Three Remarks on ERL Optics

1. Three Remarks on ERL Optics D. Douglas JLab

2. Acknowledgements • Funding by DoE, ONR, JTO • Contributions by the entire JLab FEL group!

3. Remarks • Energy recovery • magnetic compression/decompression • “incomplete” energy recovery • harmonic RF in context • CSR Management • Use of recirculation in large ERL/FEL drivers

4. oscillator E amplifier f E E E f E f f E f f 1. Remarks on Energy RecoverySchematic Longitudinal Matching for Amplifier & Oscillator injector linac dump wiggler

5. Energy Recovery Details ERL operational experience has shown how to successfully energy recover; this has implications on system efficiency Longitudinal Match to Wiggler • Inject long, low-energy-spread bunch to avoid LSC problems • need 1-1.5o rms with 1497 MHz RF @ 135 pC in our machine • Chirp on the rising part of the RF waveform • counteracts LSC • phase set-point then determined by required momentum spread at wiggler • amplifier closer to crest/smaller dp/p; oscillator farther from crest/larger dp/p • Compress (to required order, including curvature/torsion compensation) using recirculator compactions M56, T566, W5666,… • Liouville tells you the smaller the dp/p, the longer the compressed bunch • notionally goes the “right” way for both amplifier and oscillator • Entire process constitutes a parallel-to-point longitudinal image from injector to wiggler

6. Longitudinal Match to Dump • FEL exhaust bunch is short & has very large energy spread • Must energy compress during energy recovery to keep from losing beam in linac back end/during transport into dump; this dictates the longitudinal match • Highest energy must be phase-synchronous with (or precede) trough of RF wave-form • Compactions must match the slope (M56), curvature (T566), torsion (W5666),… of the RF waveform; can be supplied by transport system • As a consequence, recovered bunch centroid generally not 180o out of phase with accelerated centroid • Not all RF power recovered, but get as close as possible (recover ahead of trough), because… • Additional forward RF power may required for field control, acceleration, FEL operation; more power needed for larger phase misalignments • For a specific longitudinal match, energy & energy spread at dump does not depend on lasing efficiency, exhaust energy, or exhaust energy spread • Only temporal centroid and bunch length change as lasing conditions change • The match constitutes a point-to-parallel image from wiggler to dump

7. E E t t Key Points • “Lengthen thy bunch at injection, lest space charge rise up to smite thee” • Fixed injected bunch length means the compression (compactions) and the aspect ratio at wiggler are functions of only phase offset in linac • note that curvature effects stronger closer to crest • Longitudinal emittance of exhaust beam HUGE, and is ~2x larger for amplifier than oscillator • assumes that exhaust energy spread ~same for both types • amplifier energy spread at dump will be ~2 X that for oscillator • (image of bunch length at wiggler) • energy spread of recovered beam must be compressed during energy recovery • use momentum compaction to rotate, curve, shear bunch • large momentum spread leads to very long bunch (~30o of RF fundamental) • Bunch is too long to run 180o out of phase with acceleration • Either you run very far off crest or you run less than 180o out of phase

8. E E E t t t Energy Compression • Beam central energy drops, beam energy spread grows • Recirculator energy must be matched to beam central energy to maximize acceptance • Beam rotated, curved, torqued to match shape of RF waveform • Maximum energy can’t exceed peak deceleration available from linac • Corollary: entire bunch must preced trough of RF waveform All e- after trough go into high-energy tail at dump

9. Higher Order Corrections E • Without nonlinear corrections, phase space becomes distorted during deceleration • Curvature, torsion,… can be compensated by nonlinear adjustments • differentially move phase space regions to match gradiant required for energy compression t • Required phase bite is cos-1(1-DEFEL/E); this is >25o at the RF fundamental for 10% exhaust energy spread, >30o for 15% • typically need 3rd order corrections (octupoles) • also need a few extra degrees for tails, phase errors & drifts, irreproducible & varying path lengths, etc, so that system operates reliably • In this context, harmonic RF very hard to use…

