sFLASH SASE interference

sFLASH SASE interferencesetup & optics

rough estimation

1d estimation

3d estimation

summary

setup & opticsfrom

q 0.3 nC

estimated electron beam properties

estimated photon beam properties

Ipeak 1.5 kC

E 585 MeVErms 150 keVn 1.5 µm

modulator undulatorK = 4.3

L = 1.45 m

0

220

~

PPKLcm L

I

uu

modulation amplitude

keV 550150

FLASH @ 19 nmundulator

laser

2rms

160 165 170 175 180 185 1900

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x / my / m

quadsundulators

vertical correctors

chicane 1 chicane 2 chicane 3

160 165 170 175 180 185 190 195 2000

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1 2

(1) - energy modulation

rough estimation

kA 2.4 66.0

ˆrefc1,5612

krII

keV 550150

(saturation)

(2) - conversion to density modulation, chicane 1, r56c1 = 220 µm

kA 5.11 I

160 165 170 175 180 185 190 195 2000

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2 3

(23) - discrete impedance, L 23 m, av 10 m

if linear:

cFiZZ r

r

22

0

2

2exp2

duu

uF k 4.3Z from

ekrZI

ref

c1,5612

15 amplification of energy modulation

(3) - chicane 1, r56c3 = 170 µm

eZIkr

II

ref

1c3,56

2

3

ˆˆ

10 amplification of density modulation

4

k 4.2Z(34) - discrete impedance, L 16 m, av 10 m

1d estimation

160 165 170 175 180 185 190 195 2000

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1 2 3 4 5

1 discrete modulation12 discrete impedance, L = 2.6 m, av = 10.6 m2 discrete longitudinal dispersion, chicane 1, r56 = 220 µm23 discrete impedance, L = 4.7 m, av = 10.1 m3 discrete longitudinal dispersion, chicane 2, r56 = 3 µm34 discrete impedance, L = 17.7 m, av = 7.7 m4 discrete longitudinal dispersion, chicane 3, r56 = 170 µm45 discrete impedance , L = 16.3 m, av = 9.8 m

40E6 macro particles

space charge interaction: discrete, 1d

energy modulation: discrete in middle of modulator

no CSR interaction

next slide: explore linear domain

initial modulation amplitude keV 20

initial uncorrelated energy spread keV 10 keV 150 rms

1d estimation

longitudinal phase space current

keV 20

keV 10 rms

MeV 2 kA 1ˆ I

MeV 2

same, but Erms = 150 keV

keV 100

keV 150 rms

MeV

MeVnon linear !!!

~ 3 MeVrms energy spread

keV 500

keV 150 rms

MeV

MeVnon linear !!!

~ 3.5 MeVrms energy spread

~ 3.5 MeV rms energy spread

keV 500

~ 2 MeV rms

3D

3d estimation20E6 macro particles

space charge interaction: full 3d Poisson solver

equidistant mesh: 15 µm × 15 µm × 800 nm/(10)

step width: 2 cm (beam-line coordinate)

modulation: Emod = 250 keV discrete in middle of modulator (= instantaneous)

no CSR interaction

Emod = 250 keV3D Calculation

160 165 170 175 180 185 190 195 2000

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current

bunc

h co

ordi

nate

/ m

beam line coordinate / m

-6-4

-20

24

6

x 10-5

0

1000

2000

3000-6-4

-20

24

6

x 10-5

0

1000

2000

3000


after chicane 1 before chicane 2

Curr

ent /

A_

rms /

eV

/

eV

bunch coordinate / m

rms spread in 400 nm “slice” rms spread in 400 nm “slice”

~ 2.5 m

after chicane 2 before chicane 3


Curr

ent /

A_

rms /

eV

/

eV



~ 14.6 m

after chicane 3 before SASE undulator


Curr

ent /

A_

rms /

eV

/

eV



~ 14.2 m

~ 2 MeV rms

50 µm, 170 fsec

15 µm, 50 fsec

curr

ent /

A

bunch coordinate 1E-4 / m beam line coordinate / m

160 165 170 175 180 185 190 195 2000

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current/A

beam linecoordinate/ m

bunch coordinate/ m

current/A

beam line coordinate/ m

“side view”

period of plasma oscillation

120 m

summarymodulator:

1d estimation (without plasma osc.):

3d estimation:

gain length (Ming Xie)

keV 550150 2rms

linear gain ~ 100

saturation even with minimal modulationMeV 5.33rms

MeV 2rms plasma oscillations, period 120 m

m 29MeV 3

m 11MeV 2

rms

rms

g

g

L

L

weak amplification in 30 m SASE undulator

First Shot at Statistics

• Assume laser pulse eliminates lasing within FWHM completely• Take a few hundred SASE simulation results (0.25 nC) and apply the above • Let the ‘laser pulse’ jitter by about 100 fs

-40 -30 -20 -10 0 10 20 30 40 50 600

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s[um]

P[G

W]

P(s) at z=14 m

Comparison to Observation

0 20 40 60 80 100 120 140 160 180 200200

250

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550

600

650

700

The rough estimate Observed behavior

Electron macro pulse number

Ener

gy in

pho

ton

pulse

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sFLASH SASE interference