FEL Pierce Parameter & Gain Length Calculator
Coherent X-ray Free Electron Lasers: Calculate the fundamental Pierce parameter ($\rho$), 1D exponential power gain length ($L_g$), saturation power ($P_{sat}$), and SASE microbunching thresholds.
Electron Beam & Undulator Parameters
LCLS: 14 GeV; European XFEL: 17.5 GeV
Beam Size & Energy Spread
Must be < ρ for SASE gain
FEL Lasing & Saturation Performance
FEL Pierce Parameter ρ:
--
efficiency & coupling index
Power Gain Length L_g:
--
meters (e-folding length)
Saturation Power:
--
GW (P_sat ≈ ρ P_beam)
Sat Length L_sat:
--
meters (~20 L_g)
Resonant Wavelength:
--
Ångströms (X-ray)
Lasing Stability Criterion
Energy Spread Margin ($sigma_E / E <
ho$):
--
Peak Electron Beam Power:
--
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