Erik Hemsing SLAC National Accelerator Laboratory Designing Future X-ray FELs Workshop

Wednesday 31 August - Friday 2 September, 2016 Daresbury Laboratory

EEHG Status, Scaling, and Sensitivity

Outline

FEL temporal pulse

FEL spectrum

SASE FEL Dream FEL

•  Motivation

•  Echo Enabled Harmonic Generation

•  Recent Experiments

•  Scaling & Stability

•  Summary

Echo-Enabled Harmonic Generation (EEHG)

G. Stupakov, PRL 102, 074801 (2009) D. Xiang and G. Stupakov, 12, 030702 (2009)

Advantages •  Only small energy modulation needed •  UV laser converted to soft x-rays in single stage •  Tunable through dispersion •  Relatively insensitive to e-beam phase space

distortions

Challenges •  Preservation of fine phase space

correlations •  Sensitive to intrabeam scattering,

diffusion, and laser quality

4

Past Echo Experiments

ECHO-3 (2010) (a)

(b)

(c)

350 400 450 500 550 Radiation wavelength (nm)

600

HGHG

HGHG Echo

1590 nm laser on

795 nm laser on

Both lasers on

D. Xiang et al., PRL 105, 114801 (2010)

4th 5th 6th 7th

D. Xiang, et al, PRL 108, 024802 (2012).

ECHO-7 (2012)

Echo

HGHG

ECHO-15 (2014)

E. Hemsing, et al PRST-AB 17, 070702 (2014)

Echo

HGHG

ECHO-3 (lasing 2012)

Z. T. Zhao, et. al., Nature Photonics 6, 360–363 (2012)

Echo in high harmonic regime

∆E1 ∆E2 R56(1) R56

(2) 60 keV 100 keV 12.5 mm 484 um

∆E1 ∆E2 R56(1) R56

(2) 38 keV 84 keV 12.5 mm 600um

•  2400 nm to 40nm, 32 nm (190 MeV) •  Signals at undulator harmonics

Echo 60 Echo 75

E.H, et. al., Nature Photonics 10, 512–515 (2016)

6

Precision control of single harmonics with dispersion

38 40 42 44 46 480

0.5

1

1.5

2

2.5

3

3.5

λ [nm]

λ [nm]

R56(2

) [µm

]

38 40 42 44 46 48

38 40 42 44 46 480

1000

2000

3000

4000

λ [nm]

660 700

µmµm

660 700

µmµm

a

bλ [nm]

38 40 42 44 46 48

600

620

640

660

680

700

720

R56(2

) [µm

]

600

620

640

660

680

700

720c

d|b

|2 (x1

03 )

Inte

nsity

[arb

. unt

is] R56

(2) R56(2)

∆E1 ∆E2 R56(1)

29 keV 27 keV 12.5 mm

Simulation parameters

•  Echo harmonics with two 800 nm lasers near 40 nm •  Scan second R56 to tune harmonics •  nm-scale control of spectrum observed

Experiment Simulation

7

Scaling

Harmonic frequency

Bunching factor

Scaling parameter

Harmonic number

EEHG HGHG

8

Scaling parameter ξ

0 5 10 15 20 250

1

2

3

4

5

j H

A1

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

|e−j

H2/2

J n(−j H

A 1)|

n=1n=10n=20

0 5 10 15 20 25ï2

ï1

0

1

2

j E

A1

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

|e−j

E2 /2J n(−

j EA 1)|

n=ï1n=ï2n=ï3

Optimized in both EEHG and HGHG by maximizing

Optimum given by

only for EEHG

Ex: EEHG n=-1, A1=3:

whereas HGHG A1≈n:

9

Bunching sensitivity to manipulation errors/jitter

… on laser 1 fluctuations:

If (ΔA1/A1)EEHG=(ΔA1/A1)HGHG:

… on laser 2 fluctuations:

If (ΔA2/A2)EEHG=(ΔA1/A1)HGHG:

Bunching dependence on scaling parameter. (eg, first chicane):

EEHG less sensitive to 1st energy modulation

EEHG comparable sensitivity to 2nd energy modulation

Central wavelength shifts

Reduced sensitivity of EEHG to phase space distortions stabilizes central wavelength against jitter

Affects stability of EEHG vs cascaded HGHG

EEHG

HGHG

Linear electron beam chirp, h1 shifts harmonics according to scaling parameter Δa=-ξ h1:

E. H, et al PRST-AB 17, 070702 (2014)

Bandwidth

0.38 nm 1 nm •  Non-linear curvature adds more bandwidth to HGHG by shifting wavelengths across the beam

•  front is compressed, back is decompressed

•  EEHG less sensitive because strong initial R56 removes this smooth variation

EEHG HGHG

EEHG bandwidth has stronger dependence on linear chirp than HGHG due to stronger dispersion which changes bunch length:

Bandwidth dependence on pure quadratic chirp h2 same as for linear chirp:

12

Excitation bandwidth

Laser manipulations can also excite nearby frequencies if they are within the bandwidth of the harmonic up-conversion process.

