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Summary on Mini-Workshop on Space-Charge Effects in
FELsIgor Zagorodnov
Beam Dynamics Group Meeting17.12.07
Martin Dohlus
Space-Charge Issues of Electron Bunchesfrom Laser-Plasma-Accelerators
at Low EnergyF. Grüner, MPQ
Space-charge workshopBESSY, Dec 12-14, 2007
• basics of laser-plasma accelerators• GSSY paper• Bosch paper• GPT for GSSY/Bosch case• GPT for complete setup• analytical approach
Laser plasma accelerators:setup for table-top FEL
laser-plasmaaccelerator
undulatorfocusing
beam size: ~ µmcharge: ~ nCdivergence: ~ mradenergy: ~ 150 MeV
GSSY paper
equations according to arXiv version
their ansatz
Bosch
GSSY-chirp
(normalized) chirp over one (ideal) cooperation length
(actually ~4)
GPT for GSSY/Boschparameter: γ = 300, σz = 1 µm, σ⊥= 30 µm and zero emittance
stop at z = 0.8 m
time=2.7e-009
Std(x) = 0.000241218 Std(z) = 1.34166e-006 Avg(G) = 307.623 Std(G) = 19.1005
0.809432 0.809434 0.809436 0.809438GPT z
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G
time=7e-010
Std(x) = 5.46057e-005 Std(z) = 1.02222e-006 Avg(G) = 302.832 Std(G) = 9.7234
0.209851 0.209852 0.209853 0.209854 0.209855 0.209856GPT z
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G
time=1.4e-009
Std(x) = 0.000110291 Std(z) = 1.11039e-006 Avg(G) = 305.41 Std(G) = 14.8082
0.419706 0.419708 0.419710GPT z
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G
time=2e-009
Std(x) = 0.000168011 Std(z) = 1.20961e-006 Avg(G) = 306.694 Std(G) = 17.2786
0.599580 0.599582 0.599584GPT z
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G
steady-state chirp due to debunching(1.0 µm to 1.3 µm)
0.2m
0.4m0.6m
0.8m
α = 1.2 ≠ 10[4]
GPT for complete setupbunch evolves
accelerator exit focusing triplet undulatortransverse expansion longitudinal expansion
time=3.8e-009
1.139202 1.139204 1.139206 1.139208GPT z
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G
time=2e-011
0.005994 0.005996 0.005998GPT z
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G
z= 6 mm z= 1.1 m
ener
gy
pos. in bunch pos. in bunch
ener
gy
Conclusion
• GSSY/Bosch correct for „frozen bunch“– ever-increasing chirp
• GPT reaches soon steady-state chirp– in agreement with expansion time scales– in agreement with finite self-energy
• main question: does FEL cope with (correlated!) debunching: global debunching vs. local micro-bunching
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