SFLASH SASE interference setup & optics rough estimation 1d estimation 3d estimation summary

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 MeV

Erms 150 keV

n 1.5 µm

modulator undulatorK = 4.3

L = 1.45 m

0

220

~

P

PKLcm L

I

uu

modulation amplitude

keV 550150

FLASH @ 19 nmundulator

laser

2rms

160 165 170 175 180 185 1900

5

10

15

20

25

30

35

40

x / my / m

quadsundulators

vertical correctors

chicane 1 chicane 2 chicane 3

160 165 170 175 180 185 190 195 2000

5

10

15

20

25

30

35

40

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

5

10

15

20

25

30

35

40

2 3

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

if linear:

cF

iZZ r

r

2

20

2

2exp

2du

u

uF k 4.3Z from

e

krZI

ref

c1,5612

15 amplification of energy modulation

(3) - chicane 1, r56c3 = 170 µm

e

ZIkr

I

I

ref

1c3,56

2

3

ˆ

ˆ

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

5

10

15

20

25

30

35

40

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

5

10

15

20

25

30

35

40

current

bunc

h co

ordi

nate

/ m

beam line coordinate / m

-6-4

-20

24

6

x 1

0 -5

0

1000

2000

3000-6

-4-2

02

46

x 1

0 -5

0

1000

2000

3000

Emod = 250 keV3D Calculation

after chicane 1 before chicane 2

Curr

ent /

A

_rm

s / e

V

/ 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

Emod = 250 keV3D Calculation

Curr

ent /

A

_rm

s / e

V

/ eV

bunch coordinate / m

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

~ 14.6 m

after chicane 3 before SASE undulator

Emod = 250 keV3D Calculation

Curr

ent /

A

_rm

s / e

V

/ eV

bunch coordinate / m

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

~ 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

5

10

15

20

25

30

35

40

Emod = 250 keV3D Calculation

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

10

20

30

40

50

60

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

300

350

400

450

500

550

600

650

700

The rough estimate Observed behavior

Electron macro pulse number

Ener

gy in

pho

ton

puls

e