10. Demo Dump – core of beam off center, even though BLMs showed edges were centered

11. NOTE WELL! • “Distorted” phase space at wiggler (e.g., “S” shape with temporal tails) may be unrecoverable! • can’t energy compress phase tails, which scrape and burn up machine • As laser efficiency varies (e.g. from 0 to full efficiency as oscillator switches on) beam energy at the dump is fixed; arrival time shifts • this is due to shifts in arrival phase at linac: • compactions selected to produce conspiracies ensuring phase shift produces the required energy shift to hold Edump constant • beam loading varies; cavity tuning varies; RF drive must have sufficient power available to compensate/manage these effects • Tail of bunch must lead (or at least coincide with) trough to ensure energy compression can occur • Accelerated/recovered beams typically NOT 180o out of phase, and phase separation depends on lasing efficiency • potential for RF transients; beam timing on 2nd pass varies as lasing efficiency varies • If energy compression is correctly done, energy spread at dump depends only on bunch length at wiggler

12. Energy Flow • Energy conservation (bunch centroid): Einj + Eacceleration=Erecovered + EFEL + Edump • ERLs are generally not operated with Eacceleration=Erecovered • point-to-parallel longitudinal image from wiggler to dump • Shifts beam in phase when EFEL varies • Keeps Erecovered+EFEL constant, thus keeping Edump constant • Energy deficit is made up by linac RF drive • Cavity stored energy utilized until RF system “catches up” • Need enough RF power/RF control bandwidth to deal with transients • FEL power has to come from somewhere, • best it put it in through the linac (rather than the injector) • more RF windows, lower power/window

13. RF Drive Implications (Powers & Tennant, ERL07) • Point-to-parallel imaging of longitudinal phase space from wiggler to dump: • makes Edump, sE_dump independent of hFEL • makes tdump, bunch length vary with hFEL • Timing shifts alter beam loading, cavity tune of SRF cavities as hFEL changes • Must supply adequate RF power to • provide energy extracted in lasing • control fields in cavities • Power requirements depend on specific choice of longitudinal match and cavity design (QL) Note Well • Oscillator/amplifier may differ in details of RF drive (“2nd order effect”) • both have similar elongitudinal requirements • LSC forces injection of relatively long bunch with parallel-to-point longitudinal match to wiggler, but • amplifier needs lower dp/p, longer bunch at FEL, so must accelerate closer to crest • both may need to recover far out of trough (to compress large energy spread) • phaser misalignment differs • RF power requirements differ

14. 2. Naïve Approach to CSR Management During Transport and Compression • Understanding nonetheless that “reality is only a concept”, Chris Tennant ran Elegant benchmarks on compact lattice (FSU “BigLight”) to investigate CSR effects in Bates bends • “Interesting” results: • parasitic compressions are bad • mitigation possible; “Derbenev parameter” large at parasitic compressions in Bates bends • bending through large angle with short bunch is VERY bad • sadly, mitigation unlikely: final bend has reasonable, nondispersed spot size with not utterly ludicrous Derbenev parameter; sort of lies closer to regime where codes “work” Naively, it appears that a system attempting to transport a compressed bunch through a large angle bend is going to be in trouble…

15. CSR Driven Degradation at High Charge • “Elegant” simulation of example FEL driver transport (“BrightLight”) • CSR off (top) • CSR on (bottom) • Partial compensation might possible but is complex and imperfect • few knobs available in compact systems • Multiple parasitic compressions cause problems (phase space breaks up into multiple regions) Images by C. Tennant

16. Existing Machine Serves at Test-Bed • Effects noticeable but non-constraining at 135 pC • Used as a “tuning” cue in JLab 10 kW Upgrade; system is optimized for lasing just at onset of CSR inflation of momentum spread • Better management needed Courtesy P. Evtushenko Images by P. Evtushenko

17. Requirements • Compress bunch • Betatron match to wiggler • Provide adequate aperture (chromatic, geometric… etc) • Avoid CSR dilution of phase space – but how? Either reduce lattice response to CSR or reduce CSR excitation • Limit lattice response = • “focus like crazy” (reduce betas & etas), or • effective but introduces aberrations • “emittance compensate” – create a conspiracy to “undo” the damage… Alternatives? Limit production of CSR…?

