PowerPoint-Pr

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Numerical Simulations of CSR driven Instabilities
Frank Stulle, DESY

• Analytical Model
• TraFiC4
• Simulation Results
• Conclusion and Future Plans

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Analytical Model
derived by Saldin/Schneidmiller/Yurkov
amplification of small sinusoidal density
modulations
simple 4-bend chicane
1D pencil-like beam, no transverse emittance, no
correlated energy spread, i.e. no
compression, with and without uncorrelated energy
spread
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Analytical Model
derived by Saldin/Schneidmiller/Yurkov
strong dependence on k2p/l, l -gt 0 gt G -gt ?
gain for a beam without uncorrelated energy spread
gain for a beam with uncorrelated energy spread
suppression of the gain for small wavelengths, l
-gt 0 gt G -gt 0
ˆ
maximum at kmax2.15 gt Gmax1.16 g02
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TraFiC4
3D self consistent tracking code beam is modeled
by macroscopic sub bunches sub bunches are 3D
gaussian charge distributions 1D pencil-like beam
used for simulations (no transverse emittance)
optics bunch, tracked only
sampling bunch, tracked only
sub bunch, generates fields, tracked self
consistent
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Simulation Parameters
Beam parameter
nominal energy E0 5.0 GeV
flat top current I0 6 kA
rel. modulation depth h 10-4
uncorr. rms energy spread sE 3 10-5
norm. emittance ex,y 0 mm mrad
Chicane parameter
dipole length Ld 0.5 m
length of 1st and 3rd drift L0 5.0 m
length of 2nd drift L1 1.0 m
bend radius R 10.35 m
bending angle F 2.77 deg
momentum compaction R56 -25 mm
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Gain Curves
simulated gain without uncorr. energy spread
analytical gain without uncorr. energy spread
simulated gain with uncorr. energy spread
analytical gain with uncorr. energy spread
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Gain Development
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Phasespace and Profile
initial
initial
final
final
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Phasespace and Profile
start of last dipole
start of last dipole
end of last dipole
end of last dipole
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Wake Fields
Wake potential of a bunch with 2 mm modulation
wavelength, without uncorrelated energy spread
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Wake Fields
Wake potential of a bunch with 2 mm modulation
wavelength, without uncorrelated energy spread,
inside the last dipole
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Wake Fields
Wake potential of a bunch with 2 mm modulation
wavelength and uncorrelated energy spread
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Wake Fields
Wake potential of a bunch with 2 mm modulation
wavelength and uncorrelated energy spread, inside
the last dipole
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Wake Fields
Wake potential of a bunch with 2 mm modulation
wavelength and uncorrelated energy spread
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Wake Fields
Wake potential of a bunch with 2 mm modulation
wavelength and uncorrelated energy spread, inside
the last dipole
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Slice Emittance
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Projected Emittance
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Correlated Emittance
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Conclusion and Future Plans

• we compared analytical gain curves to TraFiC4
  simulations
• the agreement is very good
• more simulations with different sets of
  parameters are needed
• the influence of emittance on the gain is under
  study
• we are limited by CPU power and RAM size, i.e. we
  are limited in the number of sub bunches (lt10000)
• very careful modeling of the longitudinal profile
  needed