# 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

Ax/-XT =440pm/84pm=5.1

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 [4] 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 [8], 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

bunches.

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

radiator.

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 February 22, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.