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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

References [EEHG concept] G. Stupakov, PRL 102, 074801 (2009) [Mode-locked] J.R. Henderson and B.W.J. McNeil, EPL 100 (2012) 64001 Attosecond pulses: D. Xiang et al, PRSTAB 12 060701 (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, 224801 (2012) [energy scatter] G. Dattoli and E. Sabia, PRSTAB 16, 070702 (2013) 75th harmonic experiment: E. Hemsing et al., Nature Photonics 10 (2016) p.512 G. Penn