Beam tomography in two and four dimensions. [100 MeV H/sup +/ beams and 750 keV H/sup -/ beams] Page: 3 of 6
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Results
In Pigs. 1 and 2 we show plots of emlttance
area versus percentage of total bean for beams
of 100 MeV and 7SO KeV energy. In both cases,
MOTT and HART are In good agreement with the
data gained with the silt and collector method,
vhlch la assumed to yield a density distribution
closest to the true beam distribution.
Me have compared the shape parameters a and
ft by displaying the residual betatron oscilla-
tion® AR/R for MENT and MART. The true
ellipse parameters are assumed equal to those
gained with the slit and collector methcd. In
Tig. 3 we show AR/R for the 750-KeV data. Both
algorithms give excellent reconstructions of the
emlttance distribution. Similar plots for the
100 MeV data are also shown In Pig. 3 Both
methods give values of AR/R approximately equal
to 0.1. In this ca.e the KENT results more
closely match the silt and collector results.
Contour plots of the reconstructed density
distribution are shown In Fig. 4 for the slit
and collector method, In Fig. 5 for the MART
algorithm and in Pig. 6 for the MENT algorithm.
Because we envision situations where the
matching of a beam emlttance to a llnac
acceptance should result In a value of AR/R as
small as 0.1, we desire an emittance-measuring
method whose accuracy can be characterized bv a
value of AR/R smaller than 0.1. Therefore we
are seeking corrections that will reduce the
value of AR/R in Pig. 3. We have determined
that this small but significant value cannot be
attributed to errors caused by nonideal viewing
- 05
v
E
E
UJ
1 1
*-
01
MENT ALGORITHM
MART ALGORITHM
SLIT AND COLLECTOR
"no.
Fig. 1.
100 90 60 70
PERCENTAGE OF TOTAL BEAM
Total enittances versus percentage of
the 100-MeV H* beam.
o MENT ALGORITHM
* MART ALGORITHM
• SLIT AND COLLECTOR
PERCENTAGE OF TOTAL BEAM
Fig. 2. Total emlttance verBUB percentage of
the 750-keV iT* beam.
angles or any artificial asymmetric emlttance
growth caused by the pixel mapping In MART.
An additional test of the algorithms was
made using generated asymmetric Gaussian
distributions. Both MART and MENT gave nearly
exact reconstructions. In this cuse our version
of MART Is superior to earlier versions that
gave reconstructions with Jaggee peaks and
fluctuations. The improvement Id apparently the
result of reconstructing profiles from column
■urns of transformed pixels. Profiles were
previously calculated from rays intercepting
pixels.
Four-Dlmenslonal Reconstruction Method
Me hace decided to use the MENT algorithm
to reconstruct four dimersional emlttance
distributions because It gives equally good or
slightly better two-dimensional reconstruction
and because It la relatively easy to expand MENT
to four dimensions. For the present we will
only consider reconstruction in llnac sections
where no energy change takes place, where
first-order optics Is valid, and where
space-charge effects can be expressed by a
linear transfer matrix.
The phase-Bpace density function of the
beam In a reference plane z » 0 can be denoted by
2
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Sander, O. R.; Minerbo, G. N.; Jameson, R. A. & Chamberlin, D. D. Beam tomography in two and four dimensions. [100 MeV H/sup +/ beams and 750 keV H/sup -/ beams], article, January 1, 1979; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1099167/m1/3/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.