There are 6 degrees of freedom for each coil
(dx=dr, dy=dphi, dz, pitch, roll and yaw). With
8 coils, that yields 48 independent degrees of
freedom. Although the proposed measurements
( (Bx,By,Bz) along nine lines parrellel to the
beam pipe / z-axis) can have hundereds of
measurements, these are not independent!
Coils may not be shaped as designed, and may not
produce the field which TOSCA has assumed.
The technique is to look at the difference between a
measured field and the TOSCA field and try to
figure out how to shift the coils to create the
ideal TOSCA field. This may not be completely
achivable (See above).
General comments on the analysis
To analyse this data we must be driven by the
locations where the measurments are, not
just where we would like them to be.
we may need to extropolate from the
TOSCA numbers we precalculated
we may need to rerun TOSCA.
After we "fit" we may want to re-run TOSCA to
see that the TOSCA with misalignment is
near to what we measured.
If the measurement are fast and adjustments are,
and the analysis is slow we would make many
small adjustments.
After we power up the coils
First measurment - in the "neck" of the coils,
with the table on the down stream edge of
the pit. We measure the field in the
"neck" region, (about a meter? in z)
plot all componets of all nine lines
as a function of z. Compare to ideal
TOSCA. Inspect by eye.
Test which line is the most off?
fit.
perform a TOSCA calculation with the
fitted off sets. The results of this
TOSCA should be the same as what was measured.
Ajust worst coil (dx, dy, dz)
remeasure and refit
Second measurement - in the target region
maybe with more sensetive probe, which is
in only one diemension.
like the above, except fit only pitch and yaw.
perform a TOSCA calculation with the
fitted off sets. The results of this
TOSCA should be the same as what was measured.