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
With the X-band rf included at a decelerating phase, and with the proper voltage (see below),
the compression can be linearized such that a 200-µm rms bunch length is easily achievable with
no significant alteration in the temporal distribution. Figure 7.5 shows the simulation, starting
from similar conditions as the top row of plots in Figure 7.4, but with some minor S-band phase
and voltage adjustments (top row of Figure 7.5), and proceeding through the 20-MV X-band rf
(middle row of Figure 7.5), and then through the chicane (bottom row of Figure 7.5). The final
temporal distribution is nearly unaltered with the proper X-band rf compensation.
The X-band voltage, Vx, required to compensate the non-linear energy-time correlations
induced in both the L0 and the L1 linacs, as well as that of the chicane, is given by [8]
⎡ 2
1 λ
2
566
0 1 s T
⎤
E ⎢ −
2 3 ( 1−σ
z σ z0) ⎥ − Ei
⎢ 2π
R56
⎥
eVx
=
⎣ ⎦ , (7.8)
2
( λs λx)
− 1
where λs and λx are the S-band and X-band, respectively, rf wavelengths (10.50 cm and
2.625 cm), σz0 and σz are the initial and final bunch lengths, and Ei and E0 are the initial and final
beam energies at gun and BC1 chicane, respectively. The net deceleration is small due to the
large denominator in Eq. (7.8), which stems from the high harmonic number chosen (λs/λx = 4).
For parameters R56 ≈ −35.9 mm, T566 ≈ −3R56/2 ≈ +53.9 mm, σz0 ≈ 830 µm, σz ≈ 200 µm,
Ei ≈ 7 MeV, and E0 ≈ 250 MeV, the X-band voltage which removes the 2 nd -order energy-time
correlation along the bunch after BC1 is Vx ≈ 22 MV. Tracking studies show that this voltage
provides a more uniform temporal distribution after BC2 (see Figure 7.6 and Figure 7.7).
With the availability at SLAC of high-gradient X-band accelerating structures developed for
the NLC project [9], this 4 th harmonic compensation strategy becomes a practical solution for the
LCLS. A relatively low rf gradient of 37 MV/m allows a 0.6-meter long section to be used. The
mean iris radius is 4.7 mm, which is very large for the typical beam size of 100 µm (see beta
functions in Figure 7.14). The transverse wakefields of the X-band structure are strong, but the
section is very short. The alignment tolerance of the short X-band structure is therefore ~200 µm,
which is not particularly challenging.
A similar X-band section is not required at the entrance to BC2, since the quadratic
correlation in the bunch after the L2-linac is much less pronounced than that after L1, due to the
shortened bunch in L2 with respect to the S-band rf.
In addition to linearizing the compression process, the X-band rf also makes the net
compression less sensitive to rf gun-timing jitter. Since the net accelerating voltage, as a function
of beam arrival time, is more linear when the X-band rf is included, the induced energy-time
correlation along the bunch then becomes nearly independent of beam arrival time [8]. This
loosens the rf gun-timing jitter sensitivity by nearly a factor of four with respect to that published
in the LCLS Design Study Report [16] (see also Figure 7.8). The section will need a dedicated
X-band klystron, which is available at SLAC. The existing modulator at 21-2 will be used.
7-10 ♦ A C C E L E R A T O R