1. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Effects of AC Resistive-Wall Wake Upon LCLS SASE Performance: Numerical Simulation Results William Fawley - LBNL Sven Reiche – UCLA 7 April 2005 – LCLS FAC Meeting

2. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu  Summary of simulation method and wakefield algorithm  Simulation results for 1-nC “sloppy taco” case  Simulation results for 200-pC “El Chargito” case  Comparison with predictions of Huang and Stupakov Talk Outline

3. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Simulation Description ELEGANT dump of the 6D phase space distribution of LCLS start-end simulation at the undulator entrance. Distribution re-matched to the undulator lattice including breaks (provided by H.-D. Nuhn). Current profile extracted to calculate wake potential Ginger/Genesis runs with reconstruction of the 5D phase space and I(t) Shot-noise added (SASE runs). Slice spacing of about 11 as => 20K slices for 220-fs bunch length. Runs for copper and aluminum vacuum chambers and various compensating gradients (via K taper).

4. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Wakefield Algorithm Current profile extracted from particle distribution with a 1-fs smoothing window Effective wake potential calculated with two different programs (H.-D. Nuhn and S. Reiche) Resistive wall wakefield using the AC model for copper and aluminum Geometric wake with an effective gap of 0.18 m and a module length of 4 m Surface roughness wake (inductive model and synchronous mode) with an rms roughness of 100 nm and a period of 30 microns. Constant gradient added to wake potential to simulate the real-life effects of tapering undulator K to compensate wake losses.

5. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Characteristics of 1-nC “Sloppy Taco” pulse

6. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Wake Components for the 1-nC Case

7. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Simulation Code Predictions for P(t) in Cu & Al Pipe without Compensation Field Data is smoothed from raw ~12 as resolution to ~1 fs resolution Note that GENESIS data is 30 m upstream of GINGER data For Cu case, agreement between the codes is extremely good, both where there is lasing and in the actual coarse-grained P(t) amplitude Lasing appears strongest around +100 kV/m for this untapered case Time (fs)

8. Optimal Lasing occurs at ~+100 kV/m net field GINGER 1-nC

9. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Characteristics of 200-pC “El Chargito” pulse

10. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu 200-pC wake: More constant in time, lower amplitude than 1-nC “sloppy taco” case Lack of high current head spike and longer rise time both contribute to lack of strong temporal oscillation in wake field for 200-pC case Nearly all of pulse wake lies within +/- 50 kV/m of mean => easy compensation by undulator taper (300 kV/m over 130 m ~ 0.3% taper in K) 200-pC1-nC

11. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu GINGER Results for 200-pC Pulse Energy vs. Z Uncompensated 200-pC Cu & Al wake lower power ~8-10X Gain length increased ~15% but sat. point unaffected External field of ~150 kV/m makes up for wake Increasing ext. field to +300 kV/m nearly doubles power over no wake case – agreeing with Huang and Stupakov prediction

12. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Code Comparison for 200-pC Case Reasonably good agreement between codes, given complexity of calculation. 1 mJ = 7.5E11 photons @ 0.15-nm GINGER typically shows 25-50% more power, post-saturation Unclear why --- algorithms, grid resolution, physics ???

13. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Output Power vs. Time @ z=130m 200pC - Cu Pipe Data is smoothed from raw ~12-as resolution to ~1-fs resolution For 300-kV ext. field + Cu wake case, agreement between the codes is good in overall temporal dependence with GINGER showing ~1.5X greater power Compared to 1-nC “sloppy taco” case, lasing occurs over full 200-pC pulse GINGER

14. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Summary & Comparison to Theory If  = w /8  L G ~ 2.3E-4 (probable underestimate by 1.5X), then Huang and Stupakov predict an optimal energy taper (ignoring wake) of 2  E/L SAT ~ +40 kV/m Range of 40-80 kV/m above wake compensation probably works well for 200-pC case Saturation power of ~8 GW agrees well with  EI = 10 GW (factor of 1.5 included here) No wake Cu –Wake 0 kV/m Cu – wake 200 kV/m Cu – wake 300 kV/m Al – wake 200 kV/m Al – wake 300 kV/m L G (power) (m) 5.176.45.195.185.105.25 P SAT (GW) 71.8612810

15. Wm. Fawley LCLS FAC WMFawley@lbl.gov April 7. 2005 Sven Reiche reiche@ucla.edu Conclusions 1-nC case yields more energy (2 mJ for Al pipe and optimum taper), but… Temporal radiation profile is very non-uniform Only partial compensation by field taper due to strong transient in wake potential 200-pC case gives 1.5 mJ output Pulse duration ~half of 1 nC case (=> ~100% larger brightness) Almost complete compensation of wake fields (continuous radiation profile) possible via taper. Performance independent of vacuum chamber material (i.e., Al and Cu are comparable) Good agreement between theory and simulation.