# Three-Dimensional, Time-Dependent Analysis of High- and Low-\(Q\) Free-Electron Laser Oscillators
## 6 Summary and Conclusions  
The development of both low-gain/high-\(Q\) and high-gain/low-\(Q\) oscillators is an active and ongoing area of research into FEL sources over virtually the entire electromagnetic spectrum [30; 86; 91; 92; 241; 242; 243; 244; 245; 246; 247; 248]. Both types of FEL oscillators have their own merits. For example, high-gain/low-\(Q\) are typically better suited for higher peak power operation, due to a reduced mirror loading [203] and higher extraction efficiency, as found in Section 5. On the other hand, properties like gain bandwidth, and stability of the output, are closer to SASE FELs than low-gain/high-\(Q\) FEL oscillators. However, we have not yet explored the full range of feedback, and increasing the feedback may shift the performance in this respect closer to that of low-gain/high-\(Q\) oscillators.  
As we have described in this paper, great progress has been made in our ability to simulate both the interaction through the undulator and in multi-pass configurations through the undulator and the resonator. This was demonstrated in Section 4 by the excellent agreement found between the simulations and the IR Demo and 10-kW Upgrade experiments at JLab, after which the simulations of both an infrared and an X-ray RAFEL were described in Section 5.  
The combination of a three-dimensional, time-dependent FEL simulation code with an optics propagation code provides enormous flexibility in being able to study a wide range of undulator and optical resonator configurations. In particular, the use of a general FEL code such as MINERVA allows the simulation of variable polarization (Section 2.1) governed by the choice of undulator geometries (Section 2.2) and ultra-short electron bunches [249] down to the neighborhood of the cooperation length in the undulators, which defines the limit of applicability of the slowly varying amplitude and phase approximation. The use of OPC permits the simulation of arbitrary optical resonators, including thermal heating and distortion as well as Bragg reflections.  
In summary, the numerical algorithms that have been implemented for the simulation of FEL oscillators are now sufficiently mature to serve as reliable design tools for virtually any conceivable undulator and oscillator configuration.  
Both authors contributed equally to conceptualization, methodology, software, validation, analysis, writing--original draft preparation, writing--review and editing, and visualization. All authors have read and agreed to the published version of the manuscript.  
The work described was supported over the course of time by multiple contracts with the U.S. Office of Naval Research, the Department of Defense Joint Technology Office, and the Department of Energy.  
Data Availability StatementData is available from the authors on request.  
The authors would like to thank numerous staff members at JLab for many helpful discussions about the IR Demo and 10-kW Upgrade experiments. We would also like to thank [PERSON] and [PERSON] for providing assistance with understanding the data from the LCLS and thank [PERSON] for assistance concerning the SPARC data. The work described was supported over the course of time by multiple contracts with the U.S. Office of Naval Research, the Department of Defense High Energy Laser Joint Technology Office, and the Department of Energy.  
The authors declare no conflict of interest. Furthermore, the funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} BPM & beam position monitor \\ CRL & compound refractive lens \\ CW & continuous wave \\ FEL & free-electron laser \\ \end{tabular}