1. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 Optimization cathode design with gun5 D. Lipka, V. Vogel, DESY Hamburg, Germany

2. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 Tilted backplane To decrease field on cathode edge and keep high performance for beam dynamics: backplane to cathode are tilted, here 10°, On blue line field strength can be monitored

3. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 Tilted backplane The cathode holder and spring for this simulation is used like present FLASH case

4. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 1D Results > S-Parameters Length of first cell is adapted to reach 1299.9 MHz resonance frequency of  - mode

5. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 E-field on axis With this adaption the balance is almost perfect, here the maximum field strength is scaled to 60 MV/m, but The field strength on cathode is reduced due to the tilted backplane

6. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 E-field on cathode E-field strength on cathode edge is maximum with 63.11 MV/m. This is a factor of 1.37 higher compared to cathode center field strength, Compared with present case: factor is 1.39, only slight reduction

7. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 E-field on surface Diagram shows E-field strength on surface. Compared to present case: Lower field on cathode Relatively high field on iris Surface is longer due to tilt and adaption to get balance and resonance frequency

8. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 ASTRA simulation  To check the beam performance with the tilted backplane ASTRA simulations are performed  Laser beam settings:  Q=1nC, longitudinal flat-top with 20 ps time duration and 2 ps rise and fall time  Transverse size  x,y =0.75 mm radial symmetry, no thermal emittance

9. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 ASTRA simulation: fields E-field tilted backplane E-field gun5 design Solenoid field Fields as a function of distance to cathode  E-field maximum scaled to 60 MV/m, will be compared with gun5 design  Solenoid field taken from standard FLASH type  For optimization of emittance rf-phase of E-field and solenoid strength will be varied

10. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 For optimization of emittance following optimization results are found:  Tilted backplane: rf-phase between laser and highest energy gain has to be +20°, at 0° electrons are lost due to backwards acceleration, solenoid maximum strength has to be 0.23 T  Design gun5: rf-phase between laser and highest energy gain has to be +10°, solenoid maximum strength has to be 0.25 T ASTRA simulation results

11. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 ASTRA results: tilted backplane A small emittance observed, no electron loss, energy 6.3 MeV still with 20° rf phase due to longer first cell

12. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 ASTRA result: default gun5 design A small emittance observed too, energy 5.9 MeV with 10° rf phase

13. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 ASTRA results: emittance tilted backplane Emittance as a function of distance to cathode Design gun5  Tilted backplane minimum emittance of 0.8  mm mrad at z=1.54 m  Design gun5 minimum emittance of 1.05  mm mrad at z=1.25 m → still smaller emittance with tilted backplane and reduced field at cathode

14. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012  To reduce field on cathode edge the holder rounding are reduced from bending radius 3 mm to 1 mm Change design: smaller rounding holder

15. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012  Similar field distribution along z- axis like before because of only small change  Resonance frequency still at 1299.9 MHz E-field on z-axis

16. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 E-field on cathode  Field maximum strength on edge is 57.9 MV/m, a factor of 1.31 higher compared to center  The factor is reduced from 1.39 (present case)  Summary: field strength on edge is reduced from 84.6 to 63.1 (10°) and to 57.9 MV/m for smaller rounding

17. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012  Field strength in units of E/m  higher field on iris visible in both optimized design visible  Smaller field strength due to smaller bend radius  Even smaller bend increases field again E-field strength on resonator surface

18. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 H-field strength on cathode due to modification is reduced:  Default: 31.5 kA/m  10°: 28.7 kA/m  Smaller rounding: 21.1 kA/m H-field strength on cathode Field strength maximum at connection between spring and cathode Default case

19. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012  Similar settings for optimal emittance: B max =0.23 T, phase +20°  Emittance 0.89  mm mrad at 1.57 m distance to cathode ASTRA simulation results

20. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 Compare shunt impedance The shunt impedance for each case is : Default case: 7.2 MΩ 10° case: 9.0 MΩ 10° and smaller rounding: 9.1 MΩ

21. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012  Emittance reduced from 1.05 to 0.8 (10°) and 0.89  mm mrad (last case)  Maximum E-field strength on cathode surface reduced from 84.6 to 63.1 (10°) and to 57.9 MV/m (last case)  Maximum H-field strength on cathode surface reduced from 31.5 to 28.7 (10°) and 21.1 kA/m (last case) Conclusion

22. D. Lipka, V. Vogel, DESY Hamburg, Germany, Oct. 2012 Slice emittances Default case at z=1.25 m Tilted backplane at z=1.54 m Tilted backplane and smaller rounding at z=1.57 m  Slice emittances are shown as a function of longitudinal slices at the z-position with best projected emittance  Best slice emittances reached for default case in the center (about 0.2  mm mrad), only front and end contributes to the larger projected emittance  Other both slice emittances at the center higher, at the front and end are smaller compared to default case