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
plots to follow, every 1.5 cm along the undulator, at the center of every pole of ~8000 poles. The
BPM readbacks (green circles) are, in practice, the only known (measured) quantities. This
trajectory is an example of the first beam pulse in the newly installed undulator.
The first correction (step-1, Table 8.11) is to rough-steer the incoming trajectory based on the
first six BPM readbacks in the undulator, which are used in a best fit to an incoming betatron
oscillation (see black dashed line in first 20 meters of Figure 8.43). Table 8.12 shows the initial
launch conditions for this simulation both before and after the step-1, Table 8.11, rough
correction. At this rough stage, direct use of the first few BPM readbacks, before their offsets are
corrected, is still very effective in removing large incoming launch errors.
∆X/µm
∆Y/µm
1000
0
−1000
1000
−1000
〈X 2 〉 1/2 = 507.82 µm
0 20 40 60 80 100 120
S/m
〈Y 2 〉 1/2 = 287.07 µm
0
0 20 40 60 80 100 120
S/m
Figure 8.43 Simulated first beam trajectory (blue-solid) through the newly installed undulator,
including incoming trajectory bias of ~300 µm and ~15 µrad. Also shown are BPM
readbacks (green-circle), quadrupole positions (red-cross), and the fitted initial launch
using the readbacks of the first six BPMs (dash—first 20 meters only).
The launch conditions are significantly improved in this case, reducing the trajectory
amplitude and, given systematic errors such as BPM calibration and quadrupole field gradient
errors, improving the speed of convergence of the algorithm. A complete correction is not
possible at this stage since the BPMs used in the launch fit may include large offsets, and the
misaligned quadrupoles between the BPMs may kick the trajectory off of a free betatron
oscillation. Note, the quality of this correction is dependent on the specific set of misalignments
(random seed). The random seed shown here is fairly typical. The quality of this correction
impacts only the speed of convergence.
8-80 ♦ U N D U L A T O R