Alignment report (5/30/01)

The alignment of the system is a step-wise process with some steps
needing to be repeated.

Step 1.  Translational alignment  (separately) of the u-planes and the v-planes.

Requirements:  This translational plane alignment is accomplished by
using incoming straight (positron) tracks whose trajectories are nearest
to, and nearly parallel to the axis of the detector system.  These
tracks are selected via cuts on the wires hit.

The algorithm: The two halves of the detector are aligned separately. 
In each half of the detector, two planes are selected, one near the
upstream end and one near the downstream end, whose translational
positions are held fixed in the translational alignment process.  The
remaining planes are then aligned by determining their individual
translational offsets from the line connecting the centers of the two
fixed planes.  

The results:  Translational offsets have been introduced in each plane
(except the fixed planes) randomly up to 4 mm.  The alignment codes have
been able to reproduce these offsets to better than 3-4 microns.   This
can improve with more statistics.

Step 2.  Rotational alignment  (separately) of the u-planes and the v-planes.

Requirements:  This rotational plane alignment is accomplished by using
incoming straight (positron) tracks and positrons tracks from muon
decays in the target. The trajectories of these positrons are inclined
to the detector axis so as to pass through most of the planes in the
detector away from the axis of the detector system.  The intention here
is to illuminate the chambers away from the detector axis so as to
sample the rotational misalignments of the planes.  These tracks are
selected via cuts on the wires hit.

The algorithm: The two halves of the detector are aligned separately. In
each half of the detector, two planes are selected, one near the
upstream end and one near the downstream end, whose rotational
orientations are held fixed in the rotational alignment process.  The
remaining planes are then aligned by determining their individual
rotational offsets from the rotational orientation of the two fixed
planes.  This process has the possibility of building in a systematic
cork-screw rotational misalignment which must be taken out separately.

The results:  Rotational offsets have been introduced in each plane
(except the fixed planes) randomly up to 40 mrad.  The alignment codes
have been able to reproduce these offsets to better than 0.1 mrad.  
These will improve with more statistics.

Step 1-2. Combined translational and rotational offsets.

The method: In practice, the chambers will be mis-aligned in both
translationally and rotationally at the outset.  Separate tests on only
translational and rotational misalignments as described in Steps 1 and 2
were replaced by mis-aligning the planes translationally and
rotationally simultaneously and then in an iterative fashion, proceed
from Step 1 to Step 2 and back to Step 1 and Step 2.

The results: The precision of the alignment offsets noted in Steps 1 and
2 can be achieved in this method as well.

Step 3.  Unwinding the cork-screw.

Requirements:   To unwind the cork-screw systematic rotational offset,
we expect that we will  have to use helical tracks from muon decays in
the target. These helical tracks will have to be ones of rather large
radius to sample the rotational offsets seen most clearly away from the
detector axis.   These tracks are selected via cuts on the wires hit.

The algorithm: This is still in development.   Helical fitting will be
needed to pick out the proper values of the hits in the detector.  
he results:  We expect to have results in June.

Step 4.  Orthogonal alignment of the u-v planes.

Status: This is still under development.

Step 5.  Alignment with respect to the magnetic field.

Requirements:  This alignment with respect to the magnetic field will be
done with helical tracks.

The algorithm: The algorithm being developed is similar to that proposed
by Roman Tacik.  A sine function is fit to the points in (u,z) and (v,z)
separately.  If the detector is fully aligned with respect to the
solenoidal magnetic field, the axis of the sin function will be
horizontal.  If, however, there is a misalignment, the axis of the sine
function will show a systematic displacement, either up or down. 
Because the alignment will, in general be neither along the u-axis nor
along the v-axis alone, there will be systematic displacements of the
sine function axis in both the u-z plot and the v-z plot.  The space
angle of the misalignment can then be determined.  Because the two
halves of the detector have been aligned separately, their alignment
with respect to the magnetic field will also be done separately.

The results:  Results of tests with MC hit points are expected in a
couple of weeks.

In each case --

The tests: The algorithms have been (or will be) tested with Monte Carlo
(MC) tracks.  Translational, and/or rotational offsets are introduced in
each of the non-fixed planes and the alignment code has deduced these
offsets by fitting straight or helical tracks. We have used the "hits"
in the planes as given by the "hit file" from the MC. These hits have
the actual (u,v,z) location of the interaction point in each plane.  The
MC was run using energy loss and multiple scattering in order to
simulate the actual response of the detector as much as possible.  This
test is useful in that it represents the best possible alignment results.

In practice:  The hits which are to be used for the alignment will come
from the tracking code.  In the tracking code, a straight track is fit
and all the appropriate L/R ambiguities are thereby resolved.  The
actual hit locations, which are then used to fit the straight track, are
passed to the alignment codes by writing these hits to a file. Compared
to using the MC h its file, we expect that there might be some
degradation in the alignment precision when the hit points are provided
by MOFIA where the code goes from the actual drift times to the needed
space points after tracking.

We will have plots to show at the meetings.

Shirvel and Don

---------------------------------
Donald D. Koetke
Professor of Physics
Department Chair
Department of Physics & Astronomy
Valparaiso University
219-464-5377 (Voice)
219-464-5489 (FAX)
donald.koetke@valpo.edu
www.physics.valpo.edu

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