Pattern Recognition: The Importance of Dispersion in Crystal Collimation Page: 2 of 15
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September 17, 2008
The Importance of Dispersion in Crystal Collimation
University of Chicago
Brookhaven National Laboratory
One aspect of the upcoming CRYSTAL experiment is to study the dynamics of single
protons circulating the SPS in the presence of a crystal. Under some circumstances (for
example under crystal channeling) a proton may hit the crystal and the neighboring
silicon strip position detectors only once, before extraction from the SPS. In general (at
most crystal rotation angles) it is expected that single protons will hit the crystal many
times, with many accelerator turns between each hit, before escaping. Intermediate
regimes are also possible (for example under volume reflection) in which a proton hits
the crystal only a few times over many turns before being lost.
It is crucial that the data analysis of each single proton data set be able to dis-
tinguish between these different dynamical phases, and to be able to convincingly
demonstrate that the fundamental processes at play in each phase are well understood.
Distinguishing between dynamical phases depends crucially on the ability to perform
pattern recognition - at least visually, but preferably quantitatively - on the single
proton data sets.
This note shows that synchrotron oscillations significantly affect the hit pattern of
a proton on the crystal. (By hit pattern we mean either the measurement vector of
turn number and penetration depth, for each proton, or a vector that can be directly
derived from the measurement vector, such as the vector of inferred synchrotron phase
and penetration depth.) The analysis is (deliberately) as rudimentary as possible, using
an elementary linear calculation which neither includes any higher order effects in the
accelerator, nor any dynamical interactions between the test proton and the crystal or
the silicon detectors.
Single particle simulation studies need to be carried out for CRYSTAL, exploring
realistic effects besides dispersion, such as multiple scattering, dead zones, energy loss,
dispersion slope, and linear coupling. Only after analysis software becomes available
to interpret the output of such studies will it be possible to predict with any confi-
dence that it will be possible to distinguish all single proton dynamical phases in the
CRYSTAL experiment. Then reality will prevail.
Here’s what’s next.
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Peggs,S. & Shiraishi, S. Pattern Recognition: The Importance of Dispersion in Crystal Collimation, report, September 1, 2008; United States. (digital.library.unt.edu/ark:/67531/metadc893094/m1/2/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.