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Start to End for ERLP (EMMA Workshop 26-28/02/07)

Bruno Muratori ASTeC Daresbury Laboratory Cockcroft Institute. Start to End for ERLP (EMMA Workshop 26-28/02/07). (M. Bowler, C. Gerth, F. Hannon, B. McNeil*, H. Owen, S. Smith, N. Thompson, E. Wooldridge). * - Strathclyde University, Glasgow. Start to Linac for ERLP & EMMA.

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Start to End for ERLP (EMMA Workshop 26-28/02/07)

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  1. Bruno Muratori ASTeC Daresbury Laboratory Cockcroft Institute Start to End for ERLP(EMMA Workshop 26-28/02/07) • (M. Bowler, C. Gerth, F. Hannon, B. McNeil*, H. Owen, S. Smith, N. Thompson, E. Wooldridge) * - Strathclyde University, Glasgow

  2. Start to Linac for ERLP & EMMA • Overview of codes used in the design of ERLP • Main parameters of ERLP • Overview of Optics and Start to End model of ERLP • Gun & Injector • Injector transfer line – various approaches • Analytic • ASTRA & quadrupoles • GPT & full model • ELEGANT • Linac to first arc • RF focusing treatment • Outstanding Work

  3. Overview of codes used for ERLP • Injector Design (assumed S2E does not start before this) • ASTRA • Optics Layout strategy for ERLP • MAD8 • Space Charge for the ERLP • Analytical estimate • ASTRA / GPT • Start to End (S2E) model for the ERLP • MAD8 / ELEGANT • GENESIS • Beam Breakup for the ERLP • bi (Beam Instability code)

  4. Main Parameters for ERLP • Gun Energy 350 keV • 4 ps long bunches, 80 pC, at injection • 8.35 MeV Injection line around 15 m • 35 MeV Beam Transfer System (BTS) • Bunch repetition rate 81.25 MHz • Bunch spacing 12.3 ns • Average current 13 µA • Initial emittance (norm) between 2 mm mrad and 3 mm mrad • Transverse beam size ~ 1-16 mm throughout • ~ 0.4 ps long bunches at FEL

  5. Lattice Matching Lattice Matching GENESIS ASTRA Elegant Elegant 106 particles 250k particles 250k particles 250k particles Booster to FEL 8.35/35MeV FEL Interaction FEL to Dump 8.35/35MeV Gun to Booster 0 to 8.35MeV Start to End Model MAD8 MAD8

  6. Beta Functions for ERLP

  7. Dispersion for ERLP

  8. Gun & Injector

  9. Gun electrons JLab GA anode electrons

  10. Injector (TL1) • Modelling with ASTRA taking into account space charge. • Gun → solenoid #1 → buncher → solenoid #2 → booster • Bunch length/shape from a GaAs cathode?Modelling for various bunch lengths (15 ps, 20 ps, 25 ps). • Similar beam parameters can be achieved by adjusting the solenoid/buncher settings.

  11. Injector Line (TL2)

  12. ASTRA & Injector line (TL2) • AT 8.35 MeV space charge still an issue • ASTRA does (did ?) not model dipoles • Try to ignore dispersion effects & Replace dipoles with quadrupoles (obviously wrong but …) • Make sure resulting Twiss parameters almost identical • Look at emittance growth using ASTRA and initial Gaussian parameters • Validity of analytical formula with quadrupoles ?

  13. Aside: ASTRA & Drifts - Analytical Approach • Horizontal focusing given by (equivalent for vertical) • Sigma matrix transformation • New emittance • Gaussian bunch (in s)

  14. Results & Comparisons for ASTRA & Drifts – 1 mm mrad • Comparison gives ‘upper bound’ as long as flow laminar • Not true for r = 1.0 mm and r = 0.5 mm

  15. Results & Comparisons for ASTRA & Drifts – 3 mm mrad • Comparison gives ‘upper bound’ as long as flow laminar • Not true for r = 0.5 mm (laminarity depends on εN so varies)

  16. ASTRA & Quadrupoles for TL2

  17. ASTRA & Quadrupoles for TL2 • Variation of beam size not taken into account → average has to be taken for meaningful comparison

  18. ASTRA & Quadrupoles for TL2 – alternative longer model • Quadrupole ‘k’ value higher than space charge equivalent but also more local → small perturbation & can be ignored

  19. ASTRA & Quadrupoles for TL2 • ASTRA distribution from gun and booster (C. Gerth & F. Hannon) • Emittance outside transverse plane • Gaussian good approximation for emittance growth estimate

  20. GPT (General Particle Tracer) • All results so far in good agreement & can use analytical estimate for a rough guess provided laminarity insured • Different algorithms also agree • Emittance increase appears to be comparable to the analytical estimate in all cases considered • Dispersion may be left out for a rough estimate • Next: Include bends → use GPT (required modifications in fringe field treatment)

  21. GPT & Quadrupoles for TL2 • Spikes unphysical & related to calculation of emittance in magnetic elements → agreement with ASTRA

