X-Ray FEL Simulation: Beam Modeling William M. Fawley Center For Beam Physics Lawrence Berkeley National Laboratory ICFA 2003 Workshop on Start-to-End Numerical Simulations of X-RAY FEL’s

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 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 –“1 st -order” Case : Time-dependent, 5D envelope reconstruction + amplifier mode run –“2 nd -order” case: Full 5D, time-dependent macro- particle reconstruction + SASE mode runs for beam head and middle pulse regions

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 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;    =0.01% ; 1-nC: 3.4 kA, 1.2 mm-mrad  N, P IN =3.0 kW; 200 pC: 1.5 kA, 0.65 mm-mrad  N, P IN =1.0 kW) input Twiss parameters adopted from P. Emma’s ELEGANT runs constant K optimized for peak output power –“1 st -order”: time-dependent envelope parameters (  , I,  N,  x,y,  x,y ) derived from ELEGANT particle output amplifier mode run (no slippage) with K &  same as 0-order run both CSR/no CSR cases with/without undulator wake field effects

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division LCLS Test Case Design (cont.) –“2 nd -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  and   ) –“3 rd -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.

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 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

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division “0-Order” LCLS Amplifier Mode Simulations

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division Comparison of GINGER/GENESIS results for 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

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 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)  ???

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division “1 st -Order” Amplifier Mode simulations using derived time- dependent envelope parameters

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 1-nC --- NO CSR 1-nC LCLS: E-beam at undulator entrance Current (kA) RMS Delta Gamma Emittance (mm-mrad) CSR included ELEGANT results from P. Emma; envelope parameters from modified Elegant2genesis 1 2

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division P(t) at various z-locations GINGER results; 1 nC LCLS; envelope reconstruction/amplifier mode run 80 GW 60 GW 40 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

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 1-nC LCLS: “1st-order” envelope reconstruction: max P(z) vs. slice time 100 GW Some quick observations: Power suppressed in regions with high energy spread [-90:-70 fs] GENESIS shows ~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 by GENESIS GINGER GENESIS

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 200-pC LCLS: Initial Beam NO CSR with CSR ELEGANT results from P. Emma Less “rich in phenomena” than 1-nC LCLS case, especially in main body

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 200-pC LCLS: E-beam properties & predicted max. power (GINGER)

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division “2nd-Order” full SASE mode simulations using time-dependent, 5D macroparticle distributions derived from ELEGANT results

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 1nC-LCLS: SASE results – GINGER 40 GW 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)

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 1nC LCLS: SASE results - GENESIS 15 GW Some observations: GENESIS SASE runs (particle distribution derived from ELEGANT files with CSR effects; wake fields included; 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 ~ X from z=80 to 120 m (to ~10 GW)

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 1 nC LCLS: head region details 100 GW 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   ) 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 ( ~35 GW) GINGER ELEGANT

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 1-nC LCLS: Output spectra in beam head region – GINGER results Full SASE simulation with temporal resolution of 12 attosec. (=24 s /c) Bi-modal energy distribution leads to two regions of peak gain ( s ~ & nm) After initial saturation of “blue” gain region (larger current fraction), “red” gain region shows shows continued strong growth with z Nearly periodic (with ) power spike structure slightly redwards of nm – reminiscent of some post- saturation LEUTL phenomena – how real (or repeatable) is this???

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division 1-nC LCLS: Mid-pulse output spectra GINGER GENESIS Full SASE simulations with temporal resolution of 12 attosec. (=24 s /c) GINGER simulation ~3 fs; GENESIS~12 fs (??) Output spectra similar in shape but GINGER average power ~3X greater

WM Fawley – ICFA2003 – Start-to-End X-Ray FEL Sim. Accelerator and Fusion Research Division Summary Simple envelope model + amplifier mode runs provide reasonable estimate for total output power –underestimates power when simple RMS  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, second (and redward) can continue to show strong gain