COCOA, it was
decided to compose the simulated Endcap solely from objects arranged in
a 'parent-child' relationship. This means that relatively simple
collections of objects already defined in COCOA can be placed together
to compose more complex objects. In this scheme, two DCOPS sensors can
be arranged in a local coordinate system to define a CSC chamber (Figure
A.3). Four CSC chambers, in turn, are arranged to form a SLM line, three
SLM lines are arranged to form an Muon Endcap (ME) layer, and six ME
layers are assembled to form the entire CMS Endcap Muon system. The
modeling of components in this manner means that the location and
orientation of all the individual components (dowel pins, chamber active
reference centers, lasers, etc) does not need to be known in the general
CMS coordinate system beforehand. Rather, the spatial relationships
between parent and child objects can be specified directly from CMS
production drawings.

This method works very well for six of the Muon Endcaps (ME2, 3, and 4
Endcaps), however the unique construction of the inner most Endcaps
(ME 1) requires a somewhat less symmetric approach, as SLM lines do not
traverse the ME discs and a Secondary Laser Line must be introduced. For
this reason, the modeling of the ME1 Endcaps will be addressed
separately.

The extraction of the information necessary to define these
relationships from CMS production drawings involved several steps and
was not a simple exercise of comparing two points in a single drawing.
For this reason, the assignment of errors in the simulated system will
be addressed separately.

### Digital CCD Optical Position Sensor (DCOPS) Sensors

The Digital CCD Optical Position Sensor (DCOPS) is composed of 4 single
array CCDs arranged in an open frame and connected to a control circuit
fitted with an on board ADC and DSP chip. As the beam of a cross hair
laser falls incident on the DCOPS, the intersection of each leg of the
laser and CCD results in the accumulation of charge across the CCD pixel
array. The mean of the charge distribution on the array can be extracted
with a simple fit. By knowing the size of the each pixel comprising the
array, the distance between the first pixel in the array and the center
of the intersecting crosshair leg (taken to be the mean of the charge
distribution) is determined. The first active pixel in each CCD array is
referenced to the slot base of the DCOPS mounting structure on a
specially designed calibration bench. This calibration then references
the CSC strips to the laser lines.

The referencing of all CCDs to a common reference point on the sensor
allows for the location and orientation of the entire crosshair laser to
be inferred. Alternately, if the location and orientation of the
incident crosshair is already known, the charge distributions along the
pixel arrays can be used to track the position of the reference point
and orientation of the sensor. By monitoring two such reference points
and sensor orientations on each CSC chamber, the orientation and
position (transverse to the incident laser) of the chambers can be
deduced.

By convention, the local coordinate system of all DCOP sensors
originates at the common reference point to which the CCD pixel arrays
are calibrated. The axes of the local system are orientated such that
the +X axis runs away from the sensor aperture and the +Y axis runs
parallel to the sensor vertical (Figure A.4). The DCOPS sensor must be
carefully calibrated prior to use as a measurement device. Table A.1
shows a sample of what is required for the calibration of a typical
DCOPS sensor.

![](media/image4.jpeg){width="3.426388888888889in"
height="3.777083333333333in"}

Figure A.4: 3-D View of a DCOPS Sensor. The local right handed
coordinate system of the DCOPS is shown in red (Y axis runs vertically).
Calibration of the sensor is done by referencing of the first active
pixel in this local system. \[A.3\]

The initial simulation of DCOPS sensors in COCOA is based on production
drawings in which the midpoint of the active pixel arrays in the CCDs
are placed along the middle of the box frame.

Table A.1: Location of First Active Pixel of CCDs of a Typical DCOPS
Sensor in the Local DCOPS Coordinate System as Defined by Figure A.4.
Values followed by an asterisk (\*) denote a dimension which will
requires very precise calibration.