18. wake field; given to you by God also an FEL spec… peak current; given to you by the FEL designer CSR Management • Driving term: • All that’s left is (r1/3/sz1/3) ×Dq • Dependences on radius, bunch length are very weak; no knob there… • Must work angle…

19. dp/p>0 dp/p=0 dp/p<0 CSR Management, cont. Notionally: minimize the angle over which bunch is short • Last bend contributes very little to any compression (assuming dispersion suppression…) – so bunch is short across the entire bend • Therefore, final bend must have small angle • dispersion into final dipole must be small/at small angle • Previous bending must compress the bunch rapidly • M56 = ∫hdq • modulate dispersion to be large • compression can then occur very rapidly • bunch is short only over a small angle at the end of the dipole • dispersion match to last bend

20. Compression Scheme with Naïve CSR Management • Accelerate ahead of crest (manage LSC) • Recirculate using arc with M56>>0 (Debunch. A lot.) • Compress using dispersion modulated system with M56<<0 • keep dispersion large in dipoles to give rapid accumulation of M56 and force rapid compression • Have to play off emittance dilution (big h) against limiting region where excitation occurs, and hoping big Derbenev parameter helps • demagnify dispersion after last major dipole to match • Use lots of symmetry to provide handles for nonlinear correction & manage chromatic aberrations

21. Design Concept Tried various combinations; settled on: • Quad telescope to match linac to arc • 6-period, 60o FODO arc in 2nd order achromat • Allows many sextupole families for aberration control • Good aberration suppression • Compressor: • start with hybrid of old “Virginia Reel” (zig-zag) and staircase translation • modulate dispersion to give ~1 m at each of pair of center dipoles • Resolve final dispersion in a 5o final bend after demagnifying with a ¾-wavelength FODO channel • Quad telescope to match compressor to wiggler Fiddled with numbers of quads in each module, phase advances, etc to roughly optimize chromatics

22. Layout, envelopes, etc… • Just a proof-of-principle solution; • room to shrink? • fewer elements?

23. Spot sizes, chromatics…

24. Phase Space at Wiggler; CSR “on”

25. Distributions at Wiggler; CSR “on”

26. Elegant Simulations • “Elegant” simulation of example FEL driver transport • CSR off (0 charge, top) • CSR in dipoles (middle) • CSR in dipoles & downstream drifts (bottom) • Compensation possible but complex and imperfect • Adjust aberrations to “pre-stress” beam; CSR then compensates distortion (longitudinal, top to bottom) • May inadvertently introduce other effects (transverse, top to bottom) Images by C. Tennant

27. Comments • “proof-of-principle” solution, cobbled together out of junk from the attic and things found on the curb on recycling day • Seems to alleviate some of CSR issues seen in other designs (Bates bend) • Has considerable “dirty laundry” • Nonlinear corrections, other similar trickery… • Probably can shrink and simplify • e.g, combine final match + dispersion modulation, bend directly into wiggler at end… (thanks, George & Pavel) • There is no warrantee, either express or implied – especially w.r.t. LSC… • Advice welcome!

28. 3. Use of Recirculation in Large Systems • This is mostly an appeal to consider potential cost savings through use of recirculation • SRF Costs high • Multipass ERL/recirculated XFEL driver could save 100s M$ in costs • Recirculation poses challenges • System size • Quantum excitation • CSR/LSC/MBI • BBU… But… solutions are in the offing (M. Borland) Cost savings potentially high enough to pay for years of R&D on the topic – and its not clearly “impossible” to manage the effects

29. 10 yr. old JLab estimates…