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Diagram of the two-stage SPFEL. The rectangular box represents the three-dimensional computational domain used in the VORPAL simulations. The gratings and substrate are comprised of metallic boundaries. Perfectly matched layers surround the simulation limits.
Snapshot of the axial phase spaces (where is the fractional axial momentum spread) for a double (a) and single (b) grating taken at 151 ps. The lower insets on each of the plot present zoomed-in phase space over for , for which the macroparticles have been color-coded accordingly to their height within the beam. The double-grating simulation has less distinct layers, signifying more uniform bunching across the height of the electron beam. The beam parameters are and .
Evanescent wave frequency vs beam energy for the single-grating configuration (a) and evanescent wave frequency vs grating separation for a double-grating configuration (b). The markers are results from VORPAL simulations while the dashed line is obtained from the dispersion relation derived in Ref. 2. In both graphs, the green solid line denotes the minimum allowed SP frequency for a grating period of .
Snapshots at of the axial electric field and corresponding spatial distribution of the beam in the plane for a two-stage SPFEL (the colorbar units are ). The associated axial projections at two axial locations are shown in (c) and (d).
Time evolution of the magnetic field at (a) and associated FFT (b). The beam parameters are and . The inset in (b) is a zoom-in of the first harmonic peak showing the bandwidth of 1.3 GHz (FWHM). The numbers (1), (2), and (3) indicate the harmonics of the evanescent wave associated to the double grating configuration. The green vertical arrow indicates the evanescent wave supported by the downstream grating, which is below the minimum frequency allowed by SP radiation and thus only scatters off the edges of the grating.
Grating and beam parameters used for the VORPAL simulations.
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