  ------------------- ------------------- --------------- ----------------
  **Component**       **Placement in                      
                      DCOPS Reference                     
                      Frame**                             

                      **X (mm)**          **Y (mm)**      **Direction of
                                                          CCD Vector**

  CCD 1 (Upper)       -36.829\*           65.75           +X

  CCD 2 (Right)       -8.171              57.579\*        -Y

  CCD 3 (Lower)       -36.829\*           20.75           +X

  CCD 4 (Left)        -45                 57.579\*        -Y
  ------------------- ------------------- --------------- ----------------

The CCD vector is determined to run as the direction of the increase in
pixel address across each linear array. This means the CCD vectors are
orientated in the DCOPS window frame to point toward the local +X and -Y
DCOPS axes.

### CSC Chambers

The Cathode Strip Chambers (CSC) in COCOA are defined solely in terms of
the relative position and orientation of DCOPS primary calibration pin
to the active center of the chamber (with the exception of ME 1/2 CSCs,
discussed later). Although determining the location and orientation of
the cathode strip planes is the ultimate goal of the reconstruction and
simulation, there is no need to reference the location of the strips in
the fitting routine since the relationship between the active center of
the chamber and the first strip position does not participate in any
direct measurement. Once COCOA has been employed to determine the
position and orientation of the chamber in CMS, the first strip position
can be immediately specified from prior calibration.

DCOPS sensors are referenced to the cathode strips by a series of
carefully constructed mounting plates and dowel pins. The definition of
CSCs in COCOA must contain at least two vectors to describe the location
of two DCOPS dowel pins. These vectors have been initially determined
from production CSC drawings and are locally referenced to the
'Reference Center' of the chambers. The Reference Center of the CSCs is
defined to lie on the plane of the first layer of strips and
transversely positioned as the average center point of all the
individual layers. Because successive layers of strips are offset by
half the strip width, the average center point will not lie on the
active center of the first strip layer. Figure A.5 shows a diagram of a
typical CSC chamber and the relationship between the cathode strip to
the geometrical and Reference center points. If the CSCs are perfectly
constructed, the Reference Point will lie on along the geometrical
center of each chamber and panel.

![](media/image5.jpeg){width="5.499305555555556in" height="4.175in"}

Figure A.5: Strip Layout and Reference Center Definition (definition of
active center)

The active center of a CSC forms the origin of a local right handed
chamber coordinate system. In this system (shown in Figure A.3 and
Figure A.5), when the chamber viewed from the top, the local Z axis
increases with the increase in anode wire number and the local X axis
increases with the decrease in cathode strip number. The position of the
primary calibration dowel pin and orientations of the CSC mounted DCOPS
in this system are given below in Table A.2. The positioning of the
DCOPS on the CSC chambers will fall on the left or right of the CSC
geometrical center line (shown in Figure A.5), depending on the location
of the chamber in CMS. Since these positions are symmetric about the
chamber centerline, and the DCOPS are to be defined solely by the
relative location and rotation of the primary calibration pins, it
becomes necessary to place some DCOPS on the chambers with additional
180 rotations. This has the consequence of destroying any generalization
of DCOPS orientations in the CMS, but it will maintain the symmetry of
the CSC chambers and simplify the installation of alignment hardware by
forcing the primary DCOPS alignment pin to always be positioned toward
the chamber center.

Table A.2: DCOPS Primary Dowel References and Sensor Orientations for
"Left Handed" CSCs. "Right Handed" CSCs differ by rotations of 180
degrees and have inverse X values. Dimensions are given with respect to
the CSC Reference Center in local chamber coordinates. Coordinates have
been extracted from CMS CSC production drawings (FNAL). ME ±1/2 chambers
have two LINK sensors and only a single DCOPS reference sensor and are
detailed in Table A.5.

  ------------- --------- ---------- ------------ ---------- ---------- ------------
  **Chamber**   **Inner                           **Outer               
                DCOPS**                           DCOPS**               

                **X       **Z (mm)** **Rotation   **X (mm)** **Z (mm)** **Rotation
                (mm)**               about Y                            about Y
                                     (°)**                              (°)**

  ME 2/2, 3/2,  19.922    1317.833   180 + 5      280.199    1657.151   180 + 5
  4/2                                                                   

  ME 1/3 Type 1 223.292   840.437    5            373.344    874.776    5

  ME 1/3 Type 2 354.790   840.437    5            504.842    874.776    5

  ME 2/1        272.081   -992.094   10           13.107     884.330    180 + 10

  ME 3/1        272.081   -892.145   180 +10      22.158     776.567    180 + 10

  ME 4/1        272.081   -792.603   10           12.931     677.112    180 + 10
  ------------- --------- ---------- ------------ ---------- ---------- ------------

