Theoretical study of a waveguide THz free electron laser and comparisons with simulations

In a so-called waveguide free electron laser (FEL) for THz radiations, an extremely small aperture ($\sim \mathrm{mm}$) waveguide is used to confine angularly wide spread radiation fields from a low energy electron beam into a small area. This confinement increases the interaction between the electron beam and the radiation fields to achieve a much higher FEL gain. The radiation fields propagate inside the waveguide as waveguide modes, not like a light flux in a free space FEL. This characteristic behavior of the radiation fields makes intuitive understanding of the waveguide FEL difficult. We developed a three-dimensional waveguide FEL theory to calculate a gain of THz waveguide FEL including the effects of the energy spread, the beam size and the betatron oscillations of an electron beam, and effects of a rectangular waveguide. The FEL gain can be calculated as a function of frequency by solving the dispersion relation. Theoretical gains are compared with simulation results for a waveguide FEL with a planar undulator similar to the KAERI one. Good agreements are obtained.

Figure 1

The simulation (left) and the theoretical (right) results of the beam growth rate for $R_0=0.5\mathrm{mm}$, ${\gamma }_1=9.98043$ and ${\gamma }_2=10.0196$.

Figure 2

The dependence of the growth rate (red) and the resonant frequency (blue) on the waveguide size $b$ with $R_0=1\mu \mathrm{m}$, ${\gamma }_r=10$ and $\mathrm{\Delta }E/E\simeq 0.4\%$. The red and the blue curves are read by using the scale markings on the left and the right vertical axes, respectively.

Figure 3

The dependence of the growth rate on the beam size $R_0$ with ${\gamma }_r=10$ and $\mathrm{\Delta }E/E\simeq 0.4\%$.

Figure 4

The simulation (left) and the theoretical (right) results of the beam growth rate for $R_0=0.5\mathrm{mm}$, ${\gamma }_1=13.7011$ and ${\gamma }_2=13.7392$.

Figure 5

The energy spread $\mathrm{\Delta }E/E$ dependence of the maximum beam growth rate with ${\gamma }_r=10$. The simulation results (red) start to deviate from the theoretical ones (blue) in a small energy spread region.