This document describes the TPC coordinate systems as currently implemented.

Units: The unit of length is cm. The unit of rotation is radians (this violates the STAR GEANT standard, which is degrees).

STAR Global Coordinate system: The STAR global coordinate system is defined in CSN 229 . This note specifies that:

• Positive y is up
• The origin is the center of the solenoid
• Positive x points south, away from the center of the RHIC ring
• Positive z points west

STAR TPC Local Coordinate System: The TPC local coordinate system is defined relative
the center of the TPC, and uses the same definitions as the STAR global coordinate system. This system is related to the STAR global coordinate system by a translation and a rotation.

STAR TPC Pad Coordinates: This coordinate system specifies the location within the TPC in
terms of pad coordinates, i.e. sector, row, pad, and time bucket.

STAR TPC Local Sector Coordinates: We do hit reconstruction on a sector-by-sector basis, assuming that each sector is Sector 12. In this system, a position is defined by (x,y,z) in sector
12 coordinates, as well as the real sector #. Note that z increases starting at the gating grid in these coordinates, i.e. z=0cm in Tpc Local Sector coordinates is equal to z=208.707cm in TPC Local Coordinates.

---

TPC Coordinate Transformation Utilities: TPC coordinate transformations are done is several places:

1. StRoot/StDbUtilities/StTpcCoordinateTransform: This is a general utility used for transforming among the various TPC coordinate systems.
2. StRoot/StTpcDb/StTpcDb: This is a database accesor application that serves as the single point of contact between the TPC software in the database.
3. StRoot/StTpcDb/StTpcDbMaker: This routine has two purposes. First it initializes and creates the StTpcDb class. In addition, this routine wraps the StTpcCoordinateTransform so that some of these functions can be called from with the pams. Finally, this routine implements some specific coordinate transformations that are used repeatedly in the cluster and track finders. For these particular routines, StTpcCoordinateTransform is too slow.
4. StRoot/StDbUtilities/StSectorAligner: This routine takes care of sector alignments. The TPC coordinate systems assume that the TPC is perfectly constructed. Here we account for the physical position of each TPC inner and outer sector.
5. StRoot/StDbUtilities/StMagUtilities: This routine takes care of TPC distortions. The input is TPC hits in, and the output is TPC hits with the appropriate ExB corrections.  Currently we input the TPC hits in TPC local coordinates.

Order of calls: The dataflow is the following: (formerly, before SL04a library, St_tpt_Maker handled the duties of StTpcHitMoverMaker)

1. St_tpcdaq_Maker: raw pixel information (sector,row,pad,timebucket)
2. St_tcl_Maker->tcl: Convert raw pixel info to TPC hits in local coordinates (accounting for pad-by-pad t0s)
3. StTpcHitMoverMaker: Aligns sectors, "ExB" corrections, local->global:
1. StSectorAligner
2. StMagUtilities
3. StTpcCoordinateTransform (local to global)
4. St_tpt_Maker/Sti: tracking (using global hits)

---

TPC Database parameters: We use parameters from the MySQL database. We use the Calibrations/tpc, Geometry/tpc, Conditions/trg, and StarDb/tpc/***pars directories (*** refers to the three letter acronym for tpc pams, i.e. tcl or tpt). Some important tables are the following:

• Geometry/tpc/tpcGlobalPosition: This table gives the position of the TPC center relative the magnet. It also gives the rotation of the TPC relative the magnet. We have two separate rotations. There is a physical rotation of the TPC, and a rotation of the TPC E-field that is used to do an ExB correction. The rotations are defined using the right hand rule. For instance, the parameter PhiXZ controls the rotation of the E-Field in the XZ plane (i.e. around the y-axis). Howard Wieman has written a document describing the survey results. The actual transformations are described in a separate document (PS , PDF ).  Here are some specific variables in the database:

LocalXShift,LocalYShift,LocalZShift	TPC (x,y,z) position relative global magnet coordinates
PhiXY_geom,PhiXZ_geom,PhiYZ_geom	Physical rotations of the TPC relative the magnet steel around the z,y,x axes. PhiXY_geom is not well determined, and therefore not used
PhiXY,PhiXZ,PhiYZ	Magnetic field dependent rotation of the TPC E-field axis relative the magnet axis. These parameterize an effective field model rotation of a perfect E field axis relative to a perfect B field.  PhiXY is by definition 0.
XX,YY,ZZ,XX_geom,YY_geom,ZZ_geom	Diagonal elements of the rotation matrices. The rotations are generally so small that these are all unity.



• Geometry/tpc/Sector_XX/tpcSectorPosition: Position of sub-sectors relative the nominal position. Each subsector is defined be a local x and y shift, and a rotation angle. The shift is in sector 12 coordinates, so most shifts are along the padrows (i.e. in the x-direction). The rotation is taken about the middle of padrow 14 (i.e. (x,y) = (0,123cm) in sector 12 coordinates).
• Geometry/tpc/tpcDimensions, tpcWirePlanes, tpcPadPlanes: Here we have a bunch of parameters related to the nominal TPC dimensions and geometry in the anode region.
• Geometry/tpc/tpcFieldCage: Here we describe some inperfection the in the TPC field cage needed for ExB corrections. There is a shift of the innerFieldCage relative the outer field cage, as well as two "clocking" errors. "clocking" refers to the rotation of the end caps realative the nominal position. To confuse matters, the clocking is not an ExB correction, but a geometry correction. Nonetheless it is part of the ExB corrections.
• Conditions/daq/trgTimeOffset: This table gives the delay between the time of an event and when the trigger is issued to the TPC. There are two parameters, one for normal events (offset) and one for laser events (laserOffset). The offset parameter should be checked anytime Hank is near the STAR detector.
• Calibrations/tpc/tpcDriftVelocity: Here we have the drift velocity for a given run. Currently it is calculated in one of two ways. The cathodeDriftVelocity refers to the drift velocity calculated by StTpcT0Maker. Here we reconstruct the vertex independently in each half of the TPC and adjust the drift velocity such that the two vertices match. The laserDriftVelocity comes from the online analysis of the mirror positions. The T0 method is more accurate, but cannot be used in pp collisions. Note that for a given timestamp, the most recent table is retrieved. If the cathodeDriftVelocity is zero, the laserDriftVelocity is used.
• Calibrations/tpc/tpcEffectiveGeom: Because of the varying drift path/velocity in the anode region, the effective length of the TPC is different than the physical length. The drift velocity is fairly constant up to the GatingGrid, so we define the gating grid as z=0cm is sector 12 coordinates. We then define an effective pad plane position for the inner and outer sectors, and define these positions relative the gating grid with z_inner_offset and z_outer_offset. These offsets are taking from Roy Bossingham's megaboltz calculations (see SN 408 ).  The inner/outer effective displacement was confirmed by looking at TPC residuals.  
• Calibrations/tpc/tpcElectronics: The important parameters here are the samplingFrequency and the shapingTime. The sampling frequency converts from timebuckets to time. The shaping time is used to correct the TPC hits for the shaping time of the TPC electronics. We use a single average shaping time correction, when if fact the shaping time correction should depend on the cluster shape.
• Calibrations/tpc/tpcOSTimeOffsets, tpcISTimeOffsets: pad-by-pad correction of the timebuckets taken from pulser data.

---