An electrostatic energy analyzer for longitudinal energymeasurements Page: 4 of 18
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done is to replace the drift length at the exit of the cylindrical electrodes
by the observed 11 ins. instead of the calculated 6.4 ins. For this reason,
these values have questionable significance.
Coarse calculations show that space charge can easily produce the dis-
placement of the image plane by 4.6 ins. Incorporating the exact fields in-
to the paraxial calculations is impossible since the charge density between
the cylindrical electrodes is unknown. However, one can make estimates using
sheets of uniform density as models for the beamlet. One then finds that the
drift regions before and after the cylindrical electrodes can account for no
more than 1.3 ins. of displacement. A charge density between the cylindrical
electrodes not less than approximately 1/8th of the beam density of
2 x 10-5 coul/m3 could produce the additional 3.3 ins, of displacement.
The dispersion coefficient would change from 0.15% to 0.16% per wire.
A disconcerting effect of space charge is that it produces an offset in
the energy vs. voltage relation that causes equation 1 to give too high an
energy. For the model mentioned above, this offset is approximately 12%.
Comparison with time-of-flight measurements showed no discrepancy of that
magnitude. A more exact evaluation of space charge effects is required.
Not shown in Figure 1 are the widths of the cylindrical electrodes and
screening electrodes. The screening electrodes are 4 ins, wide and the cy-
lindrical electrodes are 5 ins, wide when the 1/2 in. diameter "corona rings"
are included. (The "corona rings" extend the region of acceptable electric
field values. l). In comparison, the beam width is approximately 0.8 in. at
the slit aperture.
The screening electrodes control fringe field effects and make it pos-
sible to define an effective boundary to the fields, which in this device oc-
curs approximately 0.35 in. out from the electrodes.2 If one interprets
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Sato, A.H. An electrostatic energy analyzer for longitudinal energymeasurements, report, September 1, 1985; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc876366/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.