LCLS Conceptual Design Report - Stanford Synchrotron Radiation ...

σ γ /γ 0 (percent)
∆N/N
0.02
0.01
3-2001
8560A84
0
–0.4
–0.8
–2 –1 0
z (mm)
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
1 2
σ γ /γ 0 (percent)
Ipk (A)
–0.8
0 0.1
∆N/N
0.2
0
–2 –1 0 1 2
0
–10 –5 0 5 10
∆z (mm) ∆t (ps)
Figure 6.26 Longitudinal distribution of particles in the beam at the exit of L0 for 100 K particles. In
this figure, the bunch head is at the left, as in the convention of Chapter 7,
Accelerator.
The Matching Section between L0 and L1 was designed using the simulation code MAD. A
plot of the TWISS parameters as a function of axial distance along the beamline is shown in
Figure 7.33. It is seen from the figure that the beta function gets very small, which could
potentially result in undesirable emittance growth due to the high space charge density at this
relatively low energy. To check for this possibility, the PARMELA simulation was extended
through the MS. Since the beam size aspect ratio reaches 12, cylindrical symmetry cannot be
assumed. The 100 K particle distribution shown in Figs. 6.24 to 26 was launched into the MS
using Version 3 of PARMELA. The resulting particle distribution at the end of the MS (i.e., at the
beginning of L1) is shown in Figs. 6.28 and 29 for. Note that although some small asymmetry
0
–0.4
between the x- and y-emittances creeps in, there is no significant emittance growth.
The emittance values derived from the full distribution of particles are strongly influenced by
the few particles outside the core. In Figure 6.30, the slice emittance along the bunch is displayed
for various cuts in the transverse tails. A 5% cut in the tails reduces the emittance for the central
slices by about 15%. The effect is even more dramatic when the brightness of each slice is
plotted, as in Figure 6.31.
150
100
50
6-55 ♦ I NJECTOR