ANALYSIS OF DATA FROM THE LEDA WIRE SCANNER/HALO SCRAPER Page: 3 of 4
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where the wire scanner signal rises above the noise. That
is, there must be an overlapping region where both
instruments have valid data. Once everything is set up,
the operator can elect to perform an x-scrape, a y-scrape,
or both.
3 ANALYSIS ROUTINES
It is important to know the locations where the wire
scanner and scraper signals each rise above the
background noise. An algorithm was developed using the
average and standard deviation of all the points from the
outboard edge to the point in question. The criterion used
to determine where the signal exceeds the noise is signali
- ave_1)/stdevi_1 > 2, where i is the index of the point
under examination.
Since the wire passes completely through the beam and
out the other side, both sides of the wire scanner
distribution are examined for the signal > noise condition.
Scrapers only probe the edges of the beam, so two scrapes
are performed for each wire scan. The outboard end of
each scrape is examined for signal > noise.
As the scraper marches inward, it intercepts an ever-
increasing segment of the beam. It is therefore necessary
to differentiate the scraper signal to determine the
transverse distribution. As mentioned above, the operator
can elect to take scraper data with N-times finer steps than
used for the wire scan. This finer stepping allows the
differentiation algorithm to smooth the data. The
numerical derivative is computed as the difference
between two N-point averages on either side of the point
in question divided by the spatial separation between
them. Tests with simulated random noise added to a
Gaussian distribution showed that smoothing the
derivative with N=4 increased the derivative's signal-to-
noise ratio by a factor of ten relative to N=1. Larger
values of N improve the signal-to-noise ratio even more,
but at the cost of additional time to complete the scrapes.
Difficulties in implementing the differentiation
algorithm are encountered at the ends of the data array.
When there are less than N points between the point in
question and the end of the array, the N-point-smoothing
differentiation algorithm cannot be applied. Under these
conditions, the number of points averaged is successively
reduced. For the end points of the arrays, the derivative is
computed using a forward finite difference technique.
These modifications to the nominal algorithm result in a
derivative that is noisy at the ends. While the derivative
is computed for all points, in some of the algorithms, the
end N points are ignored.
The first step in joining the scraper data to the wire
scanner data is determining where the data sets overlap.
The overlap region consists of wire scanner locations
ranging from where the wire scanner signal-to-noise ratio
is greater than 2 to the maximum insertion location of the
scraper.
Once the region of overlap has been determined, the
scraper data must be normalized to attach it to the wire
scanner data. The scaling factor is the average of wirescanner to halo scraper signal ratios at two of the three
most-inboard points in the overlap region (the most
inboard point is excluded). Once scaled, the entire
scraper data set is thinned by keeping only every Nth
scraper point and attached at the connecting points.
Measurements of wire to scraper distances were carried
out with an uncertainty of 0.25 mm. This implies a
positional attachment uncertainty of 0.25 mm.
At this point, the resulting three distributions have
been combined into a single distribution with uniform
step size. The first four moments of the combined
distribution are computed. Values are reported for the
mean, standard deviation, skew, and kurtosis.
The final routine archives the results to a file. The
information in this file includes: the names of the parent
files; the four moments of the combined distribution; the
combined data set-signal array plus locations; the two
scraper derivative sets-signal arrays plus locations; and
the locations where the wire scanner and scraper signals
rise above the noise (the measurable farthest extent).
4 RESULTS
The data to be shown were taken during an experiment
to match the beam into the halo lattice. Currents on the
four matching quadrupoles were sequentially increased by
5% and wire scans and scrapes taken at all locations. For
the case at hand, the current in quadrupole #3 was 5%
higher than nominal. Beam current was 75 mA, pulse
length was 35 ps, and the repetition rate was 1 Hz. Due to
lack of space, only the data taken in the y plane is shown.
The wire scan is shown in figure 1. Data were taken for
locations from -9 mm to +9 mm in 73 0.25-mm steps.
The ordinate is the difference in signal level (in counts) at
two time points divided by the average number of counts
from the AC toroid. The least significant bit corresponds
to -3x10-4 (1 count divided by -3000 counts
corresponding to 75 mA).
1.0E+00 a1.0E-01
1.0E-02
1.0E-03A
"
a "'""S
1.0E-04
-10 -5 0 5 10
y (mm)
Figure 1. Y-axis wire scan, 0.25 mm step size.
For this scan, the maximum halo insertion points were
computed to be -3.5 mm and 2.5 mm. The measurable
farthest extents were -4.75 mm and 3.5 mm, providing 6
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KAMPERSCHROER, J.; O'HARA, J. & A, ET. ANALYSIS OF DATA FROM THE LEDA WIRE SCANNER/HALO SCRAPER, article, May 1, 2001; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc715887/m1/3/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.