Pickup calibration in CESR beam position monitors
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CESR is a high energy particle accelerator that collides
electrons with positrons.  The energy of these collisions 
creates elementary particles that are registered in the 
detector CLEO. Furthermore CESR produces highly focused 
and intense x-ray beams for the CHESS laboratory.  These 
X-rays are used in an extremely wide range of applications, 
e.g. surface analysis and the determination of protein 
structure.  CLEO as well as CHESS rely on a precise 
knowledge of the beam position and on procedures to keep 
this position stable in time.  For this purpose, the beam 
position has to be measured with high accuracy.
 
Each beam position monitor of CESR consists of four electrodes
(pickups) arranged in different geometries.  The electric 
signals from these pickups are related to the position of 
the beam.  Our present algorithm for converting pickup 
readings to beam positions assumes perfect alignment among 
the pickups.  By making measurements of the capacitive 
coupling between the pickups, we can calculate their
relative misalignment, and incorporate this as a correction 
in our algorithm.
 
We would envision the student to complete as much of the
following as possible:
 
 1.  Model the BPM geometry and simulate the misalignment.
This justifies the mathematical approach we will use to 
correct the errors.  We already know pretty well what the 
calculations will show, but it will be educational for
the student to do these simulations for him/herself.
 
2.  Show mathematically how we can use the capacitive coupling
between the pickups to calculate the parameters in the model 
from Step 1.  How much work goes into this step will depend 
on the student's  mathematical background.
 
 3.  Measure the coupling between pickups for all CESR BPM's.
There are about 100 BPM's, but we think this can be 
accomplished in a couple of days (CESR will still be shut 
down at this point), so it shouldn't be that bad.

 4. Analyze the data to estimate what sort of improvement 
we may expect from this calibration.
 
 5.  Using the measurements, write code to compute the 
model parameters and use them to cancel misalignment errors.  
This will involve somewhat extensive FORTRAN programing, but 
fortunately code already exists to perform a similar and 
related task.  The student should be able to clone
a basic structure for his/her work without getting 
bogged down in the guts of the control system software.
 
 6.  Using stored orbit data, compare old and new beam position 
calculations to the orbit model, and evaluate the improvement.