BBA Related Issues Heinz-Dieter Nuhn, SLAC / LCLS June 28, 2004

1
BBA Related IssuesHeinz-Dieter Nuhn, SLAC /
LCLSJune 28, 2004

• Technique
• Simulations
• Earth Field Considerations

2
Basic Strategy

• Save BPM readings as a function of large,
  deliberate changes in e- energy (e.g., 14, 7, 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 (?)

Courtesy of Paul Emma
3
The Method

• BPM readings, mi, written as sum of upstream
  kicks offset, bi
• Kicks are sensitive to momentum, pk, while
  offsets, bi, are not
• Reference line defined by incoming x0, x?0 launch
  conditions

bi gt 0
s
Courtesy of Paul Emma
4
The Method

• Extrapolation to infinite momentum give BPM
  offsets

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
Courtesy of Paul Emma
5
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
Courtesy of Paul Emma
6
Constraints

• Solve with soft-constraints on resulting BPM
  and quad offsets

• 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, Earths field, etc

C. Adolphsen, 1989 PAC
Courtesy of Paul Emma
7
Schematic layout
Undulator misaligned w.r.t. linac axis with
uncorrelated and correlated (random walk)
component
original incoming launch error
x?0
x0
130
permanent magnet quadrupoles and undulator poles
suggested by C. Adolphsen

• Courtesy of Paul Emma

8
Beam-based alignment steps
3

• Courtesy of Paul Emma

9
Input Errors Used for Simulation
2
100
100
0.04
?4

• Courtesy of Paul Emma

10
Initial BPM and quad misalignments (w.r.t. linac
axis)
Now launch beam through undulator?
130
130

• Courtesy of Paul Emma

11
Initial trajectory before any correction applied
Note, all trajectory plots are w.r.t. linac axis
(except last two)
130
130

• Courtesy of Paul Emma

12
Trajectory after initial rough steering (14.3 GeV)
Save as 1st set of BPM readings
130
130

• Courtesy of Paul Emma

13
Energy now reduced to 10 GeV
Save as 2nd set of BPM readings
130
130

• Courtesy of Paul Emma

14
Energy reduced again to 5 GeV
Save as 3rd set of BPM readings Now analyze BPM
data
130
130

• Courtesy of Paul Emma

15
Fitted quadrupole offsets
results differ by straight line
similar plot for BPM offsets (not shown) Now
correct quad and BPM positions
130
use linear component of fitted offsets to
re-adjust launch
130

• Courtesy of Paul Emma

16
Absolute trajectory after 1st pass of BBA (14.3
GeV)
130
130

• Courtesy of Paul Emma

17
Possible Absolute Trajectory
Beam is launched straight down undulator, with
possible inconsequential kink at boundary
LTU
dispersion generated is insignificant
Now look at trajectory w.r.t. undulator axis ?

• Courtesy of Paul Emma

18
After 1st pass of BBA (now w.r.t. undulator line)
sx ? 48 mm
Now repeat procedure of energy changes two more
times
130
sy ? 24 mm
130

• Courtesy of Paul Emma

19
After 3rd pass of BBA (14.3 GeV)
sx ? 1.7 mm
Dj ? 100
130
RON (FEL-code) simulation shows Lsat increased by
lt1 gain-length R. Dejus, N.Vinokurov
sy ? 2.7 mm
130
Was confirmed with GENESIS simulation

• Courtesy of Paul Emma

20
Trajectory After BBA Convergence

• 2-mm BPM resolution
• 50-mm initial BPM quad offsets
• ?1-mm mover backlash
• 14-7-4.5 GeV
• Dj ? 204

Trajectory through undulator at 14 GeV after 3
passes of BBA procedure.

• Courtesy of Paul Emma

21
Verify BBA Convergence by noting orbit change
from 14 to 4.5 GeV
Before BBA procedure
14.1 GeV
drop energy, reset launch, note change
4.5 GeV
500 mm
BPM read-backs through undulator at 14 GeV (top)
and 4.5 GeV (bottom) after rough steering, but
before the BBA procedure. The energy is changed
and the launch is re-established. Trajectory
changes are expected at the 500-mm level.

• Courtesy of Paul Emma

22
Verifying BBA Convergence
After BBA procedure
14.1 GeV
drop energy, reset launch, note change
4.5 GeV
20 mm
BPM read-backs through undulator (note scale
change) at 14 GeV (top) and 4.5 GeV (bottom)
after three rounds of the BBA procedure, where
trajectory changes with energy are expected at
the 20-mm level.

• Courtesy of Paul Emma

23
0.1-Gauss Earths field in x- direction perfect
system, quads on, no steering

• Courtesy of Paul Emma

24
0.1-Gauss Earths field in x-direction perfect
system, after BBA

• Courtesy of Paul Emma

25
0.1-Gauss Earths field in x-direction standard
errors, after BBA
no Earths field standard errors, after BBA

• Courtesy of Paul Emma

26
0.2-Gauss Earths field in x-direction standard
errors, after BBA

• Courtesy of Paul Emma

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Summary

• BPMs resolve trajectory to 1 mm rms
• BPM readings drift lt1 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 lt20 of beam size
  (already demonstrated in FFTB)
• Earth magnetic field needs to be compensated

Alignment can be achieved at adequate level using
beam-based technique, given that
4
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End of Presentation