1. Computational Needs for the XFEL Martin Dohlus DESY, Hamburg

2. TOC about FELs physical challenges accelerator and SASE FEL accelerator some effects (CSR, µ-bunch instability, compression modes, noise- & parameter-sensitivity) gun to undulator tracking (segmentation, codes, LCLS & European XFEL) computational effort SASE FEL usual approximations SASE simulation (example: influence of undulator wakes and tapering) a tolerance study (impact of undulator gap tolerance) summary

3. electron beam photon beam about FELs: SASE XFEL resonant interaction: radiated power µ bunching saturation length gain length

4. what are the physical challenges? FLASH 13nm@690MeV LCLS 0.15nm@14GeV Europ. XFEL 0.1@17GeV FLASH ~ 30m LCLS ~ 120m Europ. XFEL ~ 200m (1d FEL theory) current density overlap of photon & electron beam FLASH ~ 100 µ m LCLS, E-XFEL ~ 30 µ m emittance energy spread  bandwidth normalized emittance

5. accelerator and SASE FEL beam preparation FEL & SASE gun injector BC system linac source: jitter & fluctuations driven fields: field errors, alignment self fields: space charge, CSR, wakes parameter sensitivity, µ-bunch (in)stability, undulator orbit

6. gun & injector ~ 10 … 100 A; ~ 100 MeV RF Gun drive laser external fields (field stability) space charge effects 1.5 cell cavity photo cathode waveguide coaxial coupler drive laser electron beam

7. bunch compression system  1 … 10 kA;  ~ 20 GeV external fields (field stability) space charge effects coherent synchrotron radiation wakes {dispersion free solvers, general indirect wake integrators} 1.3 GHz rf 3.9 GHz rf(linearization) bunch compression chicanes diagnostic sections

8. CSR effects radiation effectsovertaking centrifugal longitudinal field in center of bunch long transients: drift arc drift

9. with self-interaction 1 m1 m shape variation without self-interaction top view (horizontal plane), color = energy compression emittance growth … CSR effects

10. µ-bunch “instability” picture from Z. Huang, J.Wu: Microbunching instability due to bunch compression http://icfa-usa.jlab.org/archive/newsletter/icfa_bd_nl_38.pdf impedances (steady state): (free space, k  r /  << 1 ) “SC-instability” “CSR-instability”

11. wavelength before bc1 / mm gain keV 10 entrancerms,  E  after BC1 after BC2 after collimator keV 10 entrancerms,  E  after BC1 after BC2 after collimator gain after collimator keV/ entrancerms, E  5 10 15 20 25 keV/ entrancerms, E  5 10 15 20 25 wavelength before bc1 / mm contributions of the sub-sections of the linac for an uncorrelated energy spread of 10 keV overall gain for different uncorrelated energy spreads gain curves of µ-bunch “instability” ‘laser heater’ System (LCLS layout)

12. non linear effects in long. phase space before BCafter BC current / A  E / MeV z / mm current / A  E / MeV z / mm current / A  E / MeV z / mm current / A  E / MeV z / mm linear I peak  3.5 kA lost control: magnet strength changed by 0.5% I peak  15 kA I peak  3.5 kA ‘controlled’ or linearized compression ‘rollover’ compression (LCLS, European XFEL) (FLASH)

13. example: rollover compression in FLASH numerical noise & µ-bunch “instability” longitudinal phase space before 2 nd BC current after 2 nd BC red: SC calculation with good spatial resolution shot noise; wavelength ~ grid resolution  current with µ-structure blue: reduced resolution in tail E/MeV s/mm I/A

14. gun to undulator tracking (1km) … …

15. European XFEL, segmentation gun acc0 + … dogleg heater & linac 1 bc1linac 2bc2 cathode cavity solenoid module quad dipoles quads modules (1 st & 3 rd ) quads dipolesmodules quads dipoles modules quads dipoles quads undulator (with quads) main linac colli- mator …SASE1… 130 MeV500 MeV 2 GeV 17.5 GeV rf, dispersion

