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
To estimate the wake, realistic parameters of roughness, i.e. h0 = 0.28 µm (corresponding to
the rms roughness of 0.2 µm), g = 2π/κ = 100 µm, and b = 2.5 mm, are used. This gives a value
of r ≡ h0 3
bκ/2
= 0.11. The corresponding loss-factor parameter is
−6
U ≈4.5⋅ 10 , (8.56)
which indicates that the effect of the wake in this regime will be negligibly small.
Figure 8.34 Synchronous mode dispersion relation.
It is important to emphasize here that the wakefield generated by the roughness is very
sensitive to the geometry of the surface profile. The models which do not take into account the
large aspect ratio of the real roughness — the ratio of the characteristic size along the surface
(correlation length) and the typical height of the bumps — tend to overestimate the impedance
and lead to very tight tolerances for the surface smoothness. The latest models that include the
large aspect ratio into consideration predict much smaller impedance which is below the tolerable
level for the LCLS undulator, if the typical height ~ 100 nm and g ~ 100 µm. The surface
measurements [25] show that roughness with such characteristics can be achieved in a pipe with a
good surface finish.
8.10 Ion Effects
In this section the number of ions generated during a bunch passage in the 121 m long
undulator line of the LCLS x-ray FEL is calculated, emittance dilution caused by these ions is
discussed, and the acceptable vacuum pressure is estimated.
8.10.1 Introduction
This section investigates ion production by the beam and by the synchrotron-radiation
photons during a bunch passage in the LCLS undulator [38], and three different mechanisms of
emittance dilution induced by these ions. The acceptable vacuum pressure for FEL operation is
estimated from the calculated emittance growth.
8-62 ♦ U N D U L A T O R