Aside from placement of DCOPS sensors on the left or right side of the
CSC chambers, ME 2/1, 3/1, and 4/1 DCOPS placement differs slightly as
these chambers are different lengths (symmetry about the geometrical
center line is still maintained). The high degree of symmetry in the
construction of the CSC chambers means that the entire CMS Endcap system
can be modeled from four generic CSC chambers (Table A.2). Since each
CSC chamber can only be "Left Handed" or "Right Handed", there are eight
unique CSC chambers in the ME 1/3, 2, 3, 4 system.

### ME 2, 3, 4 Straight Line Monitoring (SLM) Line Layout

Placement of DCOPS sensors on the CSC chambers has been done in a way
which permits a line to be drawn parallel to a line drawn down the
center of the DCOPS sensor active areas across the CMS detector. To
avoid the beam pipe, the closest approach of this line to the CMS
detector Z axis is made at CMS R = 300 mm. These lines are designated as
Straight Line Monitor (SLM) Reference lines and denote the optimal
placement of DCOPS sensors in CMS. Furthermore, the CSC chambers and
DCOPS are orientated in a manner such that the CCD planes of the DCOPS
sensors are exactly perpendicular to these lines.

The construction of a simulated SLM lines in COCOA is done from four CSC
chambers (two left handed, two right handed), two crosshair lasers, and
two reference sensors (mounted on transfer plates) placed in a local SLM
coordinate system. The crosshair lasers are initially placed at opposing
ends of the local SLM X axis and orientated such that the center of the
crosshair beam coincides exactly with the SLM X axis. The reference
sensors (on the transfer plate) are placed facing the crosshair lasers
and offset so that the center of the DCOPS active area is on the SLM X=
0 axis with the DCOPS Y axis parallel to the SLM Y axis. The arrangement
of CSC chambers in ME2, ME-3, and ME-4 requires the SLM lines to be
constructed with left handed chambers along the +X SLM axis and right
handed chambers along the -X SLM axis. ME-2, ME3, and ME4 SLM layouts
have right handed chambers along the +X SLM axis and left handed
chambers along the -X SLM axis.

There are only two types of SLM lines in the CMS detector. Both SLM
lines have two left-handed and two right handed chambers and differ only
in which side of the +X SLM axis these chambers are placed. In practice,
there are also slight differences in the transfer plate assemblies due
to integration issues and space constraints. However, these differences
will not be important for the simulation or reconstruction of the system
in COCOA though they have been incorporated into the simulation.

Table A.3: Location and Orientation of CSC Chamber Centers Along all SLM
Lines in the CMS Detector. Dimensions are given with respect to the
local SLM coordinate system origin. Locations and orientations of
chambers in the + and - Endcap exhibit mirror symmetry about the CMS XY
plane. Coordinates have been extracted from CMS layout drawings.

  ------------------- --------------- ----------------- -----------------
  **Chamber**         **Chamber                         
                      Active Center**                   

                      **X (mm)**      **Z (mm)**        **Rotation about
                                                        Y (°)**

  ME 2/2,             5225.848        157.202           85

  ME 3/2, 4/2         5225.848        -157.202          95

  ME 2/1              2371.279        118.164           80

  ME 3/1              2469.704        -135.5275         100

  ME 4/1              2567.735        -152.813          100

  ME -2/2,            5225.848        -157.202          95

  ME -3/2, -4/2       5225.848        157.202           85

  ME -2/1             2371.279        -118.164          100

  ME -3/1             2469.704        135.528           80

  ME -4/1             2567.735        -152.813          80
  ------------------- --------------- ----------------- -----------------

The six Muon Endcap Station 2, 3, and 4 (ME 2, 3, 4) layouts are
composed of three identical SLM lines. The endpoints of the SLM lines
are designated as SLM reference points and numbered 1-6 starting with
the point closest to the +X CMS axis and moving clockwise as viewed from
the CMS Z = 0 interaction point (Figure A.6).