  22. GPT & TL2 with dipoles (beam size & angle)

  23. GPT & TL2 with dipoles (emittance) • Comparison with ASTRA & quadrupole model: • ASTRA: 2.8 mm mrad (x), 3.3 mm mrad (y) • GPT: 3.0 mm mrad (x), 3.9 mm mrad (y)

  24. GPT transverse distribution at the end of TL2 Starting with Gaussian parameters at the start of the injector line

  25. GPT longitudinal distribution at the end of TL2 Starting with Gaussian parameters at the start of the injector line

  26. Linac to first Arc

  27. Transfer Line 2 / Linac • Lattice matching with MAD8 • Keep Twiss parameters low (β < 50 m) • Dispersion free after injection/extraction bends and arcs • 1st arc: isochronous • 2nd arc: R56 = -R56 bunch compressor • Exact matching point at the entrance of the FEL • Tracking with elegant (TL2: E = 8.35 MeV, l = 10m, 4 dipoles, 12 quads)Space charge effects? • Different focusing strength of the linac in MAD8 and elegant and other models → re-matching after the linac

  28. RF Focusing – Analytical Models • Different code use different models (sometimes very !) • MAD8 / ELEGANT give different focusing • Must be accommodated in optics design • Probably both wrong ! • Important to get this correct as overall effect could be high …

  29. RF Focusing – Simulated Fields • Couplers can have a strong influence on the transfer matrix • Hard to model • Strongly affects focusing • Theory vs. Experiment very limited despite being relatively easy to do …  (difference in orbit method)

  30. after acceleration Before acceleration Transfer Line 2 / Linac Longitudinal Phase Space • Tracked bunch at end of TL2 → linac • ELEGANT used • Off crest acceleration for bunch compression later in chicane

  31. Outward arc / Compression after linac • 4-dipole chicane R56(BC) = 0.28 m • For optimum compression set the off-crest phase in main linac toφrf = 9° after BC

  32. S2E Simulation 4 1 3 2

  33. Outstanding Work • Track distribution obtained from ASTRA after the booster through injector transfer line with GPT • Try different kinds of linac focusing • Chambers model • Direct numerical integration • Krafft model • ELEGANT (different types exist within this) • ASTRA • GPT ? (given field maps – even 3D) • Experimental verification very much desired – could be done on ERLP booster and / or linac at different energies & off-crests

  34. Conclusions • Optics with no real problems so far & straightforward • Injector layout still being optimised → parameters may vary (emittance & bunch length due to varying laser spot size and pulse length) • Good agreement between ASTRA and GPT and analytical result for drifts & quadrupoles (provided flow is laminar) • Good agreement with dipoles correctly modelled • Distribution still to be tracked including latest parameters • Off-crest of 9° not a must if not going through FEL & compressing bunch later • RF focusing still to be studied but maybe not essential

  35. Reserve Slides … • Vinokurov’s Formula …

  36. ASTRA & Drifts - Analytical Approach • Elliptical beam with charge density • Electric field • Transverse motion (round beam) paraxial approximation, laminar flow

  37. ASTRA & Drifts - Analytical Approach • On boundary, , • With external focusing • Envelope for KV distribution • Therefore laminar flow given by

  38. ASTRA & Drifts - Analytical Approach • Horizontal focusing given by (equivalent for vertical) • Sigma matrix transformation • New emittance • Gaussian bunch (in s)

  39. Results & Comparisons for ASTRA & Drifts: 5 mm mrad • Laminar flow not always valid e.g. : • 4 ps, normalised emittance of 5 mm mrad, beam size 1 mm • relativistic gamma ~ 17, max. current = 8 A • LHS = 0.025, RHS ~ 0.05 → flow not laminar

  40. Results & Comparisons for ASTRA & Drifts

  41. Comparisons of ASTRA/GPT for DRIFT – 3D mesh

  42. Results of comparisons of ASTRA/GPT - 3D mesh

  43. Results of comparisons of ASTRA/GPT – 3D mesh

  44. Results & Comparisons for ASTRA & Drifts – 5 mm mrad

  45. Results & Comparisons for ASTRA & Drifts: 1, 3 mm mrad

  46. Reserve Slides … • Complete s2e …

  47. Outward arc / Compression • 4-dipole chicane R56(BC) = 0.28 m • For optimum compression set the off-crest phase in main linac toφrf = 9° • Here bunch not fully compressed φrf = 7.8° K2 = 120 m-3→ rms bunch length = 0.4 ps after linac after BC

  48. Outward arc/ Compression Longitudinal Phase Space after Bunch Compressor Sextupoles off • Sextupoles can be used to linearise the curvature induced by the sinusoidal rf during acceleration by varying T566. • The compression factor is then limited by the uncorrelated energy spread. • Simulation results appear to be too good!! - rms bunch length ~ 230 fs Sextupoles K2 = 90 m-3

  49. Sextupole Linearisation • Sextupoles in the outward arc help to achieve the shortest possible bunch length • Can actually make bunch length too short for lasing! (in theory) • Adjustable in real machine to optimise lasing properties • In practice we are likely to see disruptive effects not apparent in the model

  50. JLab Wiggler Model – Beta Functions

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