High gain harmonic generation free electron lasers enhanced by pseudoenergy bands

We propose a new scheme for high gain harmonic generation free electron lasers (HGHG FELs), which is seeded by a pair of intersecting laser beams to interact with an electron beam in a modulator undulator located in a dispersive section. The interference of the laser beams gives rise to a two-dimensional modulation in the energy-time phase space because of a strong correlation between the electron energy and the position in the direction of dispersion. This eventually forms pseudoenergy bands in the electron beam, which result in efficient harmonic generation in HGHG FELs in a similar manner to the well-known scheme using the echo effects. The advantage of the proposed scheme is that the beam quality is less deteriorated than in other existing schemes.

Figure 1

Layout of the proposed scheme; the numbers from (1) to (5) show the longitudinal positions where the electron distributions are shown later in Fig. 2 or in Fig. 5.

Figure 2

Electron distributions in the phase space at four different positions indicated in Fig. 1. The solid and dashed lines in (3) and (4) correspond to $s=+{\lambda }_s/4$ and $s=-{\lambda }_s/4$, respectively.

Figure 3

Plots of the energy distribution function $\widehat{F}$ computed with ${\widehat{\eta }}_{M0}=0.1$ and ${\widehat{\sigma }}_x=0.02$: (a) $\widehat{F}(\widehat{\eta })$ plotted as a function of $\widehat{\eta }$ for different values of ${\widehat{\eta }}_M$, and (b) $\widehat{A}=\widehat{F}(0)-\widehat{F}({\widehat{\eta }}_{M0})$ plotted as a function of ${\widehat{\eta }}_M/{\widehat{\eta }}_{M0}$. The arrow indicated in the inset of (a) shows $\widehat{A}$ when ${\widehat{\eta }}_M/{\widehat{\eta }}_{M0}=1$.

Figure 4

Same as Fig. 3, but with (a) ${\widehat{\eta }}_{M0}=0.1$ and (b) ${\widehat{\eta }}_{M0}=2$. In both cases, ${\widehat{\eta }}_M={\widehat{\eta }}_{M0}$.

Figure 5

Simulation results in terms of the macroparticle distributions: (a) after the first modulator as indicated by (3) in Fig. 1, (b) before the second modulator (4), and (c) before the radiator (5).

Figure 6

Growth of the peak power at the radiator.