## 4 Discussion and Conclusions  
In this paper, a compact accelerator-based light source is proposed to generate THz coherent radiation at mJ level with tunable frequency from 0.1 THz to 60 THz. By using a frequency beating laser modulated electron beam, coherent THz radiation is produced through undulators. Start-to-end simulations are performed, the results show that the proposed technique can produce 11.5 THz and 23 THz coherent radiations with pulse energies of 6.3 mJ and 5 mJ by amplifying the fundamental and second harmonic of the  
Figure 11: **(a)** The longitudinal phase space after the dispersion section; **(b)** the current profile after the dispersion section; **(c)** the peak power and bunching factor evolutions along the undulator; **(d)** the final spectrum. frequency beating signal. Simulations of THz radiation at the 30 THz and 60 THz are also performed, the results indicate that the pulse energy of THz radiation at 30 THz and 60 THz is 2.15 mJ and 1.6 mJ, respectively. In the proposed technique, the radiation frequency can be continually tuned by tuning the parameters of the seed laser, the electron beam energy, and the undulator gap. It should be noted that the bunched electron beam can also be used to generate THz radiation with other methods, such as coherent synchrotron radiation (CSR) and coherent optical transition radiation (COTR). In the proposed scheme, the laser power is tuned to satisfy the modulation requirement at certain frequency. A lower THz frequency requires less time delay as well as less laser power. While a larger time delay and a higher peak power are required for a higher THz frequency. To obtain a beating frequency from 0.1 THz to 30 THz, the maximum peak power of laser pulse is about 2 GW, which can be easily achieved by a commercial laser. thus, the pulse energy depends on the pulse length of final THz radiation, which is related to the radiation wavelength. According to the simulation results, the pulse energy of THz radiation at 60 THz is also at the mJ level. According to Equation (4), the generation of high frequency THz radiation requires large linear chirp rate and large time delay. Due to the effects of high-order chirps, the linear chirp may not be well maintained for a large time delay, results in a degradation of the output temporal coherence. To compensate these high order chirps, dispersion elements, such as chirp mirrors, should be adopted in the optical system. In addition, the large time delay can be avoided by increasing the linear chirp rate by using an initially shorter laser pulse. For example, if an initial laser pulse with a pulse length of 11 fs was utilized [55], the required time delay can be reduced to 850 fs for the generation of 30 THz beating frequency. The time delay is just 2.8 times of the stretched pulse length (RMS), and the linear chirp can be well maintained in this region. The proposed technique is feasible to generate coherent THz radiation with tunable frequency and pulse energy to satisfy various requirements of different scientific frontiers, especially for these require THz pulses with ultra-high pulse energy, such as THz pump-probe, THz triggered chemistry, and single-shot THz bioimaging. In addition, one can consider elliptically polarized undulator (EPU) to generate polarized THz radiation to satisfy various FEL user's requirements. Therefore, the proposed technique may open a new chapter to THz related scientific researches in biology, chemistry, material science, and so on. Conceptualization, C.F. and K.Z. ; methodology, K.Z. and C.F. ; software, K.Z., T.L. and Z.W. ; validation, K.Z., Y.K., T.L. and C.F. ; formal analysis, K.Z., Y.K. and Z.W. ; investigation, K.Z. ; data curation, K.Z. ; writing--original draft preparation, K.Z. ; writing--review and editing, K.Z., C.F. and Y.K. ; visualization, K.Z. ; supervision, C.F., W.F. and Z.Z. ; project administration, C.F., W.F. and Z.Z. ; funding acquisition, Z.W., C.F. and K.Z. All authors have read and agreed to the published version of the manuscript.