1. 3rd ATF2 Project Meeting, December 18-20, 2006
Correction of Anomalous Vertical Dispersion in the ATF2 EXT Line (v3.6)
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

2. 3rd ATF2 Project Meeting, December 18-20, 2006Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
K1(+)
K2(+)
possible location for
1 μm laserwire
σy = 1.4 μm
For MAD files see
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

3. Simulation Parameters
use Peter Tenenbaum’s Lucretia1 simulation code
included
perfect beam from Damping Ring (εx=2×10-9 m, εy=3×10-8 m) … errors begin after extraction septa, unless otherwise noted
perfect Final Focus
dipole errors2: ΔY = 100 μm (rms)
quadrupole errors: ΔX = 50 μm, ΔY = 30 μm, Δθ = 0.3 mrad (rms)
sextupole errors: ΔX = 50 μm, ΔY = 30 μm, Δθ = 0.3 mrad (rms)
BPM resolution: 5 μm (rms)
not included
wire scanner rolls: │θ│ ≤ 0.2° (uniform)
wire scanner beam size errors: σ = σ0(1+Δσrelative)+Δσabsolute
quadrupole strength errors (ΔK/K)
BPM offsets
BPM rolls
tuning in FF
1http://
2EXT dipoles BH1 and BH2 are assumed to have nonzero sextupole components
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

4. 3rd ATF2 Project Meeting, December 18-20, 2006
Simulation Procedure
apply errors
steer flat (EXT only)
launch into FF
use 2 virtual correctors
steer to 2 virtual BPMs (one at the IP and one 90° upstream)
virtual BPMs are perfect
measure dispersion in diagnostic section
scan input beam energy
measure orbits
fit position vs energy at each BPM
correct dispersion in diagnostic section
back-propagate measured η to start of diagnostic section to get η0 and η′0
use QF1X + QF6X multiknobs for ηx and η′x
correct ηy and η′y using skew quads in inflector (thin lenses at quad centers)
correct coupling
scan 4 skew quadrupoles sequentially
deduce projected εy from wire scanner measurements
set each skew quad to minimize projected εy
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

5. 3rd ATF2 Project Meeting, December 18-20, 2006
errors only (100 seeds)
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

6. 3rd ATF2 Project Meeting, December 18-20, 2006
errors, FF launch
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

7. 3rd ATF2 Project Meeting, December 18-20, 2006
errors, steer flat, FF launch
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

8. 3rd ATF2 Project Meeting, December 18-20, 2006
errors, steer flat, correct coupling, FF launch
Note: red lines represent maximum integrated strength of IDX skew quad (KLmax ≈ 0.1 T)
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

9. 3rd ATF2 Project Meeting, December 18-20, 2006
errors, steer flat, correct ηx, correct coupling, FF launch
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

10. 3rd ATF2 Project Meeting, December 18-20, 2006
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

11. ηy vs η′y at exit of KEX2 (start of diagnostic section)
100 seeds after steering EXT
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

12. ηy vs η′y at exit of KEX2 (start of diagnostic section)
perfect EXT; scan each skew quad
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

13. both ηy and η′y can be corrected with any single skew quad!
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

14. 3rd ATF2 Project Meeting, December 18-20, 2006
ηy correction: residual x-y coupling
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

15. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 1: 2 skew quads
SQ1 SQ6
βx =
αx =
ηx =
βy =
αy =
Δμx =
Δμy =
kl/klmax =
residual =
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

16. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 1
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

17. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 2: 2 skew quads
SQ2 SQ5
βx =
αx =
ηx =
βy =
αy =
Δμx =
Δμy =
kl/klmax =
residual =
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

18. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 2
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

19. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 3: 2 skew quads
SQ3 SQ4
βx =
αx =
ηx =
βy =
αy =
Δμx =
Δμy =
kl/klmax =
residual =
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

20. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 3
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

21. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 4: 4 skew quads
SQ1 SQ2 SQ5 SQ6
βx =
αx =
ηx =
βy =
αy =
Δμx =
Δμy =
kl/klmax =
residual = e-004
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

22. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 4
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

23. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 5: 4 skew quads
SQ2 SQ3 SQ4 SQ5
βx =
αx =
ηx =
βy =
αy =
Δμx =
Δμy =
kl/klmax =
residual = e-004
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

24. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 5
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

25. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 6: 4 skew quads
SQ1 SQ3 SQ4 SQ6
βx =
αx =
ηx =
βy =
αy =
Δμx =
Δμy =
kl/klmax =
residual = e-004
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

26. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 6
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

27. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 7: 3 skew quads
SQ2 SQ5 SQ8
βx =
αx =
ηx =
βy =
αy =
Δμx =
Δμy =
kl/klmax =
residual =
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

28. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 7
max(|KL|)=0.0022
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

29. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 8: 3 skew quads
SQ1 SQ6 SQ8
βx =
αx =
ηx =
βy =
αy =
Δμx =
Δμy =
kl/klmax =
residual =
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

30. 3rd ATF2 Project Meeting, December 18-20, 2006
Scheme 8
max(|KL|)=0.0021
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006

31. 3rd ATF2 Project Meeting, December 18-20, 2006
Conclusions
simulated system performance is adequate for the achievement of ATF2 goal “A” (35 nm IP σy)
if small assumed quadrupole roll errors and vertical dipole misalignments are the only sources of coupling, skew correction seems unnecessary
if quadrupole roll errors are increased by a factor of 10, coupling correction provides 20% improvement in IP σy
Mark Woodley, SLAC
3rd ATF2 Project Meeting, December 18-20, 2006