Phase Stable Net Acceleration of Electrons From a Two-Stage Optical Accelerator Page: 4 of 6
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Scanning the Piezo Mirror
(a)
**
y = (1064/800) x - 1.910 2
1064nm Phase Monitor (radians)-c
C)
m'
co
-J
C)
0
E
0
0Long-term Drift of the Phase
(b)
1064 nm phase
800 nm phase
Phase Difference
800 10642-
0
-c-2
- -4
a-
-6
-8
4C2000 3000
Time (s)FIG. 3. (Color) Phase stability of the net acceleration experiment. The figure on the left shows the linearity of the phase monitor to the
experiment laser phase while the phase is actively scanned using the piezo delay mirror. When the phase is fixed the slow drift of the
phase can be observed. Over time the experiment laser phase can wander away from the phase of the monitor system. The fast jitter is
13* rms.oscillations in the electron spectrum centroid energy, en-
ergy spread, and asymmetry.
One of the challenges to observing net acceleration and
the expected sinusoidal variation of the acceleration with
IFEL-ITR phase is the small laser-electron interaction
strength compared to the noise. In the end the measured
net acceleration was comparable to the mean energy and
energy spread jitters and much less than the total energy
spread. To help observe the acceleration, a first method
employed to analyze the data uses a frequency "lock-in"
method for obtaining small signals in a noisy background.
The piezo is driven linearly to obtain 27r of laser phase
shift every 10 seconds, or 100 events at 10 Hz. Since the
piezo has a finite range, the motion is actually a saw-tooth
function. In postanalysis the electron energy spectra quan-
tities are Fourier transformed into the frequency domain.
Figure 4 shows the discrete Fourier transform for the phase
monitor signal along with the electron spectra centroid,
spread, and asymmetry. The phase monitor duplicates the
original saw-tooth drive function to the piezo. Clearly
visible in the remaining three plots is a signal at the
original drive frequency of 0.1 Hz.
The analysis of Fig. 4 confirms that net acceleration is
taking place and that all three electron energy quantities
vary sinusoidally with the phase as expected. However,
interpreting the amplitude of net acceleration from this
analysis is less clear. In addition, a more compelling dem-
onstration of the net acceleration would be made by direct
correlation between the IFEL-ITR phase and the energy
centroid. This, however, runs into difficulties regarding
poor signal to noise, especially for discerning the energy
centroid shift. In the case of the energy spread variation,
the signal to noise is much better and the sinusoidal varia-
tion can be seen in binned correlation plots using only a
few hundred laser-electron interaction events. Observingthe other quantities requires greater statistics. However, for
long runs the possibility of the drift of the phase offset
between the laser-electron interaction and the monitor
system could potentially washout a correlation signal.
Figure 5 shows an example of this drift seen in a long
data scan of 7000 events taken over a 12 min period. Two
subsets of the data taken minutes apart show differing
phase offset in the energy spread to phase correlation
plot. Both sets clearly show the sinusoidal variation but
with much different offsets. If the two subsets were com-
bined, the variation would disappear. Thus, in order to take
advantage of greater statistics to clearly distinguish the
oscillation of the energy centroid, it is necessary to account
for the drift of the phase offset. By taking several subsets
the time evolution of the phase offset can be found from the
energy spread data. This evolution is shown in the right
plot of Fig. 5.
The phase drift observed in Fig. 5 can be used to produce
drift corrected phase correlations for the entire data set.
This is shown in Fig. 6. The data for the three correlation
plots are binned and plotted along with a fit to a cos
function. Cuts are applied to remove laser off and
"bucket-hop" events where no laser-electron interaction
occurs. The error bars are the standard deviations of the
means for each bin. With the benefit of greater event
statistics and slow phase drift correction, the sinusoidal
variations of all three energy spectra quantities are clear.
As predicted from the simulation, the asymmetry is -r
out of phase with respect to the centroid while the energy
width is - - 7r/2 out of phase. Prior to this run, the IFEL
and ITR interactions were established separately with
modulation strengths of 80 and 35 keV, respectively, and
an initial energy spread of 47 keV fwhm without laser
interactions. This gives an average bunching factor for
the beam of b1 = 0.35 [Eq. (1)] and an expected centroid1000
-2
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Sears, Christopher M. S.; Colby, Eric; England, R. J.; Ischebeck, Rasmus; McGuinness, Christopher; Nelson, Janice et al. Phase Stable Net Acceleration of Electrons From a Two-Stage Optical Accelerator, article, November 11, 2011; United States. (https://digital.library.unt.edu/ark:/67531/metadc845231/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.