x-ray fel simulation: beam modeling william m. fawley ([email protected]) center for beam physics...

X-Ray FEL Simulation: Beam Modeling

William M. Fawley([email protected])

Center For Beam PhysicsLawrence 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

– “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



LCLS Test Case DesignIn 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 , PIN=3.0 kW;

200 pC: 1.5 kA, 0.65 mm-mrad N, 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 (, 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



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 and )

– “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.



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



“0-Order” LCLS Amplifier Mode Simulations



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



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)???



“1st-Order” Amplifier Mode simulations using derived time-dependent envelope parameters



1-nC --- NO CSR1-nC LCLS: E-beam at undulator entrance

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P(t) at various z-locations

GINGER results; 1 nC LCLS; envelope reconstruction/amplifier mode run

80 GW 60 GW

40 GW 40 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



1-nC LCLS: “1st-order” envelope reconstruction: max P(z) vs. slice time

100 GW100 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



200-pC LCLS: Initial Beam

NO CSR

2808028080

28040 28040

2806028060

with CSR

• ELEGANT results from P. Emma• Less “rich in phenomena” than 1-nC LCLS

case, especially in main body



200-pC LCLS: E-beam properties &predicted max. power (GINGER)



“2nd-Order” full SASE mode simulations using time-dependent,

5D macroparticle distributions derived from ELEGANT results



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)



1nC LCLS: SASE results - GENESIS15 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 ~1.2-1.4X from z=80 to 120 m (to ~10 GW)



1 nC LCLS: head region details

100 GW

28000

28050

28100

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 ( <P> ~35 GW)

GINGERELEGANT



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~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 ) power spike structure slightly redwards of 0.1501 nm – reminiscent of some post-saturation LEUTL phenomena – how real (or repeatable) is this???



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



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

x-ray fel simulation: beam modeling william m. fawley ([email protected]) center for beam physics...

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