Table 1 Parameters of laser-driven FEL simulations comparing flying-focus and conventional laser undulators

From: X-ray free-electron lasing in a flying-focus undulator

LDFEL parameters

 Target resonant wavelength (nm)

λX0 = 2.16

 Laser wavelength (μm)

λL = 10

 Field amplitude/undulator strength

a0 = 0.35

 FEL parameter

ρ = 3.09 × 10−4

 1D cold beam gain length (mm)

Lg0 = 0.74

 Ideal saturation length (mm)

Lsat = 10.3

Electron beam parameters

 Energy (mc2)

γ0 = 35

 Current (kA)

Ib = 1

 Minimum RMS radius (μm)

σ0 = 15

 Normalized emittance (μm-rad)

ϵN 0.37

 Energy spread

Δγ/γ0 3.09 × 10−4

Conventional focus

 Transverse profile

Gaussian

 Pulse duration (ps)

T = 83

 Rayleigh range (cm)

ZR = 0.11, 1.25, 2.50

 Spot size (μm)

wC = 60, 200, 283

 Pulse energy (J)

UC = 8, 88, 176

Flying focus

 Transverse profile

Flattened Gaussian beam63

 Focal range (cm)

Lf = 1.25

 Pulse duration (ps)

T = 83

 Gaussian spot size at focus (μm)

wFF = 37.5

 Gaussian spot at lens (cm)

wl = 8.5

 Pulse energy (J)

UFF = 8

  1. The parameters of the flying-focus pulse were motivated by planned upgrades to the CO2 laser at the Brookhaven National Laboratory Accelerator Test Facility66,67. In each simulation, the electron beam enters the undulator at z = 0 with its smallest RMS radius σ0 and then expands due to the nonzero emittance and space-charge repulsion.