1. Gun Calculations by Poisson Model for Non-Uniform Distributions
animation
cathode distributions
tables
many plots
bunch prototype:
XFEL bunch,
250 pC
Gun Calculation with Astra
“rz” and restarted “xyz”
rz-case, without/with restart
xyz: shifted solenoid (1mm)
xyz: rotated solenoid (1mrad)
but: more about the rz-case

2. Gun Calculations by Poisson Model for Non-Uniform Distributions
an exemplary investigation
the bunch (prototype): 250 pC, XFEL type, see
longitudinally:
z/m
Astra generator
Lt=20psec, rt=2psec
Gun
60 MV/m, T
transversely: uniform, R = 1 mm (rms = 0.5 mm)
modifications: r(z)  halo & FLASH type
xy(z)  odd & random fluctuations
calculations with MATLAB code “stupid”, version=“less stupid”

3. r(z)-cathode distributions:
uniform
90% uniform, 10% halo
rms
80% uniform
20% halo
Flash

4. xy(z)-cathode distributions:
10% rms, cutoff=0.2mm
20% rms, cutoff=0.2mm
odd
20% rms, cutoff=0.4mm
-10%
+10%

5. slice parameters for |z|<1mm

6. uniform distribution, XFEL q/pC = 250 z/m = 2.6038
twiss,x,y/m= , 2.144
E,slice/eV =
averaged for |z|<1mm

7. 90% uniform, 10% in halo q/pC = 250 z/m = 2.6038
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

8. 80% uniform, 20% in halo q/pC = 250 z/m = 2.6038
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

9. odd odd q/pC = 250 z/m = 2.6038 /m = 0.96395, 0.98515
twiss,x,y/m= , 2.119
E,slice/eV =
averaged for |z|<1mm
-10%
+10%

10. 10% rms, cutoff=0.2mm q/pC = 250 z/m = 2.6038
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

11. 20% rms, cutoff=0.2mm q/pC = 250 z/m = 2.6038 /m = 0.9507, 1.0129
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

12. 20% rms, cutoff=0.4mm q/pC = 250 z/m = 2.6038
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

13. XFEL-bunch + Flash fields
averaged for |z|<1mm
uniform, XFEL-bunch with Flash fields
q/pC = 250
z/m =
/m = ,
twiss,x,y/m= ,
E,slice/eV =

14. Flash-bunch + Flash fields
averaged for |z|<1mm
uniform, FLASH-bunch with Flash fields
q/pC = 250
z/m =
/m = ,
twiss,x,y/m= ,
E,slice/eV =

15. uniform distribution, XFEL q/pC = 250 z/m = 2.6038
twiss,x,y/m= , 2.144
E,slice/eV =
averaged for |z|<1mm

16. 90% uniform, 10% in halo q/pC = 250 z/m = 2.6038
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

17. 80% uniform, 20% in halo q/pC = 250 z/m = 2.6038
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

18. odd
q/pC = 250
z/m =
/m = ,
twiss,x,y/m= , 2.119
E,slice/eV =
averaged for |z|<1mm

19. 10% rms, cutoff=0.2mm q/pC = 250 z/m = 2.6038
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

20. 20% rms, cutoff=0.2mm q/pC = 250 z/m = 2.6038 /m = 0.9507, 1.0129
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

21. 20% rms, cutoff=0.4mm q/pC = 250 z/m = 2.6038
twiss,x,y/m= ,
E,slice/eV =
averaged for |z|<1mm

22. uniform, XFEL-bunch with Flash fields q/pC = 250 z/m = 1.4553
averaged for |z|<1mm
uniform, XFEL-bunch with Flash fields
q/pC = 250
z/m =
/m = ,
twiss,x,y/m= ,
E,slice/eV =

23. uniform, FLASH-bunch with Flash fields q/pC = 250 z/m = 1.4553
averaged for |z|<1mm
uniform, FLASH-bunch with Flash fields
q/pC = 250
z/m =
/m = ,
twiss,x,y/m= ,
E,slice/eV =

24. Gun Calculation with Astra “rz” and restarted “xyz”
an other exemplary investigation
the bunch: 250 pC, XFEL type, see
as before
longitudinally:
z/m
Astra generator
Lt=20psec, rt=2psec
Gun
60 MV/m, T
transversely: uniform, R = 1 mm (rms = 0.5 mm)

25. case 1: axial
gun
solenoid
case 2: 1 mm shift
(not axial)
case 3: 1 mrad rotation
(not axial)

26. mirror charges are switched off at ~ 10cm
case 1: fully 2d, restarted 2d (from z=1cm), restarted 3d (from z=1cm)  z = 1m
mirror charges are switched off at ~ 10cm
but: restart without mirror charges
noise reduction (Hammersly), 1MP

27. as before, but solenoid is shifted by 1mm
case 2: fully 2d, restarted 2d (from z=1cm), restarted 3d (from z=1cm)  z = 1m
as before, but solenoid is shifted by 1mm
noise reduction (Hammersly), 200kP

28. 2d solution, without shift
case 2  case 1
z = 1m
??? noise
2d, 1MP  3d, 200kP
2d solution, without shift

29. as before, but solenoid is rotated by 1mrad
case 3: fully 2d, restarted 2d (from z=1cm), restarted 3d (from z=1cm)  z = 1m
as before, but solenoid is rotated by 1mrad
noise reduction (Hammersly), 200kP

30. 2d solution, without shift
case 3  case 1
z = 1m
??? noise
2d, 1MP  3d, 200kP
2d solution, without shift

31. BUT

32. case 1: fully 2d, restarted 2d (from z=1cm), restarted 3d (from z=1cm)  z = 1m & 2.6m

33. case 1:  z = 2.6m
Astra with 1MP, Hammersly
stupid with 3.2MP, no noise reduction (random generator)

34. ?! case 1:  z = 2.6m, Astra with 1MP, Hammersly
(a) rz, restart from 1cm & 1m
(b) restart from 1m with
doubled transverse resolution ?!