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
the FEL slippage length (~0.5 µm). The energy loss and rms energy spread induced by CSR are
5.5 MeV and 0.047%, respectively.
Figure 7.39 shows the temporal distribution of the bunch and the CSR-wakefield, from Eq.
(7.19), within the first bend of DL2, using the temporal distribution taken from tracking upstream
of DL2. The variable color traces represent the two functions sampled in each of ten points along
the bend magnet. The temporal distribution is nearly constant over the DL2 bend system due to
the small energy spread and isochronicity of the beamline. Figure 7.40 shows the horizontal
beam position, x, without CSR (left) and with CSR in all LCLS bends (right), versus axial bunch
coordinate, z, for the LCLS bunch profile (i.e., tracked through upstream systems).
Figure 7.39 Constant temporal distribution of bunch (solid: “LinearDensity”) and CSR-wakefield
(dots: “DeltaGamma”) within first bend of DL2. The variable color traces represent the
two functions sampled in each of ten points along the bend magnet.
Since the BC2 chicane also contribute a horizontal emittance growth through correlations of x
and x′ with z, these might be partially cancelled by ‘bucking’ the BC2 correlations against those
of the DL2 bends. The last bend of BC2 bends to the ‘left’, while the first bend-pair in DL2 bends
to the ‘right’, so a net horizontal betatron phase advance between these two of ∆ψx = 2nπ
provides the possibility of cancellation. The net phase is set by slight adjustments in the L3-linac
phase advance per cell. The BC2/DL2 cancellation is, of course, not completely effective, but at
least this arrangement is superior to an odd-π phase advance, which would possibly amplify the
emittance growth.
7-64 ♦ A C C E L E R A T O R