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

1. 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 0.696 0.326 0.230 Note: K is RMS undulator parameter • 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:

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 Undulator Phase shifter/attenuator Undulator parameters Will be updated in future studies e-beam parameters

8. Time-dependent, nonlinear harmonics (SXR @ Eγ ~ 1.24 keV) Psat ~ 2.8 GW • Keep in mind, nonlinear harmonics are: • ~ 1% fundamental intensity • Still need to suppress fundamental (could affect harmonic) • Subject to stronger fluctuations than fundamental FWHM ~ 0.68 eV

9. Time-dependent, nonlinear harmonics Psat ~ 39 MW Relative spectral bandwidth (using my crude FWHM measurement) is roughly constant, as expected 5.4x10-4vs 4.7x10-4 FWHM ~ 1.76 eV

10. Harmonic lasing, phase shift of 2π/3 (λ/3) Steady-state Time-dependent • Phase shifters tuned such that delay is 2π/3 or 4π/3 for fundamental • Amplification is disrupted • Same phase shift corresponds to 2πfor the third harmonic • Harmonic continues its amplification h = 3 h = 1 • 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 kill the fundamental

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 Pavg ~ 200 MW Currently not reachable by SXR undulator at the fundamental!

16. Penndulator: SXR harmonic lasing at Eγ ~ 4.1 keV

17. Harmonic lasing for HXR at Eγ ~ 5.0 keV 1.65 1.41 • Can we improve the performance of the HXR line at Eγ ~ 5.0 keVusing 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

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 P3,avg ~ 25 MW

20. HXR 5keV 1 additional phase shifter - NIMA P3,avg ~ 49 MW

21. HXR 5keV 1 additional phase shifter – NIMA recipe

22. HXR 5keV 1 additional phase shifter – random P3,avg ~ 89 MW

23. HXR 5 keV2 additional phase shifters – random, comparison with 5 keV tuned to fundamental

24. 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

25. Spectral filtering: a first look Quad Undulator attenuator • 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

26. Spectral filtering (ideal) for HXR at Eγ ~ 5.0 keV We can start to think about self-seeding at 5 keV

27. How far can we push this?

28. 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