16. parallel versions available for most codes time consuming: CSR effects by sub-bunch method SASE-FEL codes some available tracking programs Astra, Parmela, GPT: space charge effects  poisson solver external fields (magnets, cavities) Trafic 4, CSRtrack: space charge and CSR effects; PEC shielding (planar chamber); external fields (magnets) Elegant: external fields (magnets, cavities) & wakes simple 1d CSR model FEL codes FAST Genesis Ginger (2d) some more: MAFIA, ITACA, SPIEFE, TREDI, ATRAP, HOMDYN single particle: AT, BETA, BMAD, COMFORT, COSY- INFINITY, DIMAD, LEGO, LIAR, LUCRETIA, MAD, MARYLIE, MERLIN, ORBIT, PETROS, PLACET, PTC, RACETRACK, SAD, SIXTRACK, SYNCH, TEAPOT, TRACY, TRANSPORT, TURTLE, UAL (from W. Decking) some more: 3d: FELEX, FELOS, RON, FELS, FRED3D, MEDUSA, TDA3D 2d: NUTMEG 1d: FS1T, SARAH (from S. Reiche)

17. computational effort method 1 (fast) method 2 (reference) example: European XFEL ASTRA CSRtrack sub-bunch GENESISELEGANT transport matrix ASTRA CSRtrack 1d GENESIS & sc wake 30 h12 h1.5 h LINUX cluster with 20 cpus (64 bit) PC (32 bit) 4 h 30 min 20 min8 h 2 h sec…min (steady state) h…w (SASE) 3 h

18. s2u: {many codes & glue}  s2e-code European XFELLCLS

19. FEL & SASE: usual approximations particle motion and wave-particle interaction are averaged over one or more wiggler wavelength resonant approximation slowly in z and t paraxial approximation SASE: macro particles with controlled shot noise

20. SASE simulation example: European XFEL, 1nC, 0.1nm length along undulator = 135 m step along undulator: 4 u particles per slice ~ 10000 step along bunch: 64 l number of slices ~ 10000 90 min / seed 150 seeds  ~ 10 days LINUX cluster with 20 cpus (64 bit) electron beam photon beam electron slices photon slices along bunch along undulator electrons in slices long. phase space saturation beyond saturation beyond saturation S.Reiche PhD thesis along bunch along undulator

21. Igor Zagorodnov undulator-to-end simulation bunch shape and different contributions to long. wake in undulator shape geometric resistive wake head -50500 10 -10 0 010050 wake + taper no wake 0 1 2 3 4 the energy loss along the undulator can be compensated by tapering

22. Igor Zagorodnov a tolerance study (impact of undulator gap) 40 0 015105 80 20 60 steady state 1 015105 0 0.8 0.6 0.4 0.2 SASE 150 seeds steady state 100 seeds / point one slice between periodic boundaries example: European XFEL, 1nC, 0.1nm steady state 30 sec / seed 100 seeds /  ~ 1 h all points  ~ 1 day SASE 90 min / seed 150 seeds  ~ 10 days PC (32 bit), LINUX cluster with 20 cpus (64 bit) SASE model ~ 10000 slices steady state model: one slice between periodic boundaries

23. summary complicated beam dynamics even before undulator emittance compensation in gun, longitudinal compression, sensitive longitudinal dynamic, importance of wakes, SC & CSR effects, unwanted  -bunching before undulator fast approaches for particular effects e.g. parameter sensitivity,  -bunch instability, steady state gun to undulator tracking input from other investigations (wakes) few CSR codes, fewer available, non with all possibilities (e.g. resistive wakes) parallel SC & CSR programs change of phase space description use of different methods and codes (SC, CSR) careful control of computational parameters “glued” multi method computations have been done (but need experience and careful inspection of intermediate results) SASE-FEL input from other investigations (surface properties, wakes) efficient “steady state” computations, SASE is time consuming (needs parallel c.) SASE-FEL codes need experience (many parameters)