The placement of SLM lines and SLM Reference Points is the same for all
ME 2, 3, and 4 layers, though the orientation of chambers requires SLM
lines in layers ME 2, -3, and -4 to be flipped 180 degrees from the
otherwise similar ME -2, 3, and 4 SLM lines (see Table A.4). When the
SLM lines on these ME layers are constructed in this manner, the final
position and orientation of all CSC chambers, SLM lines, and SLM
Reference Points will overlap in the global CMS XY Plane. Coverage of
incident particles across R in the Endcaps is not compromised in this
arrangement since the overlapping of CSC chambers is accomplished within
individual ME layers.

![](media/image6.jpeg){width="4.1305555555555555in"
height="4.106944444444444in"}

Figure A.6: Detail of SLM Lines and SLM Reference Points 1-6 for ME 2
\[A.1\]

Table A.4: COCOA Position and Rotation of SLM Lines For All ME Stations.

+--------+-------+---------------+----------------+--------+--------+
| **ME   | **SLM | **COCOA       | **COCOA        | **Posi |        |
| L      | L     | Rotation**    | Rotation**     | tion** |        |
| ayer** | ine** |               |                |        |        |
|        |       | **About X     | **About Z      |        |        |
|        |       | (CMS) Axis**  | (CMS) Axis**   |        |        |
+--------+-------+---------------+----------------+--------+--------+
|        |       |               |                | **X    | **Y    |
|        |       |               |                | (      | (      |
|        |       |               |                | CMS)** | CMS)** |
+--------+-------+---------------+----------------+--------+--------+
| ME 2   | 1     | +90           | 15             | -7     | 28     |
|        |       |               |                | 7.6457 | 9.7777 |
| ME -3  |       |               |                |        |        |
|        |       |               |                |        |        |
| ME -4  |       |               |                |        |        |
+--------+-------+---------------+----------------+--------+--------+
|        | 2     | +90           | 255            | 28     | -7     |
|        |       |               |                | 9.7777 | 7.6457 |
+--------+-------+---------------+----------------+--------+--------+
|        | 3     | +90           | 135            | -2     | -2     |
|        |       |               |                | 12.132 | 12.132 |
+--------+-------+---------------+----------------+--------+--------+
| ME -2  | 1     | -90           | 15             | -7     | 28     |
|        |       |               |                | 7.6457 | 9.7777 |
| ME 3   |       |               |                |        |        |
|        |       |               |                |        |        |
| ME 4   |       |               |                |        |        |
+--------+-------+---------------+----------------+--------+--------+
|        | 2     | -90           | 255            | 28     | -7     |
|        |       |               |                | 9.7777 | 7.6457 |
+--------+-------+---------------+----------------+--------+--------+
|        | 3     | -90           | 135            | -2     | -2     |
|        |       |               |                | 12.132 | 12.132 |
+--------+-------+---------------+----------------+--------+--------+

### Muon Endcap Station 1 (ME 1) Layout

The chambers in the ME 1 layer are arranged into three rings rather than
two rings as in the ME 2, 3, 4 Endcaps. Each ring of chambers is
separated along the CMS Z axis. The inner ME 1/1 ring of chambers is not
within the scope of the EMU alignment proposal, however, the EMU
alignment system must reference ME 1/2 and 1/3 chambers to the tracker
coordinate system.

In the ME 1 Endcaps, the SLM line arrangement in ME 2, 3, and 4 Endcaps
cannot be duplicated due to the separation of the rings along the CMS Z
axis. The large amount of Iron behind the ME 1/1 chambers precludes SLM
laser lines from traversing the ME 1 disc. In this case, the outer
reference points for the SLM laser lines are defined by transfer plates
(as in the other ME layers) while inner reference points are provided by
the LINK Alignment Group.

