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X-Ray FEL Simulation: Beam Modeling

X-Ray FEL Simulation: Beam Modeling. William M. Fawley (WMFawley@lbl.gov) Center For Beam Physics Lawrence Berkeley National Laboratory. ICFA 2003 Workshop on Start-to-End Numerical Simulations of X-RAY FEL’s. Talk Outline. Design of test cases for LCLS parameters

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X-Ray FEL Simulation: Beam Modeling

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  1. X-Ray FEL Simulation: Beam Modeling William M. Fawley(WMFawley@lbl.gov) Center For Beam PhysicsLawrence Berkeley National Laboratory ICFA 2003 Workshop on Start-to-End Numerical Simulations of X-RAY FEL’s

  2. Talk Outline • Design of test cases for LCLS parameters • Quick summary of GINGER & GENESIS simulation codes • Comparison of GINGER & GENESIS results: • “0-order” case : Amplifier mode run - ideal beam • “1st-order” Case : Time-dependent, 5D envelope reconstruction + amplifier mode run • “2nd-order” case: Full 5D, time-dependent macro-particle reconstruction + SASE mode runs for beam head and middle pulse regions Accelerator and Fusion Research Division

  3. LCLS Test Case Design In a non-smoke-filled room, P. Emma, H.-D. Nuhn, S. Reiche and myself came up with 4 different LCLS test cases (details on SLAC S2E Web page) to benchmark FEL codes: • “O-order”: simple monochromatic, amplifier mode run • e-beam in equilibrium with “base” LCLS parameters (14.35 GeV; sg/g=0.01% ; 1-nC: 3.4 kA, 1.2 mm-mrad eN , PIN=3.0 kW; 200 pC: 1.5 kA, 0.65 mm-mrad eN, PIN=1.0 kW) • input Twiss parameters adopted from P. Emma’s ELEGANT runs • constant K optimized for peak output power • “1st-order”: time-dependent envelope parameters (sg, I, eN, ax,y, bx,y) derived from ELEGANT particle output • amplifier mode run (no slippage) with K & g same as 0-order run • both CSR/no CSR cases • with/without undulator wake field effects Accelerator and Fusion Research Division

  4. LCLS Test Case Design (cont.) • “2nd-order”: Full 5D macroparticle reconstruction from ELEGANT output particle distribution (1-nC with CSR); • Full polychromatic SASE run (shot noise + slippage effects) • concentration on two particularly interesting regions: beam head (high current; bimodal energy dist.) and beam body (nominal current; low e and sg) • “3rd-order”: Simple amplifier mode runs with undulator pole strength/BPM errors from P. Emma (see S. Reiche’s talk) • In all cases, undulator lattice chosen to correspond to “current” LCLS base case (118.6-m total length): • 3-cm period in 3.36-m blocks separated by 0.24-m gap • simple FODO focusing, 7.2-m period; 0.24-m magnet length • Output: saturated and/or max. power, gain lengths, spectra, etc. Accelerator and Fusion Research Division

  5. Comparison of GINGER/GENESIS models • Both codes: • Eikonal approximation field solver • KMR wiggle-period-averaged sources • Full 3D macroparticle mover • Slippage applied at discrete z-locations • Time-dependent wake field, beam envelope parameters, 5D ELEGANT macroparticle input accepted • GENESIS features: • uniform x-y transverse grid for fixed z-step • GINGER features: • Axisymmetric, nonlinear radial grid for field • Predictor-corrector controlled, adaptive z-step Accelerator and Fusion Research Division

  6. “0-Order” LCLS Amplifier Mode Simulations Accelerator and Fusion Research Division

  7. Comparison of GINGER/GENESIS resultsfor 1-nC LCLS “0-order” Case • Observations: • GENESIS shows very slightly longer gain length, later saturation but higher power • GINGER shows stronger post-saturation power oscillation (more deeply trapped particles?) • Method for choosing best K was slightly different for both codes Accelerator and Fusion Research Division

  8. GINGER/GENESIS results for “0-order” 200-pC case • Observations: • Again, GENESIS shows slightly longer gain length, 10-m later saturation but 15% higher power • Again, GINGER shows deeper post-saturation power oscillation • Little sensitivity (2 m, 7%) in GINGER results to 8X particle number increase • Possible reasons for differences: • bugs • slight differences in initial e-beam properties (e.g. mismatch) • grid effects (e.g. outer boundary) • ??? Accelerator and Fusion Research Division

  9. “1st-Order” Amplifier Mode simulations using derived time-dependent envelope parameters Accelerator and Fusion Research Division

