1. Gain Computation Sven Reiche, UCLA April 24, 2002
Tools for gain computation
The LCLS parameter space
Start-end simulations
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

2. Tools Fully Developed Theory Analytical Formulae
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
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

3. Harmonics, Undulator field maps
Tools
FEL Codes
Code
Non-linear
Time-dependent
Radiation field
Additional features
GINGER
yes 2D no
GENESIS 1.3 3D
Wakefields, Spon. rad.
MEDUSA
Harmonics, Undulator field maps
RON
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

4. Tools Codes for Start-end Simulations Parmela Elegant Genesis 1.3 Gun
Linac
FEL
Parmela
Elegant
Genesis 1.3
Macro particles and
Discritized radiation field
Analytical model for undulator
wakefields
Macro particles
External maps for E- and
B-field
Space Charge
Macro particles
Tracking by matrix elements
Analytical model for CSR and
wakefields
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

5. LCLS Parameter Space Design Parameters
Energy
14.3 GeV
4.5 GeV
Current
3.4 kA
Charge
1 nC
Emittance
1.2 mm mrad
Energy Spread % %
Undulator Period
3 cm
Undulator Parameter
3.7
b-function
18 m
7.5 m
Wavelength
1.5 Å
15 Å
Lowering the charge reduces bunch
length, current and emittance
(start-end simulation)
1.0 nC
strong wakefields
Charge
losses due to
spon. rad.
Operation Space
deep saturation
0.2 nC
1.5 Å
Wavelength
15 Å
LCLS DOE Review, April 24, 2002
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
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

7. Performance Limitations
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
LCLS DOE Review, April 24, 2002
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.
LCLS DOE Review, April 24, 2002
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)
LCLS DOE Review, April 24, 2002
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.
LCLS DOE Review, April 24, 2002
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.
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

12. All cases reach saturation
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
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

13. Expected Performance 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
15 GeV - 1nC
35 %
15 GeV nC
5 GeV - 1 nC
7 %
5 GeV nC
15 %
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

14. Large Bunching Factor = Richer Harmonic Content
Expected Performance
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.
Large Bunching Factor = Richer Harmonic Content
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

15. Expected Performance Power Profile
Profile similar for entire wavelength range.
Gaps in profile due to
Undulator wakes
Large emittance
Large energy spread
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

16. Expected Performance 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.
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

17. Expected Performance 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.
LCLS DOE Review, April 24, 2002
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.
Energy
71 MeV
Spread
0.1 %
Peak Current
250 A
Emittance
(projected)
2.3 mm.mrad
Undulator period
1.8 cm
Undulator parameter
0.88
After
Linac
Before
Undulator
LCLS DOE Review, April 24, 2002
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
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA

20. All four cases reach saturation
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
LCLS DOE Review, April 24, 2002
Sven Reiche, UCLA