Harmonic lasing in the LCLS-II(a work in progress…)

G. Marcus, et al.03/11/2014

2

Outline

• Motivation

• Background

• Beamline geometry and nominal (ideal) parameters

• Steady-state analysis (SXR)• 3rd harmonic

• Time-dependent GENESIS• 3rd harmonic of Eγ = 1.24 keV• Various configurations (intra-undulator phase shifts)

• G. Penn scheme for 4.1 keV photons from SXR

• Repeat for HXR (5 keV)• Include Schneidmiller NIMA phase shifter recipe

• Spectral filtering

3

Motivation

• Harmonic lasing can be a “cheap” and relatively efficient way to extend the photon energy range of a particular FEL beamline

• In comparison to nonlinear harmonics, can provide a beam that is more• Intense• Stable• Narrow-band• Therefore, an increase in brilliance

• Suppression by• Phase shifters• Spectral filtering• PenndulatorTM

4

Background

• Eigenvalue equation for a high-gain FEL with 3D effects was generalized to the case of harmonics by Z. Huang

• Solution of this equation for the field gain length of the hth harmonic while the fundamental is suppressed for the TEM0,0 mode is approximated as follows:

• Field Gain Length:

• Optimal for the harmonic:

• Coupling factor for harmonics:0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

K

AJJ

h(K)

h = 1h = 3h = 5

Note: K is RMS undulator parameter

0.696

0.326

0.230

5

Ming Xie formulas generalized to harmonic lasing

• Ming Xie formulas can also be generalized to harmonic lasing:

• The two approaches to parameterizing the gain length (field or power) agree very well

• Even outside the stated parametric constraints• Even for non-optimized β functions

• Field parameterization is useful for looking at limiting scenarios (no energy spread, optimal β matching) while M. Xie approach is useful for quickly estimating 3D effects using scaled parameters that represent essential system features

• Becomes important with energy spread in the HXR line as we will see

6

Simultaneous lasing (linear regime)• Is there a way to optimize lasing at the harmonic such that it grows faster than the

fundamental by changing β, K, etc…?

• Optimal β for harmonics (βopt) is larger than fundamental• If optimized for fundamental, harmonics are further suppressed by longitudinal velocity spread

(from emittance) caused by too tight of focusing

• Best case scenario (1D limit) for our constraints• Cold beam limit, δ → 0• Increase β even beyond optimal one for harmonic

• For third harmonic ratio still ~ 0.87. Fundamental still grows faster (no surprise for our constraints)• When one includes energy spread effects this ratio is decreased further because harmonics are

more sensitive to this parameter• Fundamental grows faster, ruins e-beam LPS, get harmonics from nonlinear interaction only

• Solution: Suppress the fundamental!

7

Beamline geometry – nominal layout

Quad

Phase shifter/attenuator

Undulator

Parameter Symbol Value Unit

Energy E 4.0 GeV

Charge Q 100 pC

Peak current I 1.0 kA

Emittance ϵn 4.3 x 10-7 m-rad

Energy spread ΔE 500 keV

Beta function <β> 12 (15) M

Parameter Value SXR (HXR) Unit

Type Hybrid PM, planar -

Full gap height Variable -

Period 39 (26) mm

Segment length 3.4 m

Break length 1.15 m

# segments 21 (32) -

Total length 99 (149) m

e-beam parameters

Undulator parameters

Will be updated in future studies

8

Time-dependent, nonlinear harmonics (SXR @ Eγ ~ 1.24 keV)

Psat ~ 2.8 GW

FWHM ~ 0.68 eV

Keep in mind, nonlinear harmonics are:• ~ 1% fundamental intensity• Still need to suppress fundamental

(could affect harmonic)• Subject to stronger fluctuations than

fundamental

9

Time-dependent, nonlinear harmonics

Psat ~ 39 MW

FWHM ~ 1.76 eV

Relative spectral bandwidth (using my crude FWHM measurement) is roughly constant, as expected

