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
1 2
Γ(1/4) c ⎛ Z 0 ⎞
≈ ⎜ ⎟ , σ /s
1 2
2 2π
2 a3σ
⎝ σ ⎠
Wx z
z
0
> 1
(8.48)
with Γ(1/4) ≈ 3.63. Combined with Eq. (8.43) it is seen that υ is 0.58 and 0.10 for the SS and Cu
cases, respectively. For an extreme 100-µm oscillation (e.g. random pulse-to-pulse jitter which is
not correctable) the emittance growth is 260% for SS and 8% in the case of Cu.
As to the effects of static errors, it is noted first that the beam tube is composed of 33 equal
pieces. With uncorrelated, random misalignments with an rms of 100 µm, the emittance growth
will be a factor of 33 less than given above. Or, conversely, the misalignment tolerance for 10%
emittance growth, assuming copper is used, is 800 µm. For a correlated, cosine variation of
misalignments of amplitude 100 µm the emittance growth is approximated by the above jitter
results multiplied by sinc 2 (∆kL), where ∆k is the deviation from the betatron wave number of the
wall oscillation wave number. Finally, if the static emittance growth has to be kept to less than
10% anywhere within the undulator, the axis of the beam tube must be aligned to the axis of the
quads to within 200 µm in the case of copper.
8.9.4 The Effect of Flange Gaps, Pumping Slots, and Bellows
The flange gaps are small cavities with a gap of g = 0.25 mm; over every 3.42-m section
there are 4, or a total of M = 132 objects in the entire undulator. For the flange gaps, since σz/a