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
½-voltage (¼-power) and crest-phase can be used to control the beam energy in DL2. A dynamic
range of ±1.7% is then possible. Larger, manual changes can be implemented by switching on or
off spare klystrons. The rf phase then only needs to be held constant to a level of a few degrees.
This might be done by occasional phase scanning using the BPMs in DL2 to check the beam
phase.
In all cases above, the energy resolution is more than adequate to drive feedback systems for
stabilization of the compression systems (see Table 7.5). The remaining critical items, which
need further study, are the resolution and time characteristics of the CSR- or cavity-based bunch
length monitors.
7.9 The Wake Functions for the SLAC Linac
7.9.1 Introduction
Obtaining wake functions for the SLAC linac structure that are sufficiently accurate to be
used in beam dynamics studies for bunches as short as 20 µm (rms) is not an easy task. It requires
an accurate knowledge of the impedance of the structure over a large frequency range, which is
difficult to obtain both by means of frequency-domain and time-domain calculations. Direct time-
domain integration, using a computer program such as the MAFIA module T2 [55], needs a very
large mesh and hence prohibitive amounts of computer time. Even then, errors will tend to
accumulate in the results. The approach actually employed, uses a frequency-domain calculation
applied to a simplified model of the linac structure, an approach that also has its difficulties. The
wake functions obtained are the wakefields excited by a point charge, as a function of distance
behind that charge. By performing a convolution over the bunch, the wakefields left by a bunch
of arbitrary shape can be obtained.
A SLAC structure is 3 m long; it consists of 84 cells. It is a constant gradient structure, and
both the cavity radius and the iris radius gradually become smaller (the change in iris radius is
0.5%/cell) along the length of each structure. In our calculations each SLAC constant gradient
structure is broken into five pieces. Each piece is represented by a periodic model with an average
iris radius, and the rounded iris profiles are replaced by rectangular ones. The wakefields for the
five models are obtained and then averaged to obtain wake functions to represent an entire
structure. Questions as to the accuracy and applicability of the calculated wake functions concern
primarily:
• The accuracy of the periodic calculations themselves,
• Transient effects and effects at the ends of a structure,
• The fact that the irises vary in the real structure,
• The effects of resistivity/roughness of the iris surface.
A C C E L E R A T O R ♦ 7-103