LCLS Conceptual Design Report - Stanford Synchrotron Radiation ...

8.12 Beam-based Alignment
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
8.12.1 Undulator Beam-Based Alignment
The electron trajectory within the LCLS undulator needs to be straight to a high degree of
accuracy so that the 1.5-Å radiation grows efficiently over each gain length. For the LCLS, this
condition requires a trajectory straightness of a few microns over a ~10-meter length. This level is
very difficult to achieve with component survey alignment techniques. For this reason, the final
alignment will rely on empirical beam-based alignment, which makes use of beam position
monitor (BPM) readings as a function of large, deliberate variations of the electron energy. The
BPM measurements at various energies are analyzed and then converted to 1) quadrupole magnet
transverse position offsets, 2) BPM readback offset corrections and 3) adjustments of the
incoming beam position and angle at the undulator entrance (initial launch conditions). The
alignment procedure is repeated three times in succession for the initial machine startup, and then
one pass of the procedure is reapplied approximately once per month, as necessary. Between
these infrequent applications, a fine steering technique will be used for daily trajectory control,
and a fast feedback system will maintain the trajectory over the time scale of a few pulses. This
section primarily discusses the most involved alignment procedure, which is applied during the
initial machine commissioning period. The effects of various errors are included in a full
simulation of the alignment procedure.
8.12.1.1 Introduction
The readback mi of the i th BPM, which measures the centroid of the transverse position of the
electron bunch at location si along the beamline, can be written as
i
mi = θjC ij
j =1
∑ – b i
, (8.64)
where θj is the kick angle at point j (< i) due to a transversely misaligned quadrupole magnet or
undulator pole field error upstream of BPM-i, Cij is the transfer coefficient which maps a beam
angle at point j to a position at point i, and bi is the readback offset (mechanical misalignment
and/or electrical bias) of the i th BPM. This is described graphically in Figure 8.40 where the
BPMs are shown as circles. The kick angles in the figure are represented as dipoles, however they
are completely equivalent to either quadrupole magnets with transverse displacements and/or
field strength errors of the undulator poles. The quadrupole focusing within the undulator is not
explicitly shown in the figure, but it is represented mathematically in the transfer coefficients, Cij.
The initial launch conditions are ignored for now (more on this below).
Since the kick angles θj are inversely proportional to beam momentum p, whereas the BPM
offsets bi are independent of momentum, variations of the beam energy (momentum) can be used
to measure both parameters simultaneously. This is clear by substituting a dipole field error, ∆Bj,
(equivalent to a quadrupole misalignment) for θj and explicitly showing the momentum
dependence of Eq. (8.64).
U N D U L A T O R ♦ 8-73