PICOSECOND-RESOLUTION "SLICE" EMITTANCE MEASUREMENT OF ELECTRON-BUNCHES. Page: 4 of 5
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R"+R'-= 21 E, 13
r YIAR y2 R3
R is the local envelope, ris the energy, IA is the van Alfven
current, I is the local current and EN is the normalized local
The emittance correction relies on a laminar flow beam
waist, which is described by the envelope equation without
the emittance term. We can define a critical beam waist
envelope size, R, by equating the two terms on the right
hand side, resulting in:
A beam waist that is larger (smaller) than the critical size,
Rc, is dominated by space charge (emittance). The
emittance dominated beam waist leads to a cross over of
electrons at that particular slice. Since Rc is a function of
the current, the low current slices will cross over while high
current ones will maintain a laminar flow.
This is not the problem with beam slices that have too
little (or too much) current. The slope of the beam ellipse in
phase space, given by R '/R, can be tracked by integrating
the envelope equation without the emittance term .
Plotting the slope at a point downstream of the solenoid
lens as a function of beam current and various focusing
powers of the lens, one learns the following:
* There are a few values of the focusing strength that
result compensated beams.
* A lower limit and an upper limit slice current exist for
each solution such that the slices with a current lower
than the lower limit or higher than the upper limit will
not align their slope with the compensated slices.
" The range of current for which the slope is constant (an
emittance compensated range) depends on various
parameters: initial conditions, position of the lens,
position of the observation point, position and gradient
of the accelerator (if there is one) and so on.
* The best solution is the first one (the lower lens
A Gaussian photocathode laser longitudinal
distribution is thus bad for emittance compensation since it
will result low current slices at the head and the tail of the
electron bunch. The laser distribution may be modified on a
sub-picosecond scale by known optical techniques. Using a
slice-emittance measurement one may observe the results
of the laser profile modification and tune the beam for a
3 TOMOGRAPHIC MEASUREMENT OF SLICE
By discussing beam ellipses or by making a-priory
assumptions concerning the distribution of the beam in
phase space in order to fit a quadrupole scan data (or other
measurement techniques) to some beam parameters we are
loosing a lot of information. As has been shown by
McKee, O'Shea and Madey , one can apply tomographic
techniques to a quadrupole scan and derive the full phase
space distribution. This is a powerful technique that,
together with the slice emittance measurement technique
can provide a greater understanding of the beams of
photoinjectors and help improve the performance.
Figure 4 shows the measured phase space density
distribution of the total beam (not just one slice). The
horizontal axis is a transverse coordinate (horizontal, in this
case) in mm, and the vertical axis is the divergence in mrad.
This is an emittance compensated beam from the ATF
photoinjector. It is possible to see the typical beam halo that
shows up in measurements even with the limitted dynamic
range (8 bits) of our frame grabber. The measured
quadrupole-scan rms normalized emittance is about 4.5 mm
mrad. However, as discussed above, the large halo causes
an underestimation of the emittance.
-2 -1 0 1 2
Figure: 4 Tomographic reconstruction of the horizontal
non-normalized phase space of the total bunch of an
emittance compensated beam. The horizontal axis is in
milimeters, the vertical axis is in miliradians.
Figures 5,6 and 7 show the (transverse-vertical) phase
space distribution of a beam slice of 50, 100 and 200 pC,
respectively. (Please notice the change of scale from Figure
4, but the units are still mm and mrad). Some of the
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BEN-ZVI,I.; QIU,J.X. & WANG,X. PICOSECOND-RESOLUTION "SLICE" EMITTANCE MEASUREMENT OF ELECTRON-BUNCHES., article, May 12, 1997; [Upton, New York]. (digital.library.unt.edu/ark:/67531/metadc892001/m1/4/: accessed January 21, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.