COORDINATES FOR TARGET, DEA AND LGD
Ben Brabson, Sasha Ostrovidov, Dave Thompson, Doren Steinike, Eric Scott)
		3/5/94

Magnet Rotation:  The magnet will be rotated to its maximum clockwise position
such that its center line is 32.8 mr relative to the undeflected HEUB beam. 
The 18 GeV/c beam bends by a total of 77.45 mr in the 1 Tesla field between z =
-124.0" and z = +292.0".  At the target position, 2 inches upstream of the
center line of the magnet, the angle of the deflected beam is 5.04 mr clockwise
from the center line of the magnet.  Since the target assembly is constrained
to be parallel to the center line of the magnet, the 5.04 mr angle of the beam
applies also to the liquid hydrogen target itself.  All coordinates below are
in inches and are given in the MPS magnet coordinate system with z = 0 at the
pivot point.  The surveyed distance of 280.211 inches from the magnet pivot
point to the face of the glass of the LGD is used throughout.  This number
comes from Eric. 

	MPS Center Line is 32.8 mr CW from undeflected HEUB.
	MPS Center Line is 5.04 mr CCW from deflected HEUB 
		at the center of the target.

Target Position:  At the z = 70 inches (center of the target) the target
position is,+0.560 inches to the beam left of the magnet centerline. 

	(Xtgt, Ytgt, Ztgt) = (+0.560 in, 0.000 in, 70.0 in) 

DEA Position:  The z coordinate of the center of DEA is 50.75 inches downstream
from the center of the target, or at (70 + 50.75 =) 120.75 inches from the MPS
pivot point.  To assure that the DEA window shadows the LGD, the geometric
center of the DEA lies on the line between the target center (0.560", 0.000",
70.0") and the geometric center of the LGD (-8.095", 0.000", 289.069") as given
below.  The DEA center is at: 

	(XDEA, YDEA, ZDEA) =  (-1.445 in , 0.000 in, 120.75 in)

LGD Hole Coordinate:  A Field93 swim of the 18 GeV/c beam to the LGD gives the
position of the deflected beam at the LGD.   This is the beam position at the
mid-depth of the LGD, 22.5 cm = 8.858" into the face.  Since the LGD glass face
is 280.211 inches from the pivot point of the magnet, we have: 

	(XLGD HOLE, YLGD HOLE, ZLGD HOLE) = (-7.308 in, 0.000 in, 289.069 in)

Beam Hole Row and Column:  Looking downstream along +z axis, the 71 columns and
43 rows of the LGD are numbered  (0 < Nx < 70) and (0 < Ny < 42) with (0,0) at
lower right.  (Increasing column number goes with increasing x and increasing
row number with increasing y.)  In this system the 2 block x 2 block hole is
the overlap of columns 35-36 with rows 21-22.  That is, the geometric center
block,  is part of the hole as is the block above it, and the two blocks to
beam left of them. 

		The 2 x 2 block beam hole is overlap of 
		LGD columns 35-36 with rows 21-22.
		The geometric center of the glass is
		(col 35, row 21)

	The center of mass of the glass of the LGD is given here.  We define
the coordinates in the MPS magnet frame of reference with the origin at the
pivot point, as usual.  The numbers are these: 

1994 LGD CENTER OF MASS Location:

	(XLGD CM, YLGD CM, ZLCG CM) = (-8.095 in, -0.787 in, 289.069 in)
	 = (0.000, 0.000, 1.000)

	The X0 coordinate is the x position of the deflected beam 22.5 cm
behind the face of the LGD.  With a 2 cm correction for the fact that the beam
hits the center of the 2 x 2 block hole and the geometric center of the whole
array is at the center of the  (row 35, column 21) block, 2 cm lower and 2 cm
to the beam right.  The Y0 coordinate of the geometric center is simply the -2
centimeters, and the Z0 coordinate is the 280.211 inches from pivot to face of
LGD plus half of the 45 cm thickness of glass.  The unit normal reflects the
fact that the magnet system and LGD are aligned in 1994. 

1993 LGD CENTER OF MASS Location:

	(XLGD CM, YLGD CM, ZLGD CM) = (-23.972 in, -0.787 in, 289.069 in)
	 = (0.02755,  0.000, 0.99962)

	The 1993 numbers are a bit trickier because the MPS magnet was rotated
counter-clockwise by (32.8 - 5.25 mr) from the 1994 position.  The LGD normal
represents this 27.55 mrad rotation. The Y0, and Z0 coordinates of the glass
geometric center are not changed by the rotation, but, of course, the X0
coordinate is. 

	To calculate X0 we need to know where the LGD was placed along the
transporter rails.  The 9 x 9 block array was roughly centered on the
projection of the beam at the center of the target, that is, it was
approximately centered on the expected produced neutrals.  Looking down stream
and looking at the LGD, the 9 x 9 block array was to beam left of the beam hole
and separated by 5 columns of blocks from the 2 x 2 block beam hole.   X0, the
coordinate of the glass geometric center in the MPS coordinate system is then
the sum of three numbers, the 1994 to 1993 shift in coordinate system due to
the 27.76 mr rotation (-7.964 in),  the beam deflection from the 1994
centerline (- 7.346 in), and the 6 block shift from the beam (in the block next
to the 9 x 9 array) to the glass geometric center (-9.449 in).  The 1993 field
on beam was also steered by +0.787 in (2 cm) to beam left.  The total is X0 = 
-23.972 in.