Experiments with a synchrotron x-ray source and conventional, ECR, and storage-ring ion sources Page: 11 of 13
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The background rates can be easily calculated with the following
approach. For the K-shell case, several electrons are removed in the
photoionization process. Therefore, single charge-changing events are
not a problem. The rate for direct Coulomb ionization of the K-shell
can be found using a luminosity for interactions vith the background
gas in the experimental straight section of 2 x 10'5 cm s' and a
K-shell vacancy production cross section of about 200 b for copper on
hydrogen at about 2.9 MeV/u beam energy. The background rate is then
found to be about 4000 Hz. This rate can be handled by conventional
detectors with no difficulty.
The signal-to-background ratio is better than 13/4000 because
advantage can be taken of the pulsed nature of synchrotron radiation
by accepting events only when the photon beam is on. The correction
for duty cycle improves the signal-to-background value. Normally, the
NSLS operates with 25 x-ray bunches which have a width of 0.6-1.0 ns
(4a) and a revolution frequency of 567.7 ns. The duty factor is then
0.026 to 0.044 at the 4a width. The duty factor is taken as about
0.03 for illustrative purposes. Therefore, we find:
Signal/Background - 13/(4000 x .03) - .11.
Accurate measurements of the signal can be made in the course of
a few minutes under these conditions. The uncertainty in the
measurement, 5, is given by:
62 m a x b/(s2 x t6)
where s is the signal counting rate, b the background counting rate,
and a is the NSLS duty cycle, 0.03. Evaluation of this relationship
for the calculated rates gives an uncertainty in the measurement of
10" for a measurement time of - 70 s and 5% for a measurement time
of less than 5 min.
Now, look at the outer shell case. The signal rate is found as
before, but now using a cross section of 1.2 Mb. The rate calculated
using the above luminosity is 516 Hz.
The background in the one-electryn loss detector is simply
calculated. The electron loss lifetime is 5000 s at a beam energy
of 2.9 MeV/u and about 14,100 s at a beam energy of 7.1 MeV/u. The
rate in the corresponding detector is then about around 5.5 x 105 Hz.
This is still a rate which can be handled with a conventional
detector. Or, the problem can be alleviated by running at reduced ion
currents or using an aperture to reduce the fraction of beam accepted,
etc.
Signal-to-background is then: Signal/Background - 516/(5.5 x 105
x .03) - .031 at the low beam energy and: Signal/Background -
516/(2.0 x 105 x .03) - .086 at the high beam energy.
The values are similar to the K-shell case calculated above and
thus accurate measurements are also feasible within a matter of
minutes. Using the formula cited above, we find that the time needed
for a measurement with an uncertainty of 5% is 24 s at a beam energy
of 2.9 MeV/u. Even if the ion beam current is reduced by an order of
magnitude, to limit the count rate, the measurement time will still
be below 5 min.
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Jones, K. W.; Johnson, B. M. & Meron, M. Experiments with a synchrotron x-ray source and conventional, ECR, and storage-ring ion sources, article, January 1, 1988; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc1107459/m1/11/: accessed May 6, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.