Comments on the Physics of Microwave-Undulators
Round 1
Reviewer 1 Report
The authors made a detailed analysis of the waveguide undulator-based FEL (WU-FEL). The detailed formalism of the related equations seems to be useful for future research.
However, discussions given in this paper have an unfair comparison with FEL based on permanent magnets. The authors claimed WU can make the FEL system compact because of the short-period feature. This is true when only an unrealistically high microwave power can be used for driving WU. If an ideal magnet having unrealistically high magnetic field strength can be used, the FEL with permanent magnets can have a similar or even better performance than that discussed in this paper. A fair comparison should be made.
In conclusion, the authors made comments that they need a high Q cavity to obtain enough high field in the WU. In this case, the authors expect the usage of a standing wave cavity with a high Q value. However, basic analysis and simulations in this paper just focus on the simple waveguide. Analysis based on a standing-wave cavity or information to convert the equation for the standing wave should be provided. I believe that it is difficult to achieve such high power in a simple waveguide with currently available microwave sources.
The information on energy spread used for some calculations is missing. As the author commented, this is a critical parameter for FEL. If the author assumed a zero-energy spread, it should be explicitly described to avoid confusion.
There are many miscitations of the figure and table in the manuscript. A careful check must be made before the submission.
Further comments are added to the attached PDF file. Please check them.
Comments for author File: 
Comments.pdf
Author Response
The Authors would like to thanks the Reviewer for the extreme accurate revision
Reviewer Comment:
The authors made a detailed analysis of the waveguide undulator-based FEL (WU-FEL). The detailed formalism of the related equations seems to be useful for future research.
Answer:
We much appreciated the comment and as reported in the attached pdf we like to underline that in our notation Wave Undulator (WU) represents a more general definition, also associated with powerful laser in the near infrared region, on the other side microwave undulator (MU) specifies high power microwave field generated by an ad hoc source (CARM-Gyrotron); we prefer, therefore, to maintain this distinction.
Reviewer Comment:
However, discussions given in this paper have an unfair comparison with FEL based on permanent magnets. The authors claimed WU can make the FEL system compact because of the short-period feature. This is true when only an unrealistically high microwave power can be used for driving WU. If an ideal magnet having unrealistically high magnetic field strength can be used, the FEL with permanent magnets can have a similar or even better performance than that discussed in this paper. A fair comparison should be made.
Answer:
The following comments have been added in the paper:
To make the comparison more fair, we should however mention that in the region above 1.5 and 1.8 cm period length, magnetic undulator of superconducting type could be exploited, the relevant performances could be comparable (if not better) than those of MU-FELs.
Shorter magnetic undulator periods becomes more problematic even for the Super Conducting option. The MU solution for shorter period is also not easily viable, either for the large intra-waveguide power involved and for the technological problems mentioned below.
Reviewer Comment:
The information on energy spread used for some calculations is missing. As the author commented, this is a critical parameter for FEL. If the author assumed a zero-energy spread, it should be explicitly described to avoid confusion.
Answer:
The information on the energy spread has been added in Tab_1 and Tab_2 with a comment.
Reviewer Comment:
There are many miscitations of the figure and table in the manuscript. A careful check must be made before the submission.
Further comments are added to the attached PDF file. Please check them.
Answer:
We apologize for many miscitations of tables/figure, unfortunately we had a problem compiling on the MDPI website platform, please see the answers to your comments reported in the attached pdf file of the manuscript.
Author Response File: Author Response.pdf
Reviewer 2 Report
The report is written in a clear way, explaining main peculiarities of physics of microwave undulators. The report has a rich reference list, which is also extremely useful for readers. Minor modification of the text is needed (for example, Fig-numbers are missing in the text or do not correspond to Fig-numbers under the plots as well as some wrong referring to the Eq.-numbers; MU and UM mixture in the text). The link in Ref.29 does not work. The self-citations by co-authors should be reduced. Concept of a design of an electron beam line to provide required energy spread (less than 0.1%) is not presented in the report. Suggestion: do not show "layout of MU-based FEL oscillator", because it does not provide any useful information. The brightness degradation effects in the case of MU-FEL are mentioned at the top of the report as the main topic of the report, but not explained in the text (except the line-width broadening effects). No conclusions in the report, which should summarize the results.
Author Response
Please see the attachement.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors answered all my previous comments and questions. However, there is missing important information. Since the authors mentioned "circulating power" and "very low losses waveguide", they are considering usage of resonant ring for enhancing the microwave power available for MU. But there are no description and citation about the resonant ring. The currently demonstrated performance of the resonant ring including the available enhancement factor and microwave frequency should be mentioned together with the required developments for realizing the parameter of MU discussed in this manuscript. From those added information, authors can much more clearly understand the possibility and difficulty of MU.
Authors mentioned that the K-value is reasonable for FEL operation. But in my feeling, the K-values of MUs discussed in the manuscript are rather small compared to that of permanent magnet undulators used in currently operating FEL facilities. In general, FEL facilities are designed with the K-value higher than 1. Since the FEL gain is strong function of undulator K-value, small available K-value needs higher performance of electron beam to have same FEL performances. I should say that the small signal gain of 30% with N=100, Ipeak=120A, sigma_E=0.1%, emittance=5mm mrad is considerably low. One reason of the small K-value is the short period length of the MU discussed in the manuscript. The authors are recommended to describe the K-value of normal undulators in the currently operated FEL facilities and compare the K-value of MUs discussed in the manuscript.
The authors put 5 keywords but Compton scattering, Gyrotron and CARM do not appear in the main text. The authors should give more relevant keywords.
I thnk that there are discrepancies between the conclusions in the abstract and that in the main text. The abstract should be modified to have same conclusion with the main text.
Line 243: footnote #2 is confusing. It looks to show the unit of MW^2.
Figure A1: The authors are recommended to arrange the same plot regions for (a) and (b). Horizontal region -0.02 to 0.02. Vertical region -0.015 to 0.015.
Author Response
Please see the attachement.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
The authors answered all of my previous comments and questions.
The minor points which I should mention is followings.
1. References are not ordered by the order of the appearence in the main text. Is this OK?
2. The authors uploaded the pdf file with images and not with text. Why did the authors make this? This is quite inconvenient for reviewer.
3. The reference #47 appear twice in the reference list. And the reference list is not ordered by the number. It's rather difficult to understand why the authors uploaded this incomplete manuscript for me. Authors should imagine the reviewers feelings when they received this kind of incomplete manuscript.
Author Response
Please find below the reply to your comments point-by-point.
The minor points which I should mention is followings.
1. References are not ordered by the order of the appearence in the
main text. Is this OK?
Answer:
The problem is just due to the ref. 47 which has been added by
mistake (as it was already in the list) during the last review
process.
2. The authors uploaded the pdf file with images and not with text.
Why did the authors make this? This is quite inconvenient for
reviewer.
Answer:
I uploaded three files, a zip file containing the latex with
figures, another zip file with only figures and the compiled pdf file
with text and figures; in order to overcome any problem (I hope) I
attached below the modified pdf file.
3. The reference #47 appear twice in the reference list. And the
reference list is not ordered by the number. It's rather difficult to
understand why the authors uploaded this incomplete manuscript for me.
Authors should imagine the reviewers feelings when they received this
kind of incomplete manuscript.
Answer:
We are sorry for the inconvinient, please, see the answer to the question 1.
Author Response File: Author Response.pdf
