1. calculation with 107 particles
Astra bunch 0.4 nC, at z=1.45 m
bunch current
calculation with 107 particles
“slice 1”
(~1keV energy spread, I=17.6 A)
slice energy
“slice 2”
(small energy spread, I=13.1 A)
slice energy
spread

2. compression: 17.6A --> 110A --> 1200A “slice 2”
~1keV energy spread, I=17.6 A
0.3mm, about 110E6 particles
compression: 17.6A --> 110A --> 1200A
“slice 2”
~250eV energy spread, I=13.1 A
0.3mm, about 82E6 particles
compression: 13.1A --> 85.5A --> 944A

3.  1D model starting after gun (z=0.5m)
slicing and densification:
criticism:
this introduces new noise as it ignores relaxation effects (due to plasma oscillations)
 1D model starting after gun (z=0.5m)
Astra distribution with 10E6 particles, but 0.4 nC /e = 2.5E9
we need 250 particles per Astra-particles
procedure:
select all particles in the given slice,
extract correlations with z (to 3rd order)
keep information about linear z-energy correlation
throw away z-information
multiply (replicate x 250) and mix the 5D-distribution
use random generator for z-coordinates
regenerate linear z-energy correlation
full shot noise simulation with Xtrack starts after solenoid field (z=1.45 m)

4. Xtrack simulations
“slice 1” (~1keV energy spread, 110E6 particles) compression: 17.6A --> 110A --> 1200A
“slice 2” (~250eV energy spread, 82E6 particles) compression: 13.1A --> 85.5A --> 944A

5. long. position and energy
“slice 1” (~1keV energy spread, 110E6 particles) compression: 17.6A --> 110A --> 1200A
long. position and energy
after BC2
after ACC2
before BC3
energy /eV
long. phase space (full period)
bunch coordinate / m
E,tot  13.5 kEV
E  9.6 kEV
long. p.s. without z-correlation
plasma oscillation
long. density

6. “slice 1” (~1keV energy spread, 110E6 particles) compression: 17
“slice 1” (~1keV energy spread, 110E6 particles) compression: 17.6A --> 110A --> 1200A
after BC3
before F2kicker
after F2seed chicane
E  127 kEV
Flash2
E  1.3 MeV
I  70 A
I  600 A

7. 1d-models 1d-particles (non-linear, real noise)
effective impedance (long. impedance transversely averaged)
tracking from 0.4m (direct after gun) to 150m (before Flash1/Flash2)
1d-particles (non-linear, real noise)
longer sample (~ 1.1mm)
distribution from random generator
very high bandwidth
LGM (linear gain model)
frequency domain
integral equation

8. random generator: uniform in z, gaussian in energy
1d particles
random generator: uniform in z, gaussian in energy
“slice 1”
~1keV energy spread, I=17.6 A
400E6 particles, about 1.1 mm
compression: 17.6A --> 110A --> 1200A
“slice 2”
~250eV energy spread, I=13.1 A
398E6 particles, about 1.1 mm
compression: 13.1A --> 85.5A --> 944A
distribution at z =150 m
7 m  500 m/Ctot
3 m  200 m/Ctot
bunch coordinate / m
bunch coordinate / m
slice rms  250 keV
total rms  1.2 MeV
slice rms  120 keV
total rms  0.6 MeV

9. “slice 1”, compression: 17.6A --> 110A --> 1200A
BC2
BC3
127 keV
beamline coordinate / m
beamline coordinate / m
log scale
log scale
“slice 2”, compression: 13.1A --> 85.5A --> 944A
3D particle tracking
253 keV
log scale
log scale

10. spectra: comparison 1d particles, LGM
“slice 1”
start
direct before BC2
“slice 2”
 = 30 m
 = 30 m
/mm  1.5
/mm  0.15
effect of plasma oscillations
these oscillations are frozen in ACC1
yes: original white noise is reduced (in some spectral ranges)

11. ? spectra: comparison 1d particles, LGM “slice 1” direct after BC2
direct before BC3
“slice 2”
 = 30 m
 = 30 m ?
unexpected growth of energy spread
 needs further investigations

12. spectra: comparison 1d particles, LGM
“slice 1”
direct after BC3
at 150m
“slice 2”
 = 30 m
 = 30 m
huge disagreement due to strong non-linear effects
even for “slice 1”, but this is not very obvious from the plot

13. energy spread versus initial energy spread
“slice 1”
“slice 2”
but with slightly different optic
but for 1.2 GeV
log scale
log scale C3
“heating” C2
conservation
of phase space

14. rms current fluctuations spread versus initial energy spread
“slice 1”
“slice 2”
but with slightly different optic
but for 1.2 GeV
log scale
log scale

15. ACC1, slice E-spread q = 1nC, Xtrack cavity amplitudes =
[1.00,1.00,1.00,1.00, 1.00,1.00,1.00,1.00] case 100,100
[0.75,0.75,0.75,0.75, 1.25,1.25,1.25,1.25] case 75,125

16. optics with matching:
horizontal/vertical
solid: case 100,100
dashed: case 75,125

17. at 19.8m (after ACC39), with matching
slice energy spread
after ACC1
at 19.8m (after ACC39), with matching

19. “slice 2” (~250eV energy spread, 82E6 particles) compression: 13
“slice 2” (~250eV energy spread, 82E6 particles) compression: 13.1A --> 85.5A --> 944A
after BC2
after ACC2
before BC3
E,tot  23 kEV
E  16.1 kEV
plasma oscillation

20. “slice 2” (~250eV energy spread, 82E6 particles) compression: 13
“slice 2” (~250eV energy spread, 82E6 particles) compression: 13.1A --> 85.5A --> 944A
after BC3
before F2kicker
after F2seed chicane
E  253 kEV
Flash2
E  407 keV
I  15 A
I  139 A

21. plasma oscillations Sp  bunch coordinate LINAC coordinate  L / m
charge
density