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

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

 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)

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

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

“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

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

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

“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

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)

? 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

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

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

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

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

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

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

“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

“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

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