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
Genesis is used for the FEL calculations. Ideally, Genesis would be used to perform full timedependent
calculations for each simulated pulse. However, this would require ~10 7
macroparticles per pulse, and is not practical. Instead, the output of Elegant is cut into 136
longitudinal slices; chosen because it is near the number of slippage lengths in the bunch. Each
slice is analyzed to obtain relevant first and second moments, i.e., energy, energy spread,
centroids of particle position and angle, rms emittances, Twiss parameters, and beam current.
Each slice is simulated independently in Genesis, under the implicit assumption that slices do not
influence each other. The low- and high-energy tails of the beam are also removed, to avoid
artificially inflating the rms energy spread.
Jitter is included in the Parmela and Elegant simulations using gaussian random numbers
with a ±3σ cut-off. The variation in gun charge output, Q, is modeled as
Q = Q0[1+(0.03)⋅∆ϕl]⋅[1+∆El/El]⋅[1+∆Vg/Vg], where ∆ϕl is the laser phase error, ∆El/El is the
relative laser energy error, and ∆Vg/Vg is the relative gun voltage error. The coefficient of (0.03)
is an empirical value obtained from experiments with a BNL-style gun at the Low Energy
Undulator Test Line (LEUTL) at APS/ANL [40].
Table 7.21 Results of start-to-end jitter simulations using Parmela, Elegant, and Genesis.
Parameter symbol units mean rms ½ quartile
range
FEL 3D power gain length L g m 3.53 0.19 0.13
FEL output power P 0 GW 6.8 1.6 1.0
Relative e − energy error (E 0 ≈ 14.346 GeV) ∆E/E 0 % 0 0.06 0.04
Peak current I pk kA 3.3 0.27 0.17
Bunch length (full-width of 80% core slices) ∆tFW fs 188 19 13
RMS e − energy spread σδ
10 −4
0.8 0.07 0.03
Horizontal normalized emittance γε x µm 0.80 0.02 0.01
Vertical normalized emittance γε y µm 0.70 0.01 0.01
Bunch arrival time 〈∆t〉 fs 0 45 31
Horizontal centroid amplitude (% of beam size) A x % 84 8.0 4.3
Vertical centroid amplitude (% of beam size) A y % 8.0 0.6 0.4
Table 7.21 lists the results of simulations with 227 different beam pulses (i.e., random seeds).
The quantities for which statistics are shown are averaged or summed over the central 80% of the
slices (the “core slices”), which excludes from analysis the ends of the bunch, which are heavily
corrupted by CSR and can be neglected for FEL evaluation. The bunch length is the full length of
the core slices. The horizontal centroid amplitude, Ax, for a slice is defined as
Ax 2 = [x 2 + (αxx + βxx′) 2 ]/(εxβx), where x and x′ are the position and angle of the centroid of the
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