1. Challenges in Simulating EEHG
G. Penn
Workshop: Designing
Future X-ray FELs
Daresbury Laboratory
1 September 2016

2. Echo-enabled harmonic genearation offers opportunities for seeded FELs
Very large harmonic jumps possible
without necessarily relying on fresh bunch
Less sensitive to energy chirps and energy spread
more likely to preserve coherence
More flexibility: less constrained in almost all parameters than HGHG (also more complicated)
Many variations to explore
it is important to break out of the habit of thinking in terms of harmonics
G. Penn

3. EEHG also brings challenges in understanding and modeling
Design issues:
how high in harmonic, how low in wavelength?
electron beam quality; limit wakefields
stable, optimized laser
commissioning
Modeling issues:
scattering a big concern: add IBS model
make sure all physics included: large chicane, CSR
complex manipulations break assumptions
it is important to break out of the habit of thinking in terms of harmonics
G. Penn

4. Ideal bunching in EEHG Complex-valued bunching parameter
ignoring issues like scatter
where
combines laser phases,
m and p are any integers which give
the desired bunching wavenumber
Recho can even
be negative!
G. Penn

5. Mixing two terms into bunching brings more coherence and flexibility
10th harmonic:
HGHG, J10
EEHG, J11 and J1
argument of J1 mixes R1 and R2, partly cancel
sensitivity to energy spread / chirp is all in J1 argument
G. Penn

6. Example: EEHG at 25th harmonic
Typical EEHG beamline: beam: 2.4 GeV, 500 A, 0.6 mm emit, 150 keV sE 200 nm seeds, 300 keV modulation
200 nm laser wavelength
radiator at 8 nm, pre-bunched beam
seed 1
seed 2
8 nm output
modulator
modulator
3 undulators to saturation
G. Penn

7. Phase space for echo at 25th harmonic
initial (Bill Fawley style plot)
1st modulation
1st chicane
final
first chicane, R56 of 7.3 mm
second chicane, R56 of 289 micron
200 nm to 8 nm, could follow with HGHG stage down to 2 nm
2.4 GeV beam, peak current 500 A, 0.6 micron emittance, 150 keV energy spread
G. Penn

8. Phase space after radiating at harmonic
15 m (halfway to saturation) at saturation
G. Penn

9. Bunching properties at end of EEHG
Local current (500 A nominal) Bunching parameter Many harmonics besides additional one; could also have substantial bunching around lX/2, or even 2lX depending on choice of parameters
G. Penn

10. Electrons move O(micron) in EEHG
Zoom out of modulated beam At end of EEHG
main contributions to bunching come
from electrons that started ~1 micron away
G. Penn

11. Color-coded by original energy
Yet another view (no scatter this time)
G. Penn

12. Many variations based on EEHG
Special pulses: mode-locked, attosecond, OAM
3+ energy modulations [G. Stupakov]
Maximize or minimize energy modulation
Echo-fresh: couple with fresh-bunch HGHG [B. Fawley]
Weak EEHG
first half barely stripes beam
still tolerates 2 × sE
good fit with Echo-fresh
HGHG
echo
bunching 9%
final energy spread
440 keV
250 keV
first R56
0.1 mm
1.4 mm
acts like R56 =
14 micron
7 micron
LG at 4 nm
1.83 m
1.72 m
G. Penn

13. HGHG (m=0) “weak” EEHG (m=1)
Differences are still due to differences in the phase space at very fine detail
G. Penn

14. Summary of EEHG modeling needs
Scattering and other physics:
IBS, ISR (including in chicane), CSR, wakefields
Radiation fields:
inputs: realistic laser models, with unrelated wavelengths
multiple frequencies; useful as diagnostic tool?
either neighboring frequencies or large jumps
typically outside FEL bandwidth, but not always
Strong phase space manipulations
Dramatic changes in current profile, phase space
Small length scale variations in bunching
Large length scale modulated behavior
coupling with microbunching, maybe wake fields
If use slicing, particles must be re-arranged, preferably > once
G. Penn

15. Particle shuffling Particles move large distances in first chicane
displacement , 2nd term usually ~1
in units of lX, scales as (lseed/lX)2/2p
bigger than cooperation length
Head and tail of bunch can have extreme behavior
Microbunching can radically change
First attempt, use Genesis to account for this behavior
still rough, Puffin or newest Genesis version will be better
G. Penn

16. Original Genesis simulation
400 fs FWHM lasers at 260 nm particles fixed in slices radiates 32 microJ at 1 nm
G. Penn

17. Simulation with reshuffled particles
particles shuffled into new slices shifts from modulation alone, up to 5 microns radiates 22 microJ at 1 nm pulse significantly narrower
numerical noise
from rebinning
G. Penn

18. Chicane brings big changes in profile
R56=15 mm beam overlaps itself
particle distribution from
Ji Qiang, using Impact
after R56=15 mm (w/o energy modulation)
EEHG params: 260 nm to 1 nm
first modulation 1.5 MeV, second 3 MeV
R56=15 mm, 4 GeV beam
particles shift about 5 microns
G. Penn

19. Chicane brings big changes in profile
tried index=2, R56=7.5 mm: current still piles up in the tail more sensitive to energy spread not as good
G. Penn

20. References
[EEHG concept] G. Stupakov, PRL 102, (2009) [Mode-locked] J.R. Henderson and B.W.J. McNeil, EPL 100 (2012) Attosecond pulses: D. Xiang et al, PRSTAB (2009) J. Yan et al, NIMA 612 (2010) p.97 A. Zholents and G. Penn, NIMA 612 (2010) p.254 [OAM] E. Hemsing and A. Marinelli, PRL 109, (2012) [energy scatter] G. Dattoli and E. Sabia, PRSTAB 16, (2013) 75th harmonic experiment: E. Hemsing et al., Nature Photonics 10 (2016) p.512
G. Penn