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Three Remarks on ERL Optics

Three Remarks on ERL Optics. D. Douglas JLab. Acknowledgements. Funding by DoE, ONR, JTO Contributions by the entire JLab FEL group!. Remarks. Energy recovery magnetic compression/decompression “incomplete” energy recovery harmonic RF in context CSR Management

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Three Remarks on ERL Optics

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  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…

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