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Advanced Optical Interference Setup and Estimation for High-Energy Electron Beams

Explore advanced interference setup and optics estimation for electron beams with FLASH properties, including modulation and impedance calculations for energy and density modulation. Evaluate 1D and 3D estimations for beam properties, including longitudinal dispersion and energy spread. Simulate current distribution and behavior post-chicanes for SASE undulators.

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Advanced Optical Interference Setup and Estimation for High-Energy Electron Beams

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  1. sFLASH SASE interference setup & optics rough estimation 1d estimation 3d estimation summary

  2. setup & optics from

  3. estimated electron beam properties E 585 MeV Erms 150 keV n 1.5 µm q  0.3 nC Ipeak 1.5 kC estimated photon beam properties modulator undulator K = 4.3 L = 1.45 m

  4. modulation amplitude undulator FLASH @ 19 nm laser

  5. x / m y/ m vertical correctors quads undulators chicane 1 chicane 2 chicane 3

  6. rough estimation 1 2 (1) - energy modulation (2) - conversion to density modulation, chicane 1, r56c1 = 220 µm (saturation)

  7. if linear: 2 3 4 (23) - discrete impedance, L  23 m, av 10 m from  15 amplification of energy modulation (3) - chicane 1, r56c3 = 170 µm  10 amplification of density modulation (34) - discrete impedance, L  16 m, av 10 m

  8. 1d estimation 1 2 3 4 5 1 discrete modulation 12 discrete impedance, L = 2.6 m, av = 10.6 m 2 discrete longitudinal dispersion, chicane 1, r56 = 220 µm 23 discrete impedance, L = 4.7 m, av = 10.1 m 3discrete longitudinal dispersion, chicane 2, r56 = 3µm 34 discrete impedance, L = 17.7 m, av = 7.7 m 4discrete longitudinal dispersion, chicane 3, r56 = 170 µm 45 discrete impedance , L = 16.3 m, av = 9.8 m

  9. 1d estimation 40E6 macro particles energy modulation: discrete in middle of modulator space charge interaction: discrete, 1d no CSR interaction next slide: explore linear domain initial modulation amplitude initial uncorrelated energy spread

  10. longitudinal phase space current

  11. same, but Erms = 150 keV

  12. MeV MeV non linear !!! ~ 3 MeV rms energy spread

  13. MeV MeV non linear !!! ~ 3.5 MeV rms energy spread

  14. ~ 3.5 MeV rms energy spread 3D ~ 2 MeV rms

  15. 3d estimation 20E6 macro particles modulation: Emod = 250 keV discrete in middle of modulator (= instantaneous) space charge interaction: full 3d Poisson solver equidistant mesh: 15 µm × 15 µm × 800 nm/(10) step width: 2 cm (beam-line coordinate) no CSR interaction

  16. 3D Calculation Emod = 250 keV current bunch coordinate / m beam line coordinate / m

  17. 3D Calculation ~ 2.5 m Emod = 250 keV after chicane 1 before chicane 2 Current / A rms spread in 400 nm “slice” rms spread in 400 nm “slice” _rms / eV  / eV bunch coordinate / m

  18. 3D Calculation ~ 14.6 m Emod = 250 keV after chicane 2 before chicane 3 Current / A rms spread in 400 nm “slice” rms spread in 400 nm “slice” _rms / eV  / eV bunch coordinate / m

  19. 3D Calculation ~ 14.2 m Emod = 250 keV after chicane 3 before SASE undulator Current / A 50 µm, 170 fsec rms spread in 400 nm “slice” rms spread in 400 nm “slice” _rms / eV ~ 2 MeV rms 15 µm, 50 fsec  / eV bunch coordinate / m

  20. 3D Calculation Emod = 250 keV current / A bunch coordinate  1E-4 / m beam line coordinate / m

  21. current/A beam line coordinate/ m bunch coordinate/ m “side view” current/A period of plasma oscillation  120 m beam line coordinate/ m

  22. summary modulator: 1d estimation (without plasma osc.): linear gain ~ 100 saturation even with minimal modulation 3d estimation: plasma oscillations, period  120 m gain length (Ming Xie) weak amplification in 30 m SASE undulator

  23. 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

  24. Comparison to Observation The rough estimate Observed behavior Energy in photon pulse Electron macro pulse number

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