As previously discussed, the Link Alignment System is charged with
transferring the tracker coordinate system to the Endcap and Barrel
Alignment Systems. The transfer is accomplished by a series of laser
lines that reference the tracker coordinate system to the six rigid MAB
structures. The primary Link laser lines that are used in this process
are split with a rhomboid prism to create a secondary Link laser line
that runs parallel to the primary laser line. This Secondary Link laser
line is then used to provide alignment to the ME 1/2 ring of chambers
and establish an inner reference for the ME 1 SLM lines. Figure A.7
shows the arrangement of the ME 1/2 and 1/3 chambers as well as the
location of the ME 1 SLM and Secondary Link laser lines.

![](media/image7.jpeg){width="5.99375in" height="6.055555555555555in"}

Figure A.7: ME 1 Chamber Arrangement and Placement of SLM and Secondary
Link Laser Lines. Overlap of MAB Structures is shown, though they do not
touch ME1. ME 1/1 chambers are not shown. Note SLM lines do not cross
the disc, but terminate at the edge of the ME1/2 rings. \[A.1\]

Since the secondary Link laser line is a beam and not a crosshair laser,
DCOPS sensors cannot be used to reference this laser line to the ME 1/2
chambers. The sensors employed to reference the secondary Link line to
the ME 1/2 chambers are two dimensional transparent sensors developed by
the Link group that employ photosensitive strips etched onto a highly
transparent glass substrate. Once these sensors determine the location
of the ME 1/2 chambers, a DCOPS sensor attached to the outer end of the
chamber can then be used as the endpoint of the SLM crosshair laser
line. Figure A.6 illustrates the arrangement of the Secondary Link laser
line and the inner SLM DCOPS reference sensor. Table A.5 and Table A.6
detail the precise definition of these lines in the COCOA simulation.
Table A.7 details the placement of DCOPS sensors on the ME ±1 chambers.

Table A.5: COCOA Position and Rotation of SLM Lines For ME 1 Stations.
ME 1 SLM lines do not traverse the entire ME disc, rather they terminate
at the reference DCOPS sensor placed on the ME 1/2 frame. The SLM lines
project along lines parallel to the Secondary Link Lines from (0,0,
6782), but offset 66mm.

+---------+------------------+-------------------+----------+---------+
| **SLM   | **COCOA          | **COCOA           | **Po     |         |
| Line**  | Rotation**       | Rotation**        | sition** |         |
|         |                  |                   |          |         |
|         | **About X (CMS)  | **About Z (CMS)   |          |         |
|         | Axis**           | Axis**            |          |         |
+---------+------------------+-------------------+----------+---------+
|         |                  |                   | **X      | **Y     |
|         |                  |                   | (CMS)**  | (CMS)** |
+---------+------------------+-------------------+----------+---------+
| 1       | -90              | 15                | -17.0821 | 63.7511 |
+---------+------------------+-------------------+----------+---------+
| 2       | -90              | 75                | 63.7511  | -       |
|         |                  |                   |          | 17.0821 |
+---------+------------------+-------------------+----------+---------+
| 3       | -90              | 135               | 46.6690  | 46.6690 |
+---------+------------------+-------------------+----------+---------+

Table A.6: COCOA Position and Rotation of Secondary Link Lines In ME 1.
All Primary Link Lines project from (0, 0, 6690). Secondary Link Lines
run parallel to Primary Lines and are offset by 66.000 mm in the CMS XY
Plane.

+-------------+--------------------------+--------------+-------------+
| **Secondary | **COCOA Rotation**       | **Position** |             |
| Link Line** |                          |              |             |
|             | **About Z (CMS) Axis**   |              |             |
+-------------+--------------------------+--------------+-------------+
|             |                          | **X (CMS)**  | **Y (CMS)** |
+-------------+--------------------------+--------------+-------------+
| 1           | 15                       | 12.941       | -48.296     |
+-------------+--------------------------+--------------+-------------+
| 2           | 75                       | 48.296       | -12.941     |
+-------------+--------------------------+--------------+-------------+
| 3           | 135                      | 35.355       | 35.355      |
+-------------+--------------------------+--------------+-------------+
| 4           | 195                      | -12.941      | 48.296      |
+-------------+--------------------------+--------------+-------------+
| 5           | 255                      | -48.296      | 12.941      |
+-------------+--------------------------+--------------+-------------+
| 6           | 315                      | -35.355      | -35.355     |
+-------------+--------------------------+--------------+-------------+

