1. Beam-Based Alignment of the LCLS Undulator Paul Emma, SLAC April 24, 2002
Motivation
Technique
Simulations
LCLS
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

2. Undulator Design planar hybrid type 3.42 m undulator line length 122 m
undulator period, u 3 cm
undulator parameter, K
3.71
1-mm BPM  cavity and button-type in compact package (G. Decker, ANL)
planar hybrid type QF QD
BPM
3.42 m
undulator section
vacuum pump
Quad-magnets and undulator sections on independent movers
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

3. b-functions through undulator
Undulator Optics
33 undulator sections, L = 3.4 m
~4000 undulator periods (3 cm)
Permanent magnet quadrupoles
~13º b-phase adv./cell, 18 m
Magnet movers on each quad (x,y)
Movers on each undulator section
1-mm BPM at each quad (x,y)
Quads aligned w.r.t. adjacent undulator sections to <50 mm
b-functions through undulator
18 m
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

4. Alignment Motivation Need good overlap of e-/photon beam (30 mm rms)
1.5-Å phase slippage between photons and e- sensitive to trajectory
e- undulator trajectory must be straight to <5 mm over 10-m gain length
difficult to achieve with survey methods
rely on beam-based alignment…
e- with large b-osc. amplitudes will ‘slip’ w.r.t. photon beam…
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

5. Basic Strategy
Save BPM readings as a function of large, deliberate changes in e- energy (e.g., 15, 10, and 5 GeV)
Calculate and correct quad & BPM misalignments and adjust ‘launch’
Repeat ~3 times with first application
Re-apply one iteration per ~1 month (?)
LCLS
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

6. The Method
BPM readings, mi, written as sum of upstream kicks + offset, bi
Kicks are sensitive to momentum, pk, while offsets, bi, are not j
ith BPM
bi > 0
DE < 0
DE = 0 s
quad offsets and/or pole errors
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

7. The Method
Reference line defined by incoming x0, x0 launch conditions mi
linear only if Cij independent of p
offset = -bi
1/p
p
(15 GeV/c)-1
(10 GeV/c)-1
(5 GeV/c)-1
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

8. The Method Define… then solve the linear system… BPM readings at p1
BPM offsets
BPM readings at p2
quad offsets
known optical functions at each pk
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

9. Constraints
Solve with ‘soft-constraints’* on resulting BPM and quad offsets
~1 mm
Without this ‘reasonability’ weighting, resulting BPM and quad offsets can stray out to large values at low frequencies
Scanning beam energy gives sensitivity to (and ~correction of) all field errors, including undulator poles, Earth’s field, etc…
* C. Adolphsen, 1989 PAC
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

10. permanent magnet quadrupoles and undulator poles
Schematic layout
Undulator misaligned w.r.t. linac axis with uncorrelated and correlated* (‘random walk’) component
original incoming launch error
BPMs
quads
~300 mm
x0
LINAC
best final trajectory x0
steering elements
UNDULATOR
(120 m)
permanent magnet quadrupoles and undulator poles
* suggested by C. Adolphsen
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

11. Beam-based alignment steps×3
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

12. Input errors used for simulation
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

13. Initial BPM and quad misalignments (w.r.t. linac axis)
+ Quadrupole
positions
o BPM readback
quad positions
BPM offsets
Now launch beam through undulator
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

14. Initial trajectory before any correction applied
+ Quadrupole
positions
o BPM readback
e trajectory
‘real’ trajectory
fit used to smooth launch
quad positions
BPM readings
Note, all trajectory plots are w.r.t. linac axis (except last two)
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

15. Trajectory after initial rough steering (14.3 GeV)
+ Quadrupole
positions
o BPM readback
e trajectory
Save as 1st set of BPM readings
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

16. Energy now reduced to 10 GeV
+ Quadrupole
positions
o BPM readback
e trajectory
Save as 2nd set of BPM readings
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

17. Energy reduced again to 5 GeV
+ Quadrupole
positions
o BPM readback
e trajectory
Save as 3rd set of BPM readings
Now analyze BPM data…
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

18. Fitted quadrupole offsets
Fit results
Actual offsets
‘real’ offsets
fitted offsets
results differ by straight line…
similar plot for BPM offsets (not shown)
Now correct quad and BPM positions…
use linear component of fitted offsets to re-adjust launch
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

19. Absolute trajectory after 1st pass of BBA (14.3 GeV)
+ Quadrupole
positions
o BPM readback
e trajectory
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

20. Possible Absolute Trajectory
Beam is launched straight down undulator, with possible inconsequential kink at boundary
LINAC
dispersion generated is insignificant
Now look at trajectory w.r.t. undulator axis 
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

21. After 1st pass of BBA (now w.r.t. undulator line)
+ Quadrupole
positions
o BPM readback
e trajectory
sx  48 mm
Now repeat procedure of energy changes two more times…
sy  24 mm
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

22. After 3rd pass of BBA (14.3 GeV)
+ Quadrupole
positions
o BPM readback
e trajectory
sx  1.7 mm
Dj  100°
rms beam size: 30 mm
RON (FEL-code) simulation shows Lsat increased by <1 gain-length;
R. Dejus, N.Vinokurov
sy  2.7 mm
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC

23. Summary
BPMs resolve trajectory to ~1 mm rms
BPM readings ‘drift’ <1 mm over 1-2 hr (temperature)
Magnet movers are settable to within 1 mm (or use coils)
BPM readings are not sensitive to variable beam size, etc.
Trajectory is stable enough to <20% of beam size (already demonstrated in FFTB)
Alignment can be achieved at adequate level using beam-based technique, given that…
LCLS
LCLS DOE Review, April 24, 2002
Paul Emma, SLAC