The Application of the Principal Curve Analysis Technique to Smooth Beam Lines Page: 4 of 10
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Further Improvements to the Technique
Two immediate improvements are suggested through our experience. The first
involves the weighting of points in the smoothing routine so that a small area of
magnets can be "patched in" to existing elements. This would enable one to force
the direction of the beam line if movements of one section were not desirable. The
second improvement is not quite as straight forward. It involves the definition of
what is smooth. How does one stop the iteration process on sections of a beam
line where the alignment tolerances are not as well understood as they are for the
arcs. If this problem can be solved a general smoothing algorithm for any beam
transport line could be developed.
Conclusion
Through the application of principal component analysis a successful smooth-
ing procedure was developed for the highly coupled SLC beam line. The routine
allows for a flexible yet repeatable fitting of data which may be superimposed with
with unmodeled systematic measurement errors. A smoothness criteria was devel-
oped which reflected beam alignment tolerances and still allowed the number of
magnet adjustments to be minimized. The technique still needs improvement to
make it a general smoothing program but its application to the SLC has already
been highly successful.-155-
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Friedsam, H. & Oren, W. The Application of the Principal Curve Analysis Technique to Smooth Beam Lines, report, August 12, 2005; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc879026/m1/4/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.