TrackerAlignment

Alignment Definition

This section explains how the tracker alignment is defined.

• There are four places that alignment corrections are applied
  • A transform between the whole tracker and the nominal Mu2e detector coordinate system
  • A transform between each plane and the aligned tracker
  • A transform between each panel and the aligned plane
  • A correction to the end positions of individual straws and wires within a panel
• transforms
  • apply rotation before displacement
  • a rotation is defined as right-handed about the local x, then y, then z axes (rad)
  • add an offset in position (mm)

Tracker Geometry Build

Here is how the geometry is conceptually built up, including the alignment

1. Straws are placed within the panel
   • this uses the local panel coordinate system, defined as UVW, a right-handed coordinate system. These correspond to the XYZ coordinates of the Duke panel X-ray mapper, defined in Mu2e document 5703.
   • The straw direction points along the +U axis, which points from the High Voltage (HV) side of the DRAC electronics board to the Calibration (cal) side.
   • straw 0 is the longest, innermost straw, straw 95 is the shortest, outermost straw.
   • V points radially outwards, from the center of straw 0 to the center of straw 94.
   • W is perpendicular to the panel, and to U and V, pointing from the back of the base plate to the cover. This is roughly from the center of straw 1 to the center of straw 0
   • panel U=0 is defined by the nominal symmetry axis of the panel
   • pane V=0 is defined to be midway between innermost and outermost straw centers, between straws 47 and 48.
   • panel W=0 is defined to be midway between the straw layers, which is also midway between the innermost and outermost straw centers
2. Apply the straw alignment. Note that straws are not rigid bodies due to gravitational sag, electrostatic displacements and construction-induced distortions, so rigid-body transforms are not applicable. Instead, Straw alignment is defined in terms of displacements in V and W at either end (HV and Calibration) of the straw, where the straw intersects the manifold (radius=700 mm) and is held rigidly in place. The mylar envelope (straw) and wire have separate corrections. To first order, the wire may be approximated as a line between these points, as the gravitational sagitta expected for nominal tension is < 50 microns. The precise geometric description of the entire straw requires dynamic information such as the tension, High Voltage.
3. Apply the panel alignment of rotations and displacements. These are rigid body rotation and translations WRT the local panel UVW coordinate system.
4. Place the panel in the nominal plane. This involves rotating the nominal panel center to its nominal phi position around the z axis, and adding its nominal displacement in Z and radially outwards. By convention, the nominal plane is defined as plane 0, described in Mu2e document 888. The nominal plane coordinate system (XYZ) is centered on the plane, with directions as defined by the Mu2e detector coordinate system.
5. Apply the plane alignment of rotations and displacements, with respect to the nominal plane coordinate system.
6. Place the plane within the nominal tracker. This involves moving it along the z axis, and rotating half the planes around the Y axis by 180 degrees. The pattern of plane rotations is defined in Mu2e document 888. It amounts to building a station by rotating one plane around Y by 180 degrees, then rotating every-other station around Y by 180 degrees.
7. Place the tracker within the Mu2e detector coordinate system by applying the tracker alignment. The detector coordinate system is defined as the nominal (perfect) tracker coordinate system.