Some Simulations for the Proposed Hard X-Ray Self-

Seeding on LCLSJ. Wu et al.

Feb. 25, 2011

Possible experiment at LCLS• DESY’s scheme for 8 keV HXRSS

– Low charge 20 pC, 0.4 mm-mrad emittance, slice energy spread 1.3 MeV

– Plan to take the section 15 undulator out to implement the chicane and single crystal

• Numerical Simulation – with ideal electron bunch– with start-to-end electron bunch

• Additional details– Energy tuning– X-ray angular divergence

Ideal simulation• SASE FEL performance

13-46.8,14-50.4,15-54

SASE FEL at exit of Und.13• Plan to take out the 15th undualtor, • SASE FEL from the exit of 13 undulator on the

single crystal– We reserve the 14th for safety consideration

Single crystal monochromator

• FEL spectrum after the single-crystal monochromator

Single crystal monochromator• FEL after the single-crystal monochromator

Self-seeded FEL at exit of und 10

• There are 18 undualtors after the monochromator– FEL at the exit of 10 undulator (no tapering) –

minimum bandwidth

2.8E-5

Maximum power with taper• Taper the 18 undualtors after the

monochromator– Taper starts at 25 m, quadratic taper of 2 %– At the end of 18 undulator (60 m magnetic

length), FEL power reach 100 GW (< 1 mJ for low charge 20 pC)

Self-seeded FEL at exit of Und 18

• There are 18 undualtors after the monochromator– FEL at the exit of 18 undulator

1.0E-4

Start-to-end e- bunch: und.-comp.

t (s) z (mm)

d(m

m)

Courtesy of Y. Ding

Start-to-end simulation• SASE FEL performance

– Taper starts at 25 m, quadratic taper of 2 %

13-51.9,14-55.8,15-60

S-2-E electron bunch• Simulation with S-2-E electron bunch

– SASE @ 132 m, blue: raw data, green, smoothed data (2%), red: Gaussian fit

FWHM BW:2.5E-3FWHM BW:

3.3E-3

Start-to-end simulation• Seeded FEL (5 MW seed) performance

13-51.9, 18-72

S-2-E electron bunch• Simulation with S-2-E electron bunch

– Pseed= 5 MW @ 15 m, blue: raw data, red: Gaussian fit

FWHM BW:2.5E-3FWHM BW:

9.4E-4 FWHM BW:1.1E-4FWHM BW:

1.3E-4

S-2-E electron bunch• Simulation with S-2-E electron bunch

– Pseed= 5 MW @ 15 m

S-2-E electron bunch• Simulation with S-2-E electron bunch

– Pseed= 5 MW @ 51.9 m, blue: raw data, green, smoothed data (0.25%), red: Gaussian fit

FWHM BW:2.5E-3FWHM BW:

9.4E-4 FWHM BW:1.1E-4FWHM BW:

2.6E-4

S-2-E electron bunch• Simulation with S-2-E electron bunch

– Pseed= 5 MW @ 51.9 m

S-2-E electron bunch• Simulation with S-2-E electron bunch

– Pseed= 5 MW @ 72 m, blue: raw data, green, smoothed data (0.1%), red: Gaussian fit

FWHM BW:2.5E-3FWHM BW:

9.4E-4 FWHM BW:1.1E-4FWHM BW:

2.8E-4

S-2-E electron bunch• Simulation with S-2-E electron bunch

– Pseed= 5 MW @ 72 m

FEL Energy Tuning• The plan is to have a tuning range from 1.4 Å to

1.6 Å• Rocking curve:

– The bandwidth in the rocking curve depends on |C = cos(2qB)| for p - polarization, and |C = 1| for s - polarization

p - polarization

s - polarization

8 keV energy-jitter case• Spectrum on the left, temporal profile on the

right– l =1.4 Å; Bragg angle: 51.72o

– p - polarization

8 keV on-energy case• Spectrum on the left, temporal profile on the

right– l =1.5 Å; Bragg angle: 57.25o

– p - polarization

8 keV energy-jitter case• Spectrum on the left, temporal profile on the

right– l =1.6 Å; Bragg angle: 63.78o

– p - polarization

8 keV energy-jitter case• Spectrum on the left, temporal profile on the

right– l =1.4 Å; Bragg angle: 51.72o

– s - polarization

8 keV on-energy case• Spectrum on the left, temporal profile on the

right– l =1.5 Å; Bragg angle: 57.25o

– s - polarization

8 keV energy-jitter case• Spectrum on the left, temporal profile on the

right– l =1.6 Å; Bragg angle: 63.78o

– s - polarization

Maximum power with taper• Taper the 18 undualtors after the

monochromator– Taper starts at 25 m, quadratic taper of 2 %– Divergence along the undulator

Self-seeded FEL at exit of 18 undulators

• There are 18 undulators after the monochromator– FEL at the exit of 18 undulator

Angular divergence• To incorporate the x-ray beam divergence into

dynamic theory of diffraction• We take a phenomenological approach, we

define the effective Darwin width as

where W is the FWHM beam divergence• Then we follow the derivation in dynamic theory

of diffraction by introducing an effective deviation parameter

sisrsisrs ii ddddd 22222 22 W

sisr

os

i dd

qq22 22 W

-

Angular divergence• The transmitted intensity is then

withand t being the crystal thickness.

2

212

21

02

)(

1

/1/12/exp14

m

--

--

tI hodo

1/;/exp;/exp 221 -- pp Bitit

Rocking curve• Left plots for p - polarization, and right plots for s - polarization

– The red curve is for ideal parallel incident beam, the blue is for rms sx’ = 2 mrad, and the green is for rms sx’ = 4 mrad.

On-going work

• Refine the S-2-E simulation for 20 pC• Optimize the tapering• Simulation for 40 pC case• Find out the minimum seed power to

dominate the SASE in the second undulator