5.4x10-4 vs 4.7x10-4

10

Harmonic lasing, phase shift of 2π/3 (λ/3)

Phase shifters kill the fundamental

Steady-state Time-dependent

• In a SASE FEL, the amplified frequencies are defined self-consistently

• Get a frequency shift depending on position and magnitude of phase shift

• Weaker suppression effect• Suppression depends strongly on ratio of

distance between shifters and gain length• Smaller ratio → better suppression

• Phase shifters tuned such that delay is 2π/3 or 4π/3 for fundamental

• Amplification is disrupted• Same phase shift corresponds to 2π

for the third harmonic• Harmonic continues its amplificationh = 3

h = 1

11

Suppressing the fundamental

12

Suppressing the fundamental

Phase shifter recipe

• Fill different modes (resonant, red shifted, blue shifted) and significantly increase the bandwidth of the FEL

• As a result, saturation is significantly delayed

• Harmonic can gain to saturation because beam quality unaffected by fundamental

13

Harmonic lasing – 3rd harmonic

P ~ 342 MW vs. 39 MW for NL FWHM ~ 0.99 eV vs. 1.76 eV for NL

14

The PenndulatorTM (G. Penn scheme)

• We don’t always have the option of adding in many additional phase shifters

• Tune such that 3rd harmonic is at desired wavelength

• Use phase shifters to suppress the fundamental

• Tune such that 5th harmonic is at desired wavelength and equal to 3rd harmonic upstream

• Fundamental from upstream is non-resonant

• Use phase shifters to suppress the fundamental and third harmonic

15

Penndulator: SXR harmonic lasing at Eγ ~ 4.1 keV

0 20 40 60 80 100 120100

102

104

106

108

1010

z [m]

P [W

]E,f ~ 4.1 keV

1.38 keV4.1 keV0.83 keV2.5 keV4.1 keV

Pavg ~ 200 MW

Currently not reachable by SXR undulator at the fundamental!

16

Penndulator: SXR harmonic lasing at Eγ ~ 4.1 keV

0 5 10 150

0.2

0.4

0.6

0.8

1

s [m]

P [G

W]

5th harmonic @ E ~ 4.1 keV

4130 4131 4132 4133 4134 41350

0.5

1

1.5

2

2.5

3 x 1010

E [eV]

P(

) [a.

u.]

17

Harmonic lasing for HXR at Eγ ~ 5.0 keV

• Can we improve the performance of the HXR line at Eγ ~ 5.0 keV using harmonic lasing?

• Look at the scaling of the harmonics versus the retuned (K) fundamental- 5 keV at fundamental: Krms ~ 0.41

- 5 keV at third harmonic: Krms ~ 1.6

• First, neglect energy spread effects (δ = 0) and assume β is optimized in both cases• Ratio of the gain length of the retuned fundamental mode to the gain length of the hth

harmonic is given by:

• Harmonic has a shorter gain length

0 1 2 3 4 50

0.5

1

1.5

2

2.5

3

3.5

4

K

L g(1K

) /LG(3

)

Only valid for K > (h-1)1/2

3rd harmonic

5th harmonic

1.65

1.41

18

What about 3D effects?

• Must consult the M. Xie harmonic generalization for our parameters

• The harmonic gain length is still better even in the presence of 3D effects given that we can effectively suppress the fundamental effectively

• Fixed current and emittance, looking only at sensitivity to these parameters

19

HXR nonlinear harmonics

0 50 100 150102

104

106

108

1010

z [m]

P AV

G [W

]

Gain curve for fundamental (blue) and 3rd harmonic (red)

0 5 10 150

2

4

6

8 x 109

s [m]

P 1 [W]

Fundamental power longitudinal profile

1620 1640 1660 1680 17000

2

4

6

8

10 x 1013

E [eV]

P(

) F [a.u

.]

