Gain Computation Sven Reiche, UCLA April 24, 2002

1. Gain ComputationSven Reiche, UCLAApril 24, 2002 • Tools for gain computation • The LCLS parameter space • Start-end simulations Sven Reiche, UCLA

2. Tools • Fully Developed Theory • Impact of Beam Parameters (Energy Spread, Emittance, Beam Size, Detuning) • Diffraction of Radiation Field (3D Theory) • Shot Noise, Slippage, Short Bunch (Time-Dependent Theory) • Analytical Formulae Gain length, shot noise, saturation power and length as a function of electron beam , undulator and radiation field parameters. Spread sheet calculation / estimate of FEL performance Sven Reiche, UCLA

3. Tools • FEL Codes Sven Reiche, UCLA

4. Tools • Codes for Start-end Simulations Gun Linac FEL Parmela Elegant Genesis 1.3 Macro particles and Discritized radiation field Analytical model for undulator wakefields Macro particles Tracking by matrix elements Analytical model for CSR and wakefields Macro particles External maps for E- and B-field Space Charge Sven Reiche, UCLA

5. LCLS Parameter Space Design Parameters Lowering the charge reduces bunch length, current and emittance (start-end simulation) 1.0 nC strong wakefields losses due to spon. rad. Charge deepsaturation Operation Space 0.2 nC Wavelength 1.5 Å 15 Å Sven Reiche, UCLA

6. Performance Limitations Spontaneous Radiation • Energy loss due to spontaneous radiation. Weak taper of undulator field to compensate change in resonance condition • Quantum fluctuation of hard X-rays increases energy spread. No compensation possible ! Spon. rad. FEL process FEL process Quantum fluctuation Sven Reiche, UCLA

7. PerformanceLimitations Undulator Wakefields Caused by • wall resistivity, • surface roughness, • changes in aperture. Resistive wall wakefields are the dominant contribution to the total wake potential. Larger undulator gap does not increase output power but the saturation length! Current Profile Wake Potential Without wakefields With wakefields Sven Reiche, UCLA

8. Beam Quality Issues • If magnitude of correlated energy spread is larger than the FEL bandwidth, the frequency spectrum is broader. • The matching of the projected phase space ellipse to the focusing lattice causes a mismatch and misalignment along the bunch. • Wakefields have a ‘local’ effect, resulting in a position-dependent change in energy, which cannot be compensated by tapering. Slippage length, over which beam information is transported via the radiation field, is 500 nm. Many parts of the bunch amplify the spontaneous radiation independent of each other. Beam quality is better parameterized by sliced values than projected ones. Sven Reiche, UCLA

9. Beam Quality Issues The longitudinal variation of the electron beam quantities has to be estimated and used as input for FEL simulation. Therefore modeling the LCLS FEL performance requires: • Input from consistent simulations of the LCLS beam line (start-end simulations) • Further improvement can be achieved by comparison with measurable quantities such as • Autocorrelation • Fluctuation in FEL output power • Characteristics of spikes in frequency spectrum • Slicing by applying energy chirp to electron beam • Consistency with non-FEL measurement (e.g. bunch length) Sven Reiche, UCLA

10. General Performance The most critical parameter is the transverse emittance. A large emittance corresponds to a large spread in transverse and, thus, longitudinal velocity. The effective number of electrons, which are in resonance with the radiation field, is significantly reduced. The emittance effects dominate over the energy spread, which also causes a spread in longitudinal motion. 1.7 mm.mrad is the largest slice emittance, which allows saturation within the LCLS Undulator (120 m, including gaps between modules), assuming a local current of 3.4 kA. Sven Reiche, UCLA

11. General Performance The variation of the beam parameters along the electron bunch causes different saturation powers and length for each slice. Beside emittance, energy spread and b-mismatch have the stron- gest impact on the FEL performance. Despite a variation in the beam para- meters, transverse coherence is achieved after approx. 45 m for the 1.5 Å case. Full longitudinal coherence is never obtained. Sven Reiche, UCLA

12. Expected Performance • Start-end simulation using PARMELA-ELEGANT-GENESIS 1.3 • 4 cases (1nC and 0.2 nC at 1.5 Å and 15 Å) • Low charge cases are modeled in PARMELA after the GTF results and then imported into ELEGENT for the transport through the LCLS beam line. • The simulations includes: • Space charge in the gun • Emittance compensation • Wakefield and CSR effects • Optimized beam transport (Jitter) • Spontaneous Undulator Radiation All cases reach saturation Sven Reiche, UCLA

13. Impact of Wakefields Large wake amplitude due to spikes in the current profile at the beginning and end of the electron bunch. Stronger at 1.5 Å: Smaller bandwidth Longer accumulation Power reduction at undulator exit Expected Performance Sven Reiche, UCLA

14. Microbunching + Higher Harmonics Overall efficiency of microbunching reduced for 1.5 Å cases. The modulation of the microbunchng at higher harmonics is rather driven by the non-linear terms of the interaction with the fundamental radiation wavelength then the interaction with the higher harmonics of the radiation wavelength. Expected Performance Large Bunching Factor = Richer Harmonic Content Sven Reiche, UCLA

15. Power Profile Expected Performance Profile similar for entire wavelength range. • Gaps in profile due to • Undulator wakes • Large emittance • Large energy spread Sven Reiche, UCLA

16. Spectrum at 1.5 Å Spectrum shows a slight shift towards longer wavelength due to the net energy loss by the wakefields. Low charge case is less effected by wakefields, thus, showing a shorter resonant frequency. The RMS widths of the spectra are 0.13% and 0.07% for the high and low charge case, respectively. Expected Performance Sven Reiche, UCLA

17. Spectrum at 1.5 nm The operation in deep saturation causes the growth of the sideband instabilitiy and a reduction at the resonant wavelength. It can be compensated by a low current, but The FEL growth would stronger be affected by the undulator taper and wakefields The spectral power at resonance frequency is not higher. Expected Performance Sven Reiche, UCLA

18. Analysis of Measurements • Start-end simulation used to analyse the results from the VISA FEL experiment (850 nm). • Compression and ‘clipping’ in the transport from the linac to the entrance of the 4 m undulator. After Linac Before Undulator Sven Reiche, UCLA

19. Analysis of Measurements Results agree well with measured data • Energy value and fluctuation • Near and far field distribution • Spectrum width and # spikes Measured angular profile GENESIS simulations Sven Reiche, UCLA

20. Conclusion • FEL performance is defined by ‘sliced’ beam parameters. • Beam transport and compression can introduce a strong variation of the beam parameters along the bunch. • Wakefields and quantum fluctuation of the spontaneous radiation degrades FEL performance. • Importance of start-end simulations • Start-end codes PARMELA, ELEGANT and GENESIS 1.3 successfully benchmarked against VISA experiment. All four cases reach saturation Sven Reiche, UCLA