Table A.7: DCOPS Primary Dowel References and Sensor Orientations for ME
±1/2 CSCs. Sensors on the ME ±1/2 chambers have rotations of -185 or 5
degrees and two possible locations for the placement of the reference
DCOPS (designated as type 1 or 2), both are dictated by the projection
of ideal laser lines along the ME±1 SLM lines. Dimensions are given with
respect to the CSC Reference Center in local chamber coordinates.
Coordinates have been extracted from CMS CSC production drawings (FNAL).
ME ±1/2 chambers have two LINK sensors and only a single DCOPS reference
sensor.

  ----------- ---------- --------- ------------ ---------- ---------- ------------
              **Inner                           **Outer               
              Sensor**                          Sensor**              

              **X (mm)** **Z       **Rotation   **X (mm)** **Z (mm)** **Rotation
                         (mm)**    about Y                            about Y
                                   (°)**                              (°)**

  Link        194.571    880.221   -185 or 5    348.589    880.221    -185 or 5
  Sensors                                                             

  DCOPS Ref   N/A        N/A       N/A          498.330    1014.108   -185 or 5
  Type 1                                                              

  DCOPS Ref   N/A        N/A       N/A          498.330    1002.539   -185 or 5
  Type 2                                                              
  ----------- ---------- --------- ------------ ---------- ---------- ------------

### Transfer Lines

The Transfer Lines in the COCOA simulation are not modeled as distinct
objects in the simulation since the placement of transfer plates at each
SLM Reference Point on the individual ME layers form the bulk of the
transfer system. The only additional component required to complete the
system are the placement of crosshair lasers and additional Mechanical
Alignment Bar (MAB) reference sensors.

The positioning of the MABs in CMS is dictated by the placement of the
Barrel Muon Stations and the mounting brackets which affix the Barrel
Muon Chambers to the RF iron. Since the arrangement of the Barrel Muon
chambers is not symmetric in CMS , the placement of the MABs and
Transfer Lines cannot be symmetric in CMS.

The MAB structures are approximated as compound objects consisting of a
DCOPS sensor and a proximity sensor (to provide CMS Z monitoring). In
the final reconstruction of the EMU alignment system, these simulated
MAB structures will have to be replaced by DCOPS sensors affixed to MABs
that are interfaced to the LINK alignment group. The placement of the
MAB sensors in the simulation is dictated by the predefined orientation
and location of the transfer lasers (Table A.8).

Table A.8: COCOA/CMS Position of Transfer Lines and MAB Reference
Sensors

  ------------ ------------ --------- -------------- ----------- -----------
  **Transfer   **Transfer             **MAB Sensor               
  Line \#**    Line                   Positions In               
               Positions In           CMS**                      
               CMS**                                             

               **()**       **R       **X (mm)**     **Y (mm)**  **Z (mm)**
                            (mm)**                               

                                                                 

  1            14.052       7250      7033.049       1760.317    6650.000

  2            74.099       7250      1986.326       6972.590    6650.000

  3            135.901      7250      -5206.504      5045.277    6650.000

  4            195.948      7250      -6970.958      -1992.045   6650.000

  5            254.052      7250      -1992.045      -6970.958   6650.000

  6            314.099      7250      5045.277       -5206.504   6650.000
  ------------ ------------ --------- -------------- ----------- -----------

As previously discussed, the Transfer Plates are to provide a physical
coupling between the SLM and Transfer Lines. This is accomplished by
constructing a mechanical assembly consisting of two DCOPS sensors
(Figure A.8). These assemblies are designed to be placed along the SLM
Lines such that one DCOPS sensor is centered along the SLM Line and the
second DCOPS sensor is centered along the Transfer Line. The local
coordinate system of the Transfer Plate is taken to be the same as the
local coordinate system of the reference SLM DCOPS sensor. This means
that the location of the Reference SLM DCOPS sensor will be (0,0,0) on
all transfer plates with all local coordinate axes overlapping. Due the
varying location of the Transfer Lines in CMS, 21 unique Transfer Plates
are required to completely couple all Transfer Lines to the SLM Lines.

