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
7.2.5 Longitudinal Tracking Summary
In this section the longitudinal geometric wakefield and other beam dynamics effects are
applied in a 6D tracking simulation to graphically summarize the compression process through
the accelerator. (A full 6D tracking summary is presented in Section 7.6.) A more detailed
description of the wakefields for the SLAC S-band accelerating structures, as well as a
justification for the use of the asymptotic wake, is given in Section 7.9. The tracking code used
here is Elegant [10], which includes non-linearities such as T566, U5666 (the second and higher-
order compression terms), longitudinal geometric wakefields of the rf-structures, resistive-wall
longitudinal wakefields (where significant), the sinusoidal rf accelerating voltage, and the
incoherent and coherent synchrotron radiation in the bends (CSR is a 1D line-charge model). The
tracking proceeds from the output of the LCLS injector, at 150 MeV, to the undulator entrance at
14.3 GeV. The 6D input particle coordinates are from Parmela [11] after tracking through the
LCLS injector to the end of L0 at 150 MeV [12]. The tracking uses 2⋅10 5 macro-particles.
A more complete summary of the tracking is presented in Section 7.6. The Elegant
simulations ignore space charge effects, since the compression process takes place at energies
well above 150 MeV. The input particle coordinates from Parmela do, however, include the
effects of space charge forces at energies below 150 MeV.
Figure 7.6 and Figure 7.7 show longitudinal phase space, energy distributions, and axial (z)
distributions at various points in the compression process. The input gun-laser pulse has a
uniform temporal distribution with a 1-psec rise/fall-time and the RF gradient in the gun is
120 MV/m. After acceleration to 150 MeV, the temporal distribution becomes slightly rounded,
as shown in the figures, with a 0.83-mm rms bunch length (2.8-ps rms, or 10.2-ps FWHM) and
0.11-% rms projected relative energy spread at 150 MeV, with a bunch population of 6.25×10 9
ppb (1 nC). The rms incoherent energy spread is very small at just 3 keV (2×10 −5 of 150 MeV).
As Figure 7.6 and Figure 7.7 show, the compression process has been arranged so that many
of the non-linearities, such as rf-curvature and wakefield effects, will be compensated, leaving a
narrow energy profile at 14.3 GeV. The final rms bunch length is 22 µm with >3.0 kA of peak
beam current all along the bunch. Tails exist in the energy distribution (shown on 3 rd row of
Figure 7.7). The core of the beam, however, has an rms energy spread of ~0.01% with ~80% of
the particles contained within a ±0.1% energy window. The energy tails (|∆E/E0| > 0.1%), which
comprise 20% of the beam, have been cut out of the bottom row of Figure 7.7 (14.3 GeV) to
show the core beam more clearly, while all particles are shown in the 3 rd row of Figure 7.7. Note,
the incoherent component of the final energy spread at any particular slice of the bunch core
(0.75 µm slice > FEL slippage length) is 0.008% rms, including the incoherent synchrotron
radiation of the high-energy bends. The slight micro-bunching seen in the final temporal profile is
a result of the CSR effects in the two compressor chicanes, and may be somewhat exaggerated
here by possible overestimates of a 1D line-charge CSR model and also by the statistical noise
levels of just 2×10 5 macro-particles. A superconducting one-period wiggler is added just before
the BC2 chicane in order to add incoherent energy spread and damp this CSR-induced micro-
bunching. This subject is covered in more detail in Section 7.4.2.
A C C E L E R A T O R ♦ 7-13