5 10 15 200

10

20

bunc

hing [

%]

λ [nm]

5 10 15 20

|b20||b|

12.5 13 13.50

10

20

bunc

hing

[%]

h [nm]

12.5 13 13.50

0.5

1|bï1,21|

|b|eïj

2/2

Can be made smaller than ρ broadband

satellite

13

Influence of initial energy modulation

An initial, pure sinusoidal modulation

modifies the bunching spectrum

At the harmonic bunching frequency (q=0):

Modulation kills the bunching whenever

So because EEHG can tolerate larger initial energy modulations than HGHG.

14

Influence of multiple energy modulations at different frequencies (eg, MBI)

5.185 5.19 5.195 5.2 5.205 5.21 5.2150

1

2

3

4

5

6

7

8

9

h [nm]

|b| [

%]

10ï4 10ï20.75

0.8

0.85

0.9

0.95

1

relative bandwidth

fract

ion

of p

ower

5.185 5.19 5.195 5.2 5.205 5.21 5.2150

1

2

3

4

5

6

7

8

9

h [nm]

|b| [

%]

10ï4 10ï2

0.7

0.8

0.9

1

relative bandwidth

fract

ion

of p

ower

5.185 5.19 5.195 5.2 5.205 5.21 5.2150

1

2

3

4

5

6

7

8

9

h [nm]

|b| [

%]

10ï4 10ï2

0.4

0.6

0.8

1

relative bandwidth

fract

ion

of p

ower

Broadband modulations with total effective amplitude A0 appear as pedestal

Excitation bandwidth << ρpedestal

satellite

EEHG survives, HGHG completely suppressed.

Moving to x-rays: EEHG vs Self Seeding @ LCLS

0

5.0×1012

1.0×1013

1.5×1013

2.0×1013

2.5×1013

3.0×1013

539 539.5 540 540.5 541

#γ/e

V

Eγ [eV]

s [µm]

E [G

eV]

0 5 10 15 20 25 30 35

3.484

3.486

3.488

3.49

3.492

3.494

3.496

!

Images courtesy of G. Penn, G. Marcus, and D. Ratner.

Simulation comparison with SRXSS results Echo seems more robust to MBI •  Spectral pedestal suppressed, narrower

bandwidth •  Cascaded HGHG performs worst •  More dedicated simulation work needed

SXRSS

ECHO

EEHG looks like a promising method to obtain a cleaner pulse with higher spectral brightness,

but needs more benchmarking with experiments and theory.

16

Physics Issues

Fine-grained phase space correlations susceptible to wash out from •  Intrabeam scattering (Coulomb collisions) •  Quantum diffusion (ISR) •  Higher order transport contributions Bunching compromised by •  Laser variations (temporal, x-verse, spectral phase…) •  Structure in e-beam phase space (nonlinear curvature,

MBI)

17

Simulations

Codes must handle highly non-linear transformations in transport AND during lasing Strong slice to slice variations in current (λ2 periodic) and energy Physics issues (e.g, scattering) should be included self consistently

Summary

•  Echo 60 and 75 observed. Results in good agreement with theory •  EEHG now in same harmonic regime as cascaded HGHG -> soft x-

rays from UV lasers •  Individual harmonics tuned with dispersion. Sub-wavelength control

over harmonic envelope •  EEHG scaling favorable for tunability/stability in SXRs •  SLAC exploring EEHG options for LCLS-II •  Collaborations with FERMI ramping up for various possible EEHG

experiments at soft x-rays

•  Thanks to NLCTA team •  And Thank you for your attention!

This work was supported by the US DOE Office of Basic Energy Sciences under award no. 2012-SLAC-10032 using the SLAC NLCTA facility, which is partly supported by US DOE Office of High Energy Physics under contract no. DE-AC02-76SF00515.