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
the 3% of the structures that follow the 4 m gaps. Therefore, using the asymptotic wakefields to
represent the entire SLAC linac, and ignoring the transient effects, should result in very little
error even for a 20-µm bunch.
There are three other effects that can be important for short bunches: (1) The so-called
“catch-up distance” effect: If the head of the beam generates a wakefield at a certain position in
the linac, due to causality the tail does not feel the effect until a distance ~0.5a 2 /σz, which in
this case is 2.5 m, later. Since this is a small fraction of the 550-meters of accelerating structure
after the second compressor, this effect should not be important. (2) For σ z ≤ a/γ, which in this
case is 0.3 µm, the impedance drops dramatically. Since the minimum bunch length is 20 µm, this
effect should also not be important for the LCLS. (3) The effect of the resistivity of the iris
surface is shown, in the following section, not to be a significant effect for the LCLS accelerator.
Finally, it should be noted that the above estimates all assume that the bunch is gaussian,
which it is not. The real bunch shape is rectangular with spikes at the edges of the distribution
(see bottom of Figure 7.7). The Fourier transform of such a bunch shape reaches to higher
frequencies than the gaussian approximation, and therefore the short bunch effects will become
somewhat more pronounced than estimated above. However, even with this consideration, the
calculated wake functions will accurately represent the wakefield effects in the linac for the
LCLS project.
7.9.4 Confirmations
There have been confirmations, both theoretical and by measurement, of the calculated SLAC
wake functions and, more recently, of the similarly calculated wake functions for the NLC and
the DESY-SBLC linac. All of the measurements, however, have been done for bunch lengths
significantly larger than the 20-µm of interest here. As to theoretical comparisons, the calculated
SLAC wake functions have been confirmed, for gaussian bunches down to σz ≈ 0.5 mm, using the
time domain program TBCI [61]. A time domain program exists that is able to obtain accurate
results for short bunches in accelerating structures [62]. For a 100-µm bunch in the NLC
structure, the results of this program, as well as the results of an independent frequency domain
program [63], agree with our frequency domain results to within a few percent.
As to confirmation by measurement in the SLC linac, the total wakefield-induced energy loss
[64] and more recently the wakefield-induced voltage of a bunch [65], [66] have been shown to
agree quite well, for bunch lengths down to 0.5 mm. Also, in the ASSET test facility, the short
range transverse wakefield of a 0.5-mm bunch in the NLC structure has been measured, and the
results agree quite well with the calculated results [67].
7.9.5 Resistive Wall Wakefields
In addition to geometric wakefields, the micro-bunch beyond BC2 experiences a longitudinal
resistive wall (RW) wakefield which introduces a small coherent energy spread along the bunch
[68], [70]. For a bunch which is much longer then the characteristic length, s 0,
A C C E L E R A T O R ♦ 7-107