  10. 1-nC --- NO CSR 15 28100 10 Current (kA) 28050 5 28000 RMS Delta Gamma 1-nC LCLS: E-beam at undulator entrance CSR included ELEGANT results from P. Emma; envelope parameters from modified Elegant2genesis 2 1 Emittance (mm-mrad) Accelerator and Fusion Research Division

  11. P(t) at various z-locations 80 GW 60 GW • Different temporal slices reach saturation at different z locations • Consequently, we chose max P(z, t) as the best comparison diagnostic for time-dependent power 40 GW 40 GW 40 GW GINGER results; 1 nC LCLS; envelope reconstruction/amplifier mode run Accelerator and Fusion Research Division

  12. 100 GW 1-nC LCLS: “1st-order” envelope reconstruction: max P(z) vs. slice time 100 GW GENESIS GINGER • Some quick observations: • Power suppressed in regions with high energy spread [-90:-70 fs] • GENESISshows ~2-3X greater power than GINGER for no-wake cases • For runs including wake fields, GINGER shows somewhat more peak power for the main body (but more localized in time) • Beam centroid wander may be important – better modeled byGENESIS Accelerator and Fusion Research Division

  13. 200-pC LCLS: Initial Beam NO CSR with CSR 28080 28080 28060 28060 28040 28040 • ELEGANT results from P. Emma • Less “rich in phenomena” than 1-nC LCLS case, especially in main body Accelerator and Fusion Research Division

  14. 200-pC LCLS: E-beam properties &predicted max. power (GINGER) Accelerator and Fusion Research Division

  15. “2nd-Order” full SASE mode simulations using time-dependent, 5D macroparticle distributions derived from ELEGANT results Accelerator and Fusion Research Division

  16. 40 GW 1nC-LCLS: SASE results – GINGER • GINGER SASE runs (particle distribution derived from ELEGANT files with CSR effects; no wake fields or spontaneous emission energy loss) • “First” saturation at z~60 m with 1.5X more power than “0-order” test case (simple monochromatic amplifier) • Average gain lengths same for SASE as for simple amplifier • SASE power grows ~1.5X from z=80 to 120 m (to ~32 GW) Accelerator and Fusion Research Division

  17. 15 GW 1nC LCLS: SASE results - GENESIS • Some observations: • GENESIS SASE runs (particle distribution derived from ELEGANT files with CSR effects; wake fieldsincluded; no spontaneous emission energy loss) • “First” saturation at z~65 m but with ~0.6X less power than “0-order” case • Average gain lengths same for SASE (middle pulse) as simple amplifier but longer for head region • SASE power only grows ~1.2-1.4X from z=80 to 120 m (to ~10 GW) Accelerator and Fusion Research Division

  18. 28100 100 GW 28050 28000 1 nC LCLS: head region details GINGER ELEGANT • Some observations from ELEGANT+GINGER runs: • Bi-modal energy distribution in temporal region [-95:-55] fs • Envelope models predict essentially no FEL gain in this region (suppresion by artificially large sg) • 5D macroparticle reconstruction predicts strong gain for both amplifier mode runs (i.e. non slippage) and full SASE runs (but without wake field) • Some SASE spikes grow to ~200 GW peak power ( <P> ~35 GW) Accelerator and Fusion Research Division

  19. 1-nC LCLS: Output spectra in beam head region – GINGER results • Full SASE simulation with temporal resolution of 12 attosec. (=24 ls/c) • Bi-modal energy distribution leads to two regions of peak gain (ls~0.1500 & 0.1506 nm) • After initial saturation of “blue” gain region (larger current fraction), “red” gain region shows shows continued strong growth with z • Nearly periodic (with l) power spike structure slightly redwards of 0.1501 nm – reminiscent of some post-saturation LEUTL phenomena – how real (or repeatable) is this??? Accelerator and Fusion Research Division

  20. 1-nC LCLS: Mid-pulse output spectra GINGER • Full SASE simulations with temporal resolution of 12 attosec. (=24 ls/c) • GINGER simulation ~3 fs; GENESIS~12 fs (??) • Output spectra similar in shape but GINGER average power ~3X greater GENESIS Accelerator and Fusion Research Division

  21. Summary • Simple envelope model + amplifier mode runs provide reasonable estimate for total output power • underestimates power when simple RMS dg used to represent bimodal energy distributions • Reasonably good (but not perfect!) quantitative agreement between GINGER and GENESIS • some pulse regions appear to require full transverse modeling • closer inspection of differences needed including sensitivity to centroid wander and wake fields • Full SASE mode runs show that bimodal energy distributions can lase at both resonant wavelengths • Following saturation at one resonant l, second (and redward) l can continue to show strong gain Accelerator and Fusion Research Division

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