Short pulse generation by laser slicing at NSLSII Page: 4 of 5
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photon beam size axT = 84 pm from the modulated
electrons is a convolution of natural beam size determined
by beta function, the dispersion beam size, and the photon
beam size determined by diffraction limit. Take the
dispersion D. =6.5cm, the separation from the core
is Ax = DX (AE)_ / E = 440p1m. This leads to
Experiences from other lab require the separation ratio
larger than 5, so we need dispersion -6.5cm . For soft x-
rays beamline, because the larger divergence angle of the
soft x-rays radiation, a mixed coordinate and angle
separation gives better separation. Based on experiences
from SOLEIL  it is estimated to have dispersion
q=4.8cm, rW'=25mrad. Optimization of a mixed coordinate
and angle separation will be carried out later.
Flux of short pulses
The fraction 71 of the modulated electrons fall within
the observation window in one optical period is found to
be 0.14. Thus for the whole bunch the fraction is
;7 L / rb = 0.14x50 fs/30 ps ~ 2,3 x10-4. Photon flux
from EPU49 for 500mA core current is S=2x10'5
photons/s/0.1%BW at 1.4 keV. Assume 1000 bunches in
the ring , with revolution period 2.63 ps, the photon flux
per pulse for core bunch current 0.5mA is S x2.63 ps
/1000=5.3 x106 photons/0.1%BW . With the fraction
2.3x10 , the short pulse photon flux per pulse is then
1300 photons/0.1%BW. Assume repetition rate of
f,=1kHz, the short pulse photon flux is then 1.3 x106
photons/0. 1 %BW.
Short pulse fluxfor camshaft bunch of 5 mA
If we use camshaft bunch with current of 5mA, the
bunch lengthening is expected to reach 55ps instead of
15ps , the peak current is expected by extrapolation to
increase by a factor 10x15/55=2.7. Hence the photon flux
per pulse is 1300x2.7=3500 photons/0.l%BW.
Repetition Rate and energy spread
When the repetition rate fL of the laser increases, the
energy spread increases. Estimated by random walk, the
energy spread squared is found to be proportional to the
repetition rate with growth rate fLp 2TL / zb /2 =48/s,
where p=7.5 is the ratio of energy modulation over initial
energy spread, as calculate before. With radiation
damping rate 80/s we expect the energy spread increase
due to the modulation is not very large. However if we
increase the repetition rate to 10 kHz, to avoid the energy
spread increase, we may need to use 10 camshaft
Pulse duration in short straight section
In the transport process between the modulator and the
radiator, the short pulse length is expected to increase by
R due to the finite energy spread, contribution from
R5 and R5 is negligible. For a lattice without
dispersion in the straight sections we find R56 = 9.6 mm.
With energy spread 9 x10 , the spread of the path length
is Ae =9, m , and pulse length stretch is
2 A /c ~ 60 fs. The pulse of the modulated electrons
is a convolution of the laser pulse length and the slippage
length (see subsection 2 above), both 50 fs, so its length
without the stretch is -I2iTL = 70 fs . With the stretch,
the total output pulse length is 91 fs. A reduction of
R 56 in the lattice design with dispersion will be able to
reduce the pulse stretch. In a first attempt as shown in the
following, in a lattice with the desired dispersion we are
able to reduce R 56 to 4.8mm from 9.6 mm. Thus the total
output pulse length is found to be76fs.
Laser input and exit port and Rayleigh
Exit port is used for initial laser alignment. The position
and size of the laser input and exit port will affect the
design of the vacuum chamber in the long straight
section. Use the Rayleigh range formula, we find beam
waist w = 660pi m. At the photon shutter positioned at
L=18.5m, we find the laser beam size 7.2mm. The current
photon shutter widow size is about 3-4mm, hence we may
need to modify the photon shutter for the experiment,
unless we can find a method to initially align the laser
with only a part of the laser spot.
Lattice with dispersion at short straight section
The NSLSII lattice is designed without dispersion in the
straight sections. The introduction of dispersion in the
radiator in one of the many short straight sections requires
a modification and will break the symmetry of the ring.
Furthermore, since it is desired to have both soft and hard
x-ray beamlines, we need to modify the next long straight
section to have dispersion, thus generate distortion to
three sections among all the 30 sections. This distortion of
the lattice has to be corrected both linearly and non-
linearly and need extensive works. In addition, to
optimize the separation of modulated beam from the core,
there is a need for optimization of a mix between
coordinate and angular separation. This in turn requires a
dispersion with a slope in the straight section of the
As a first step we study the effect of introducing a
dispersion with z1=4.8cm, q'=25 mrad into the short
straight section immediately following the long straight
section where the modulator is located (figure 3). For this
lattice both horizontal and vertical tune between the two
centers of the long straight section remain the same as
without dispersion, the beta functions change is
minimized. The horizontal and vertical beta function in
the radiator are P,=1.7m, 8y=1.26m, near their original
values without dispersion. Maximum horizontal and
vertical beta functions are both 30 m. Figure 3 shows the
second half of the super-cell (26m-52m) is significantly
different from the first half, breaking the symmetry.
After sextupole optimization of the lattice, the tune
footprint and frequency map is shown in figure 4 and 5
respectively. We introduced 30p m misalignment errors
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Yu, L.; Blednykh, A.; Guo, W.; Krinsky, S.; Li, Y.; Shaftan, T. et al. Short pulse generation by laser slicing at NSLSII, article, March 28, 2011; United States. (digital.library.unt.edu/ark:/67531/metadc839917/m1/4/: accessed September 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.