![](media/image8.jpeg){width="4.569444444444445in"
height="3.1645833333333333in"}

Figure A.8: Sample Layout of Transfer Plate. The figure shows the
relative orientation of the two DCOPS sensors on a ME2 Point 2 transfer
plate as well as the location of the SLM crosshair laser. The dashed red
line on the Transfer DCOPS sensor denotes the slot assembly for the
calibration pin.

Table A.9: Transfer Plate Definition. ME4 Transfer Plates are identical
to those in the ME3 layer. ME-3 and ME-4 Transfer Plates are mirror
symmetric to ME2 Transfer Plates with the exception of ME-3 Plate 5.
ME-2 Plates are mirror symmetric to ME3 plates.

  ------------- ------------ ---------- ---------- ------------ ---------- ---------
  **Transfer    **Transfer                         **Transfer              
  Plate \#**    Sensor                             Sensor                  
                Placement                          Rotation                
                (Relative to                       (Rotation               
                TP Reference                       about TP                
                Point)**                           Axes)**                 

                X (mm)       Y (mm)     Z (mm)     X            Y          Z

                                                                           

  ME1 Plate 1   -230.950     19.150     -9.350     -90          180        0

  ME1 Plate 2   -225.000     19.150     -9.350     -90          180        0

  ME1 Plate 3   135.000      19.150     -9.350     -90          180        0

  ME1 Plate 4   141.000      19.150     -9.350     -90          180        0

  ME1 Plate 5   -230.950     19.150     -9.350     -90          180        0

  ME1 Plate 6   -225.000     19.150     -9.350     -90          180        0

                                                                           

  ME2 Plate 1   -464.951     84.250     -9.350     -90          180        0

  ME2 Plate 2   141.000      84.250     -9.350     -90          180        0

  ME2 Plate 3   -231.000     84.250     -9.350     -90          180        0

  ME2 Plate 4   374.951      84.250     -9.350     -90          180        0

  ME2 Plate 5   -464.951     84.250     -9.350     -90          180        0

  ME2 Plate 6   141.000      84.250     -9.350     -90          180        0

                                                                           

  ME3 Plate 1   374.951      84.250     -9.350     -90          180        0

  ME3 Plate 2   -231.000     84.250     -9.350     -90          180        0

  ME3 Plate 3   141.000      84.250     -9.350     -90          180        0

  ME3 Plate 4   -419.951     84.250     -9.350     90           0          0

  ME3 Plate 5   419.951      -302.250   -203.350   90           0          0

  ME3 Plate 6   -231.000     84.250     -9.350     -90          180        0

                                                                           

  ME-2 Plate 5  375.000      84.250     -9.350     -90          180        0

  ME-3 Plate 5  -419.951     -302.250   -203.350   90           0          0
  ------------- ------------ ---------- ---------- ------------ ---------- ---------

Table A.10: COCOA/CMS Position of Transfer Plate. ME4 Transfer Plates
locations along the SLM lines are identical to those in the ME3 layer.
ME-3 and ME-4 Transfer Plate locations are mirror symmetric to ME2
Transfer Plate locations and orientations with the exception of ME-3
Plate 5. ME-2 Plates are mirror symmetric to ME3 Plates with the
exception of ME-2 Plate 5.

