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