Here are some ideas concernig of alignment after today's meeting and
talk with Dave. 

Alignment of spectrometer includes:

1) Alignment of the yoke and solenoid;
2) Alignment (mapping) of wire planes;
3) Alignment of the beam and magnetic field;
4) Alignment of the wire chamber stack and magnetic field (or beam).

I.
I do not discuss of an alignment of solenoid and yoke here. 

II. Alignment of wire planes

At first, wire map should be obtained for compressed stack using
standard
way. It could be done anywhere (in solenoid or outside).
Getting of the map means that Z axis of stack as whole along with U(V) 
coordinate and rotation angle of each wire are known.
Here I define Z axis of i-th plane Zi as a line crossing the center of
i-th 
plane perpendicular to that wire plane.
In an ideal case when no shifts, rotations, tilts etc. centers of all
planes
coincide and define Z axis. These is not a case when we have shifts or 
rotations of planes (U and/or V planes) or tilted planes (Z direction).
Z axis of full stack is defined as average (centroid?) of Zi of all
planes. 
So for each plane we know coordinate where selected by this way Z axis 
crosses that plane. That Z axis will be unchanged while stack stays 
compressed.
In case we are insensitive to Z direction (i.e. we can't detect tilt of 
planes) and define Z position of each plane by thickness of citals all 
Zi will be parallel to each other. 

III. Alignment of the beam and magnetic field

Assuming that yoke is aligned to solenoid one can do next step - to
align 
beam to magnetic field. 
Procedure proposed by Bob for alignment of the detector with respect 
to the magnetic field (see Bob's note, 3 July, 2000, on the alignment
group 
bulletin board) should be used here (in fact, this procedure does not
work for 
alignment of the detector and magnetic field).
It seems alignment should be done with 29.8 MeV/c muon beam (in this
case 
only upstream half of the spectrometer will be used for alignment of 
beam-field and chamber stack because muons stop in the target). In case
we 
will use higher momentum (40-50 MeV/c) one can get another beam angle
and 
align field to this (incorrect) angle (is it correct?). 
Chambers are not aligned with field/beam yet and stay in some relative 
position. 
The two steps proposed by Bob are used to align magnetic field and beam. 
At first, measure beam profile in each plane with magnetic field off. 
Having beam focused in fringe field region beam distributions become
wider 
from the first plane to last one. Centroids of these distributions will 
give beam direction. Multiple scattering increases width of
distributions 
but should not move centroids. 
Second, measure beam profiles with magnetic field on. We do not have to 
reconstrust helices, one need just to see beam profile. Particles will 
spiral along magnetic field axis and distribution of centroids in all 
planes will show magnetic field direction: if the magnetic field and 
beam are aligned all centroids will be situated exactly on the same 
straight line (Beam  distributions in all planes should be similar
unlike 
of case with magnetic field off. Multiple scattering increases width 
of distributions from first plane to last one while energy loss
decreases it).  
Otherwise centroids will "spiral" around field axis. Axis of this
"helix" 
shows field direction. 
(Probably it will be possible to align the magnetic field and beam
without 
step 1 if centroids are defined with high precision(?) We need just to 
put all centroids on straight line).    
Difference between centroids axes directions with field off and on show 
misalignment of beam with respect to the magnetic field. Changing beam 
direction one can coincide of axes of two sets of centroids, i.e. to 
align magnetic field and beam. 
  
IV. Alignment of the wire chamber stack with respect to the magnetic
field 
and beam. 

Having magnetic field and beam aligned and knowing of Z axis of full
stack 
we can align stack with beam (or the same, with field). This 
alignments could be done with field on or off because in both cases 
centroids of beam distributions on each plane coinside and give beam 
and field direction. Alignment of stack with field-beam means
coincidence 
beam-field axis and Z axis of stack as it defined in section I. 
   

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 Yuri Davydov (davydov@triumf.ca)       (604) 222-1047 ext.6198
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