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

setup & optics from

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

modulation amplitude 19 nm undulator laser

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

12 (1) - energy modulation rough estimation (saturation) (2) - conversion to density modulation, chicane 1, r56 c1 = 220 µm

23 (2  3) - discrete impedance, L  23 m,  av  10 m if linear: from  15 amplification of energy modulation (3) - chicane 1, r56 c3 = 170 µm  10 amplification of density modulation 4 (3  4) - discrete impedance, L  16 m,  av  10 m

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

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

longitudinal phase spacecurrent

same, but E rms = 150 keV

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

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

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

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

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

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

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

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

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

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

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

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

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