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
demonstrated by studying the new machine parameters required over a wide range of bunch
charge values.
The injector’s beam emittance and bunch length is first estimated by applying scaling laws
derived for a 1.6-cell S-band rf photo-cathode gun [14]:
ε
N
[ µ m] ≈1.45⋅ 0.38⋅ Q[ nC] + 0.095⋅ Q[ nC] + 0.22⋅Q[ nC]
σ
z
0
4/3 8/3 2/3
[ mm] ≈ 0. 83 ⋅Q
[ nC]
1/3
(7.10)
Here Q is the bunch charge (nC), εN is the normalized rms emittance (µm), and σz 0 is the
initial rms electron bunch length (mm) after the gun. The last term in the emittance relation
represents a thermal emittance, which scales with the laser spot radius on the cathode. The bunch
length scaling constant has been increased here (0.63 mm in reference [14] becomes 0.83 mm), to
a less challenging level, in order to be consistent with the 1-nC nominal design described above.
The peak current required for SASE saturation at ~87 m, is given approximately by (see
Chapter 5)
3 2
I pk[A]
≈233⋅ εN + 1343⋅ εN + 834 ⋅ εN
+ 63 , (7.11)
where the slice energy spread is assumed to be