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
injector). Because of the large off-crest rf phase angle and the relatively long bunch, the rms
energy spread in L1 rapidly increases from 0.1% to 1.7%. Therefore, dispersion generated by
misaligned quadrupoles, and transverse wakefields generated by misaligned rf structures, are both
potential sources of emittance dilution. At this energy, however, space charge forces are
insignificant (see Chapter 6).
To choose the best focusing lattice for L1, several lattice designs have been simulated using
Liar [15] and Elegant [10]. These computer programs calculate the transverse emittance dilution
along a linac and include both longitudinal and transverse wakefields, random quadrupole, BPM,
and rf-structure misalignments and the dispersion these generate. They also provide various
trajectory correction algorithms.
Several different quadrupole spacing schemes were simulated (see Section 7.3.2 of reference-
[16]), with a simple 3-meter spacing settled upon. In order to insert quadrupole magnets and
BPM-steering pairs at a 3-meter spacing, 18-cm of waveguide will be cut off from the
downstream ends of the first two L1 rf sections (21-1b and 21-1c). This same cut-off technique
has been used in the past for various SLC modifications.
In order to find the best L1-linac focusing strength, the betatron phase advance per cell (there
are only 1.5 cells) was varied from 15° to 90° in 15° steps. The simulations are made with Liar
and use 300-µm rms random quadrupole, BPM, and rf-structure transverse misalignments (with
gaussian distributions cut at 3-σ). These are pessimistic conditions in order to optimize the lattice.
The same 10 seeds were then run for each lattice, and one-to-one steering was applied at each
BPM in both planes. A horizontal and vertical corrector, and a BPM which reads both x and y, are
used near each of the three L1 quadrupole magnets.
Figure 7.13 Horizontal relative emittance growth (from Liar) versus phase advance/cell for L1 lattice
over 10 seeds (solid: wakes-ON, dash: wakes-OFF). Quadrupole, BPM, and rf-structure
misalignments of 300 µm rms and one-to-one steering are applied. Vertical behavior
(not shown) is similar. Error bars show spread over ten seeds.
A C C E L E R A T O R ♦ 7-29