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Performance Analysis Using Genesis 1.3 Sven Reiche LCLS Undulator Parameter Workshop Argonne National Laboratory 10/24/03

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Overview Modeling in Genesis 1.3 SASE - Performance Undulator Taper Tolerance Study

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Modeling - Electron Beam Using Design Parameter Flat profile (~70 m FWHM) Current of 3.4 kA Normalized emittance of 1.2 mm. mrad RMS energy spread of 5.5 MeV No variation of beam parameters along bunch No runs with start-end distributions Correct bunching statistic up to 3rd harmonics Up to 20000 Slices à 32000 macro particles for full bunch (= 700 million macro particles) 2 weeks of CPU time on single node 1.7 GHz processor

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Modeling - Undulator For SASE simulations ( z=8. u ) Module length: 112. u Quadrupole length: 8. u (gradient: 12.74 T/m / -12.59 T/m) Drift length: 16. u (no super-period) Energy loss by SR and taper excluded. For taper simulations ( z=4. u ) Similar as above but with super-period Drift length: 16/16/20. u Stepwise taper (constant field per module) For field error simulations ( z= u /2) Steady-state simulation only For simpler analysis no drift spaces

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Modeling - Wakefields 3 mm bore radius Copper plated chamber 100 rms roughness with 500:1 aspect ratio Transient amplitude reduced from 250 keV/m to 180 keV/m, but longer transient region (20 m) Flat current profile

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Modeling - FEL Process SASE Process at Ångstrom level very CPU intensive. Full bunch simulation only for 1.0, 1.5 and 15 Å, with and without wake fields. Subsection of about a third of full bunch length used for tapered SASE FEL at 1.5 Å. Dependence on emittance, energy spread, beam offsets and field errors in steady-state mode (FEL amplifier). Change in saturation power, saturation length or gain length with respect to ideal case.

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 SASE-Results 15 Å 1.5 Å 1.0 Å WavelengthSat. PowerSat. LengthGain LengthTrans. Coh. 1.0 Å1.5 GW122 m10.96 m96 m 1.5 Å2.9 GW103 m7.38 m65 m 15 Å8.3 GW35 m1.95 m17 m Wakefields included. Gain length determined by linear fit to exponential growth of radiation power. Transverse coherence obtained from statistic of instantaneous power.

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Wakefield Impact Reduction of up to 50% ~ 25% by gap in profile due to transient in wake potential ~ 25% by slight energy loss of 30 keV/m at core of bunch 15 Å 1.5 Å 1.0 Å

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Quantum Fluctuation Lower undulator parameter and beam energy reduce impact of quantum fluctuation, although not a big effect even for the old design. 15 Å 1.5 Å 1.0 Å Increase of of 0.9 over 80m for 1.0 Å case.

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Profile and Spectrum at 1.0 Å Gap in profile and shift in resonant wavelength due to wakefields.

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Profile and Spectrum at 1.5 Å Gap in profile and shift in resonant wavelength due to wakefields.

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Profile and Spectrum at 15 Å Impact of wakefields strongly reduced. Strong sideband instability in deep saturation regime.

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Bandwidth Growth of bandwidth for 15 Å case by factor of 3 in deep saturation regime. 15 Å 1.5 Å 1.0 Å

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Bunching New shot noise algorithm in Genesis Growth of bunching at higher harmonics does not agree with theory at short wavelength (needs investigation) 15 Å 1.5 Å 1.0 Å

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Bunching Statistic at 1.0 Å

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Bunching Statistic at 1.5 Å

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Bunching Statistic at 15 Å

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Taper Taper required to compensate for losses due to the spontaneous radiation. Additional taper can be applied to increase performance. SASE-run of 20 m subsection of bunch at 1.5 Å (wakefields excluded). No SR & no taper Taper compensating SR Additional taper after 90 m

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Taper (cont’) WavelengthTaper GradientPost Saturation 1.0 Å-1.15. 10 -5 m -1 - 1.5 Å-9.27. 10 -6 m -1 -9.76. 10 -5 m -1 Steady-state model Blue - 1.5 Å / Red - 1.0 Å Solid - taper optimized Dot - optimized for other wavelength. Taper for 1.5 Å SASE run

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Emittance Dependence Most Sensitive Parameter! Saturation beyond LCLS undulator length of 120 m for 1.0 mm. mrad at 1.0 Å and 1.4 mm. mrad at 1.5 Å. 1.0 Å 1.5 Å 15 Å

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Energy Spread Dependence Rather weak dependence (phase spread is dominated by emittance effect). 1.0 Å case does not saturate for any value of the energy spread. 1.0 Å 1.5 Å 15 Å

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Field Errors and Related Field errors effects the FEL process by Degraded synchronizations between electron beam and radiation field (phaseshake) Exitation of trajectory distortion (overlap) Both effects are coupled by are differently exited, depending on the cause (pole field errors, quadrupole misalignment, undulator misalignment, initial offsets and angle). OverlapPhaseshake Initial OffsetsCorrelated Errors Undulator MisalignmentQuad Misalignment Uncorrelated Errors

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Offset Tolerances at 1.5 Å Due to large period length of betatron oscillation, an initial offset has almost no impact on the longitudinal synchronization except for a constant slow-down, which is compensated by a higher energy (or self-adjustment for SASE FEL). No Saturation

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Phaseshake Ponderomotive phase =(k+k u ) z t- t depends implicitly on the undulator field and residual betatron motion. The collective change in the phase is given by A linear change in is compensated by a change in the mean energy. After subtracting the linear fit the phase shake is obtained. a w = 1% rms x<100 nm rms (correlated errors)

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Phaseshake (cont’) Saturation power and length difficult to estimate for large field errors. Use ‘integrated gain length’ instead. Results for correlated errors with a trajectory distortion below 100 nm rms. 1% 0.1% 0.01%

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Tolerance Summary Wavelength1.0 Å1.5 Å15 Å Emittance< 1.1 mm.mrad1.4 mm.mrad> 2.1 mm.mrad Energy Spread0.02 %0.04%> 0.15% Orbit- 17 m - Phaseshake-1.2 rad- Values indicate a successful operation to reach saturation within the 125 m of the LCLS undulator.

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ANL - 10/24/03Sven Reiche - Analysis with Genesis 1.3 Summery Saturation of SASE FEL at 15 and 1.5 Å, close to saturation for 1 Å Compared to old design saturation length increases by 20m and power drops by 50% Degradation of up to 50% by wakefields Additional tapers after saturation push output power to 20 GW. Maximal change of field due to extra taper is 0.3% Tighter tolerances for emittance, energy spread, but reduced for beam orbit Start-end simulation not done yet.

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