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
optimal stability is best found with a complete computer simulation that includes the important
non-linearities and wakefield effects.
7.2.2 Design Optimization Technique
In order to determine the best parameter set which provides the correct acceleration,
compression, machine stability, and final energy spread, a fast computer program is used which
semi-analytically models the longitudinal beam dynamics and minimizes a penalty function while
varying the key system parameters [5]. The varied parameters are:
• 1 st and 2 nd compressor strengths (R56-1, R56-2),
• RF phases of L1, L2, and L3 (φ1, φ2, φ3),
• Energy (or location) of 1 st and 2 nd compression stages (EBC1, EBC2).
The penalty function, which is minimized, includes:
• The deviation of the final and intermediate bunch lengths from the desired ones,
normalized to an allowable error (e.g., 22 µm ± 0.1 µm rms at undulator, and 200 µm
± 100 µm after BC1),
• The energy deviation at both compressors and at the undulator, with respect to the
desired energy, each normalized to an allowable error (e.g., 14.35 GeV ± 0.02 GeV at
undulator, or 250, +250, −50 MeV at 1 st compressor),
• The deviation of the final correlated energy spread at the undulator with respect to
the desired energy spread, normalized to an allowable error (e.g., 0.01% ± 0.002% —
this is a signed quantity allowing for a positive or negatively correlated energy chirp
as a desired outcome),
• The four sensitivities of: 1) final relative energy error vs. gun-timing error, and 2) vs.
bunch-charge error; 3) the final peak current vs. gun-timing error, and 4) vs. bunch-
charge error, all normalized to an allowable error (e.g., 0 ± 100 Amps/psec).
The parameters are varied over a reasonable range by constraining the minimization scan. The
parameters constrained are:
• The two R56 values (e.g., −10 mm to −40 mm),
• The mean rf accelerating gradient per linac section (e.g., 18 MV/m upper limit),
• The three rf phases per linac section (e.g., −50˚ to +50˚),
• The net active S-band linac length available to the LCLS beam (~900 m).
The semi-analytic model includes longitudinal wakefields, non-linearities (T566 and sinusoidal
rf), and the effects of errors (timing, phase, charge and energy). The model also includes the X-
band rf section, its wakefield, and its four-fold frequency increase. The details of the model and
its range of validity are reviewed in reference [5]. The final chosen parameters, which provide for
optimum machine stability, as well as the undulator peak current and energy spread requirements
A C C E L E R A T O R ♦ 7-7