Fundamental spectrum

0 5 10 150

5

10

15 x 107

s [m]

P 3 [W]

3rd harmonic power longitudinal profile

P3,avg ~ 25 MW

20

HXR 5keV 1 additional phase shifter - NIMA

0 50 100 150102

104

106

108

1010

z [m]

P AV

G [W

]

Gain curve for fundamental (blue) and 3rd harmonic (red)

0 5 10 150

0.5

1

1.5

2 x 109

s [m]

P 1 [W]

Fundamental power longitudinal profile

1620 1640 1660 1680 17000

2

4

6

8

10 x 1012

E [eV]

P(

) F [a.u

.]

Fundamental spectrum

0 5 10 150

0.5

1

1.5

2 x 108

s [m]

P 3 [W]

3rd harmonic power longitudinal profile

P3,avg ~ 49 MW

21

HXR 5keV 1 additional phase shifter – NIMA recipe

0 10 20 30 40 50 60 700

1/3

2/3

Phase shifter #

Phas

e sh

ift [

]

24

HXR 5keV 1 additional phase shifter – random

0 50 100 150102

104

106

108

1010

z [m]

P AV

G [W

]

Gain curve for fundamental (blue) and 3rd harmonic (red)

0 5 10 150

2

4

6

8

10

12 x 108

s [m]

P 1 [W]

Fundamental power longitudinal profile

1620 1640 1660 1680 17000

0.5

1

1.5

2 x 1013

E [eV]

P(

) F [a.u

.]

Fundamental spectrum

0 5 10 150

0.5

1

1.5

2

2.5

3 x 108

s [m]

P 3 [W]

3rd harmonic power longitudinal profile

P3,avg ~ 89 MW

27

HXR 5 keV 2 additional phase shifters – random, comparison with 5 keV tuned to fundamental

0 50 100 150102

104

106

108

1010

z [m]

P [W

]

Ideal beam comparison

5 keV @ fund.5 keV @ 3rd harm.

4980 4990 5000 5010 50200

2

4

6

8

10

12

14

16 x 1012

E [eV]

P(

) [a.

u.]

Spectrum comp. at sat.

Fundamental3rd harmonic

28

0 20 40 60 80102

104

106

108

1010

z [m]

P [W

]E,f ~ 5.0 keV

1.67 keV5 keV1 keV3 keV5 keV

Penndulator: HXR harmonic lasing at Eγ ~ 5.0 keV

Pavg ~ 32 MW

Ratio of phase shifter distance to fundamental gain length is not small enough

Spectral filtering: a first look

• Ideal spectral filters are placed periodically along the undulator• Perfectly absorb fundamental• No effect on the harmonic

• Assumed chicane that displaces e-beam around phase shifter washed out any residual bunching

• e-beam slice properties are saved at each filter location and used to define a new particles file that is quiet loaded

• Track the third harmonic field

• This can be tested at LCLS

Quad

attenuator

Undulator

30

Spectral filtering (ideal) for HXR at Eγ ~ 5.0 keV

0 50 100 150102

104

106

108

1010

z [m]

P [W

]Pavg ~ 290 MW, Pavg,nom ~ 160 MW

E = 1.67 keV

E = 5 keV

E,nom = 5 keV

We can start to think about self-seeding at 5 keV

31

How far can we push this?

0 50 100 150102

103

104

105

106

107

108

z [m]

P [W

]7 keV

32

Conclusions

• Harmonic lasing is an attractive option to create more intense, stable, narrowband, higher brightness photon beams

• Can also extend the photon range of a given FEL beamline• Need to consider implications for downstream optics (ie. SXR line to Eγ = 4.1 keV)

• Future work:• Play with β matching to optimize harmonic production

- β too large → current density too small → weak gain- β too small → longitudinal velocity spread from emittance suppresses FEL- Find the optimum!

• Look at smaller slice emittance simulations• Look at larger slice energy spread

- 3 BC config

• More realistic attenuator modelling • Lambert-Beer law• Chicane tracking