The coherent effect of undulator radiation has been investigated using a low-energy, low-gain, waveguide-mode Free-Electron Laser (FEL). Using a relativistic photoelectron beam produced by a Q-switched Nd-YAG laser beam, the coherent undulator radiation was observed and its measured power was $10^3$ times stronger than that of theoretically predicted incoherent radiation. For further increase of the radiation power, an ultra-short and high current photoelectron beam was generated by 0.5 ps UV excimer laser pulse and the emitted radiation power reached $10^6$ times that of incoherent radiation. These results show that the high power coherent undulator radiation can be generated when the duration of RPE is comparable to or shorter than the wavelength of the undulator radiation.
Analytic consideration of the undulator radiation power shows the possibility of the coherent radiation, which scales as square of the electron number in a bunch. The generation of the coherent undulator radiation was achieved using a RPE produced by the fourth harmonics of a Q-switched NdYAG laser. The Q-switched laser pulse contains a burst of 30 ps micropulses superposed with a weak 8 ns pulse. The current and shape of the RPE was controlled by changing the incident laser intensity. The temporal structure of the RPE was measured using the Cherenkov radiation emitted by relativistic electrons impinged on an optical fiber. When the irradiated laser intensity is stronger than 5 MW/㎠, the wave from of the RPE does not show any microstructure, which is due to the saturation of the RPE current density by the space-charge effect. The measured radiation power from the RPE having no microstructure was near the noise level of a microwave diode, even though the current was much larger than that of the RPE having micropulses. With irradiated intensity less than 1 MW/$cm^2$, the temporal structure of the RPE closely follows that of the laser pulse. The measured power of the undulator radiation generated by micropulses was more than $10^3$ times stronger than that of the theoretically predicted incoherent radiation and tends towards quadratic dependence on the electron beam current. The enhancement and tendency is due to coherent radiation emitted by electron beam micropulses whose typical bunch lengths are comparable to the radiation wavelength.
When the bunch length of the electron beam is shorter than the distance between cathode and anode, high current density of the electron beam can be generated due to the decrease of the space-charge force. The measured value of the maximum RPE current density (~20A/㎠) having bunch length of 100 ps was 3 times higher than that of the long elecron beam (~6A/㎠). When an ultra-short(0.5 ps), UV(248nm) excimer laser pulse was used for the generation of ultra-short, high current electron beam, maximum current density of the electron beam was increased to more than 1 kA/㎠. Measured power of the coherent radiation emitted by ultra-short electron beam was $10^4-10^6$ times higher than that of the incoherent radiation. The expected pulse broadening of the electron beam can be analyzed from the dependence of the coherent radiation power on the number of electrons in a bunch.
With further development of an electron gun and electron beam accelerator to generate and accelerate subpicosecond, high current electron beam, the high intensity, coherent undulator radiation will provide means for new strong and tunable light source in the far infrared and millimeter wavelength region.