LCLS Conceptual Design Report - Stanford Synchrotron Radiation ...

L C L S C O N C E P T U A L D E S I G N R E P O R T
step-1-corrected launch bias, and 2) the correlated component of the BPM and quadrupole offset
errors (the random walk-off effect of the initial survey). A line is then fit to the calculated BPM
and quadrupole offsets. The slope and offset of the best line fit is used to readjust the initial
launch position and angle at the undulator entrance.
X/µm
Y/µm
1000
500
0
−500
〈X 2 〉 1/2 = 293.78 µm
−1000
0 20 40 60 80 100 120
1000
500
0
−500
〈Y 2 〉 1/2 = 208.82 µm
−1000
0 20 40 60 80 100 120
S/m
Figure 8.46 Trajectory (blue-solid) at 5 GeV. BPM readbacks (green-circle) and quadrupole positions
(red-cross) are also shown. These BPM readings are saved for analysis.
Figure 8.48 shows the new electron trajectory after the launch conditions, the quadrupole
magnet movers and the BPM offsets are corrected. The BPM offsets and the mover corrections
applied are the differences between the best line fit and the data (error bars). In addition, a final
steering using a minimum number of steering coils is applied to remove any remaining detectable
betatron oscillation (based on BPM readback). At each stage in the simulation, the real magnet
mover limitations (calibration errors) and BPM errors (calibration and resolution) are
incorporated.
The linear component, which remains in the Figure 8.48 trajectory is due to the correlated
quadrupole and BPM offsets (random walk of initial tunnel survey). Since these offsets are due
dominantly to the difference between the line defined by the linac beamline axis and the slightly
different line established by the undulator beamline, the alignment procedure inevitably launches
the electrons straight down the undulator vacuum chamber, which presumably follows these
correlated tunnel survey errors. The true trajectory shown in Figure 8.48 is then actually the most
desired trajectory, where a slight change in beam
U N D U L A T O R ♦ 8-83