+------------+----------+--------+--------+--------+--------+--------+
| **Transfer | **       |        |        | **Tr   |        |        |
| Plate \#** | Transfer |        |        | ansfer |        |        |
|            | Plate    |        |        | Plate  |        |        |
|            | P        |        |        | O      |        |        |
|            | lacement |        |        | rienta |        |        |
|            | (        |        |        | tion** |        |        |
|            | Relative |        |        |        |        |        |
|            | to SLM   |        |        | **(Rot |        |        |
|            | Center   |        |        | ations |        |        |
|            | Point)** |        |        | About  |        |        |
|            |          |        |        | SLM    |        |        |
|            |          |        |        | A      |        |        |
|            |          |        |        | xes)** |        |        |
+------------+----------+--------+--------+--------+--------+--------+
|            | **X      | **Y    | **Z    | **X**  | **Y**  | **Z**  |
|            | (mm)**   | (mm)** | (mm)** |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
|            |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME1 Plate  | 7282.907 | -43.25 | 22.5   | 0      | -90    | 0      |
| 1          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME1 Plate  | 7283.007 | -43.25 | 154.5  | 0      | -90    | 0      |
| 2          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME1 Plate  | 7283.004 | -43.25 | 22.5   | 0      | -90    | 0      |
| 3          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME1 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 4          | 7282.907 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME1 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 5          | 7282.907 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME1 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 6          | 7283.004 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
|            |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME2 Plate  | 7282.907 | -43.25 | 22.5   | 0      | -90    | 0      |
| 1          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME2 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 2          | 7282.907 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME2 Plate  | 7282.907 | -43.25 | 22.5   | 0      | -90    | 0      |
| 3          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME2 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 4          | 7282.907 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME2 Plate  | 7282.907 | -43.25 | 22.5   | 0      | -90    | 0      |
| 5          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME2 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 6          | 7282.907 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
|            |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME3 Plate  | 7282.907 | -43.25 | 22.5   | 0      | -90    | 0      |
| 1          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME3 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 2          | 7283.003 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME3 Plate  | 7283.007 | -43.25 | 22.5   | 0      | -90    | 0      |
| 3          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME3 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 4          | 7282.907 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME3 Plate  | 7088.908 | -43.25 | 22.5   | 0      | -90    | 0      |
| 5          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME3 Plate  | -        | -43.25 | -22.5  | 0      | 90     | 0      |
| 6          | 7283.004 |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
|            |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME-2 Plate | 7282.907 | -43.25 | 22.5   | 0      | -90    | 0      |
| 5          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+
| ME-3 Plate | 7088.908 | -43.25 | 22.5   | 0      | -90    | 0      |
| 5          |          |        |        |        |        |        |
+------------+----------+--------+--------+--------+--------+--------+

### Script Labeling Conventions

Based on the COCOA scripting syntax and the parent-child relationships
between components, the labeling conventions in Table A.11 have been
adopted for EMU elements in COCOA Simulation Scripts.

Table A.11: Labeling of EMU Objects in COCOA Scripts.

  --------------------------------------- -------------------------------
  **CMS Designation**                     **COCOA Script Designation**

                                          

  ME 2 SLM 1-4                            slm21

  ME -2 SLM 1-4                           slm-21

  ME 2 Laser 1                            las21

  ME 2/2/3                                me22_3

  ME 2/1/10                               me21_10

  ME 2/1/10 Outer DCOPS                   cops_outer21_10

  ME 2/1/10 Inner DCOPS                   cops_inner21_10

  Transfer Line 1                         Not Needed in Script

  MAB Sensor at Transfer Point 1, Z =     mab1
  +6500 mm                                

  MAB Sensor at Transfer Point 1, Z =     mab-1
  -6500 mm                                

  Transfer Laser 1 (located in + Endcap)  transfer1

  Transfer Laser -1 (located in - Endcap) transfer-1

  ME 2 Transfer Plate 1                   transfer_plate21

  ME 2 Transfer Plate 1 SLM Reference     me2_reference1
  DCOPS                                   

  ME 2 Transfer Plate 1 Transfer Line     me2_transfer1
  DCOPS                                   
  --------------------------------------- -------------------------------

### Final Scripts Compared to Theoretical Placement

The complete model of the CMS EMU Alignment System constructed with the
components previously detailed show layout and placement errors in the
COCOA EMU simulation components of \<5 m along the Transfer Line
(average deviation of .05 m) and 10 m along the SLM Line (average
deviation of .81 m). The discrepancies on SLM on the order of 10 m occur
only on the placement the inner ME21/ ME-21 DCOPS sensors relative to
the ME21/ME-21 CSC chamber centers. It has been decided that this error
lies in the corresponding ME21/ME-21 production drawings. The decision
has been made to match components in the COCOA simulation to the final
production drawings rather than a perfect CMS geometry. It is expected
that the tolerance on the construction of the components comprising the
system will greatly exceed any of these small discrepancies in the
production drawings.