Shaping Micro-Bunched Electron Beams for Compact X-ray Free-Electron Lasers with Transverse Gradient Undulators

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper describes a compression scheme for a compact short-wavelength FEL, based on combination of eSASE concept with transverse-gradient undulator. The dynamics is studied both analytically and numerically, all essential effects are included. Even though I am strongly impressed by an improvement w.r.t. the standard eSASE approach, the scheme adds more flexibility to the design and might be helpful for different applications. I like the effet of emittance reduction at the position of a current peak.

I think the paper can be published as is.

 

Author Response

We thank the referee for their kind words and for their careful reading of the manuscript. 

Reviewer 2 Report

Comments and Suggestions for Authors

First of all, I would like to acknowledge a very high quality of academic writing. It was a pleasure to read the manuscript.

Regarding the content, the idea is neat and it was interesting to see that the emittance is reduced in the core of the bunch by pushing off-axis particles out. Though the final emittance with and without TGU is almost the same.

Overall, the analysis is thorough and complete. I recommend the manuscript for publication in its present form.

Author Response

We thank the referee for their kind words. We also like the slice emittance reduction concept, and though it doesn't actually help us much in our working point we hope we properly conveyed that, for different beam conditions, it could be beneficial. 

Reviewer 3 Report

Comments and Suggestions for Authors

The main novelty of this paper is to use a transverse gradient undulator (TGU) to increase the micro-bunch width in enhanced self-amplified spontaneous emission (eSASE) schemes, and thus improve the FEL radiation power while reducing collective effects. However, I find this approach questionable and not well justified. In conventional eSASE schemes, one can also achieve longer micro-bunches by using decompression (with smaller R56 than the optimized value) or overcompression methods (similar to Figure 2e). Although overcompression requires a larger chicane strength, the increase should be very small. I need the authors to include decompression and overcompression cases in their section 3 simulations, to demonstrate more clearly the necessity of adding a TGU.

Author Response

We thank the referee for their comments. If we understand the comments correctly, we believe that the requested information is already represented in Section 3. Figure 6 shows the peak current and emittance achievable by scanning the chicane momentum compaction for three different modulation amplitudes -- this of course naturally scans through the undercompression and overcompression working points. We are particularly interested in addressing the design desires for the UCXFEL, and therefore achieving 4 kA peak currents. For any normalized modulation amplitude greater than 16.5, this can only be done by undercompression or overcompression, as indicated by the fact that for A=34 or 50, there are two values of B that achieve 4 kA peak current (shown in Fig 6).

Fig 6 shows in particular that for the larger B values for each modulation amplitude to hit 4 kA (those which overcompress the micro-bunches), the emittance is more than double its nominal value. For that reason we focused on the undercompression working points in the Genesis simulations that follow. 

We would also like to push back on one claim by the referee, just to make sure we are using the same terminology here. The referee states that one can achieve longer micro-bunches by using decompression -- this is not true if you want to fix the final peak current. This is exactly what Figure 2 aims to show -- if we restrict ourself to 10x compression, full compression (A=1/B) occurs for A=16.5. For any larger value of A, 10x compression can be achieved by two different values of B, one giving undercompression and one overcompression. However, the undercompression working points always yield shorter micro-bunches than the full compression at A=16.5 or the overcompression working point for the particular value of A (Fig. 2b). If we did not fix the peak current we could lengthen the micro-bunches by reducing B at a fixed A, but the peak current would then be smaller and the FEL gain length would increase. 

We hope that we have understood the referee's comments correctly and properly addressed their points above. We thank them again for their reading of the manuscript and contribution to making it stronger. If the referee agrees with our statements above but believes we did not make them clear enough in the manuscript, we are happy to expand on the discussion there. 

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for your response to my comments. I agree with your statements. I still think that you could improve your manuscript by providing more explanation on Fig. 6 in the main text. This figure is very important as it shows the trade-off between the peak current and the emittance for different modulation amplitudes and momentum compactions. It would be helpful for the readers to understand the advantages of your method.

Author Response

Thank you for your new comments, we agree completely that these things deserve to be better explained in the main text. We have expanded the discussion, similarly to our response to your first comments, at the end of the paragraph in which Fig. 6 is first mentioned, as well as the beginning of the paragraph after that. We hope that it is now clearer, please let us know if it is not.