Effect of emittance and rms phase error on angular flux density and pinhole flux-a simulation study of two undulators at 10.5 mm gap including very high harmonics. Page: 2 of 13
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Device and Emittance
A series of calculations was performed with the code UR1 to study the effect of the APS
emittance and beam energy spread on the angular flux density and pinhole flux for two devices
that show a large difference in the rms phase error at the same gap setting (10.5 mm): undulators
type A, 1) a 2.1-m-long "canted" insertion device with period length 3.3 cm and 3.70 rms phase
error, and 2) a similar device with 6.80 with rms phase error.
Two emittances are compared at 7.0 GeV beam energy and 100 mA current: i) the
routinely-used low-emittance lattice with emittance 2.5 nm-rad, coupling 2.9%, and beam energy
spread 9.6x10-4 (beam parameters from a typical run from May 30, 2003 were used), ii) the high-
emittance lattice2 with emittance 7.7 nm-rad, coupling 1.0%, and beam energy spread 9.6x10-4
(same as for the low-emittance lattice).
Results
The results are summarized in five tables and five figures below. Table 1 shows the
performance ratios for the angular flux density and table 2 the pinhole flux ratios at 10.5 mm
gap. Table 3 is a summary table for the lower odd harmonics that shows the author's estimate of
the expected performance for both quantities, and table 4 shows additional calculations at the
larger gap of 18.5 mm. The very high harmonics (up to and including harmonic 33) are
examined in table 5 for energies up to 100 keV. The figures are complementary to the tables and
show calculated spectra (figs. 1 - 4) and predicted intensity degradation due to field errors and
emittance (fig. 5).
The listed intensities are the peak values. The ratio for first harmonic is always close to
100% and was omitted (except in table 5). The calculated values of the ratios in this study are
accurate to about 1% for the angular flux density and 2% for the pinhole flux for the specific
set of measured field files being used. For another set of measured field files (or for an assembly
average of measured field files) with approximately the same rms phase errors, one may get
ratios that differ from the results here by twice the values given above-it is an estimate only as
a statistical study was not done.
1 R.J. Dejus and A. Luccio, Nucl. Instrum. Methods, A347, 61 (1994).
2 R.J. Dejus, I.B. Vasserman, S. Sasaki, and E.R. Moog, Argonne National Laboratory Report, ANL/APS/TB-45,
May 2002, p. 31.2
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Dejus, R. Effect of emittance and rms phase error on angular flux density and pinhole flux-a simulation study of two undulators at 10.5 mm gap including very high harmonics., report, March 9, 2004; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc781145/m1/2/: accessed May 8, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.