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) 3 rd harmonic Time-dependent GENESIS 3 rd harmonic of E γ = 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 Penndulator TM

4 Background Note: K is RMS undulator parameter

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 (β opt ) 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 ~ 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 e-beam parameters Undulator parameters Will be updated in future studies

8 Time-dependent, nonlinear harmonics E γ ~ 1.24 keV) P sat ~ 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 P sat ~ 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-stateTime-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 amplification h = 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 – 3 rd harmonic P ~ 342 MW vs. 39 MW for NLFWHM ~ 0.99 eV vs eV for NL

14 The Penndulator TM (G. Penn scheme) We don’t always have the option of adding in many additional phase shifters Tune such that 3 rd harmonic is at desired wavelength Use phase shifters to suppress the fundamental Tune such that 5 th harmonic is at desired wavelength and equal to 3 rd harmonic upstream Fundamental from upstream is non-resonant Use phase shifters to suppress the fundamental and third harmonic

15 Penndulator: SXR harmonic lasing at E γ ~ 4.1 keV P avg ~ 200 MW Currently not reachable by SXR undulator at the fundamental!

16 Penndulator: SXR harmonic lasing at E γ ~ 4.1 keV

17 Harmonic lasing for HXR at E γ ~ 5.0 keV Can we improve the performance of the HXR line at E γ ~ 5.0 keV using harmonic lasing? Look at the scaling of the harmonics versus the retuned (K) fundamental -5 keV at fundamental: K rms ~ keV at third harmonic: K rms ~ 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 h th 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 P 3,avg ~ 25 MW

20 HXR 5keV 1 additional phase shifter - NIMA P 3,avg ~ 49 MW

21 HXR 5keV 1 additional phase shifter – NIMA recipe

22 HXR 5keV 1 additional phase shifter – reverse NIMA P 3,avg ~ 51 MW

23 HXR 5keV 1 additional phase shifter – reverse NIMA recipe

24 HXR 5keV 1 additional phase shifter – random P 3,avg ~ 89 MW

25 HXR 5keV 2 additional phase shifters – random P 3,avg ~ 238 MW

26 HXR 5keV 2 additional phase shifters – random recipe

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

28 Penndulator: HXR harmonic lasing at E γ ~ 5.0 keV P avg ~ 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 E γ ~ 5.0 keV We can start to think about self-seeding at 5 keV

31 How far can we push this?

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 E γ = 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