Analysis of the Hourglass–Spindle-Shaped Trajectory Generated by the Collision of Circularly Polarized Laser Pulses with Electrons

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this work, Li et al introduce the results of a theoretical study of the trajectory induced on electrons after a collision with circularly polarised laser pulses.

The novelty of the work is the demonstration of a new type of trajectory, specifically induced by chirped laser pulses, consisting in a hourglass-shaped motion.

The manuscript is well-organised, and most of the results are exhaustively discussed, showing the temporal evolution of the electron motion and commenting on the different shapes.

Herewith my suggestions and comments to the authors:

1. The title mentions a “hourglass-shaped” trajectory, but in the abstract a “funnel-shaped spindle” trajectory is mentioned. It is not clear if the authors name the same trajectory in two different ways or not. Please clarify.
2. Line 25. Some of the most significant laser parameters used for precise control should be mentioned, aimed at giving more information also to non-experts in the field (e.g. pulse shape, beam waist, repetition rate, and so on).
3. Line 27. For the same reason as comment #2, being Applied Science a journal followed by a broad range of readers, few lines should be dedicated to briefly introduce non-linear Thomson scattering.
4. Lines 42-48. In this paragraph, I suggest the authors to better highlight the significance of their work, for instance by enlisting some example applications which may take benefit from the obtained results. Being “Applied Science”, the paper should have also an applicative cut, in  my opinion.
5. Line 50. Authors mention “in the equation”, but it is not clear what equation they do mean. In addition, define “k0” and “ω0”.
6. Line 77. Define the symbol “I”.
7. Line 85. I suggest the authors to explain why the electric field components have been expanded exactly up to the fifth-order.
8. Line 136. The beam waist is here indicated as “b0” whereas it is indicated as “w” at line 77. Please choose one unique symbol for consistency.
9. Figure 3 should be necessarily enlarged. In addition, the different values for “tspan” should be indicated.
10. Lines 198-223. The four different phases are accurately described, but no references to Figures 3 and 4 are given. I suggest to link the description to what is shown in the figures, it would be very helpful to the reader.
11. Line 310. What do the author intend with “below 6k”? Is it for ω0 < 6000? It should be clarified.
12. Figure 7. The temporal and spatial distributions of the radiation are not adequately commented. I suggest the authors to elaborate a little bit more on this point, by describing more accurately the different figures, especially the temporal evolution.
13. Line 322. Authors mention a “gourd-shaped” trajectory never mentioned before. As far as I can see, trajectories are: “hourglass”, “spiral” and “spindle”. Please pay attention to this and avoid misleading interpretations.
14. As a final comment, I notice that the electron moves in the same direction of propagation of the laser pulse (z-axis). What if the directions are different and a collision angle is present? Are the obtained results on the trajectory shapes of general validity and extendable to more complex initial conditions? I suggest the authors to add a few lines about this in the concluding remarks.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Editor,

The manuscript entitled “Analysis of the hourglass-shaped trajectory generated by the collision of circularly polarized laser pulses with electrons” is a purely theoretical work that investigates the shape of electron trajectories when a free electron is under the presence of  an ultra-strong chirped and circularly polarized laser pulse. The behavior of electrons in such extreme conditions is a topic beyond academic interest, as for example, the injected electrons in plasma bubbles.  However, in this work I fail to see the coherence between realistic interactions of electrons and such laser pulses with the interaction studied in this work.  I mean where does this free electron come from? Is it ionized from an atom by the laser pulse pedestal? Is it an electron in a plasma formation (bubble)? In any case the authors should address this to drive their work beyond academic interest for a journal with title “Applied Sciences”. Even in this case the trajectories of these electrons are enormous. From figure 1 an area of diameter ~0.1 lambda. i.e. 0.1x1000 nm = 100 nm is covered. What are  the chances that an electron is not affected by neighboring ions since in these conditions the gas is fully and multiply ionized?  In addition, the role of the parent ion (also multiply ionized) is not considered in their analysis. As a last point I would ask the authors to address the question of what the experimental signature is that they suggest for testing the results of their findings. From my perspective, these questions should be clearly addressed in the manuscript before considering it for publication in Applied Sciences.  

Other details in the manuscript are as follows:

1. The references are misplaced. I think that Refs [4-7] should be [4-6], [8] in line 31 should be [7], [8] in line 32 should be [9]. I think Ref. [8] in line 31 should be included in Refs [10-14]. Also, Ref [15] does not correspond to the text.
2. Line 66. “Where” should read “where”.
3. Line 113. How did the electron acquired its initial velocity and why it is opposite to the direction of the laser beam propagation?
4. Line 135. Correctly written 10^{19} W/cm^{2}
5. Line 139. The parameter “gm_0” is given for the first time in the text and not defined earlier. Why is the value 2 and how it was chosen?
6. Figure 3.  The caption should be more self-explanatory aiding the reader. The numbers are very small and barely readable even when zooming. They should be increased to the size of the fonts in the text.
7. Figure 4. There is no reference for figure 4 in the text.
8. Throughout the text the authors mention the laser (e.g. line 210, speed of laser) while what they should accurately say is the “laser pulse”.
9. Lines 234-254. This paragraph is repeating earlier paragraphs on the interpretation of the results. Should be removed or modified.
10. Line 291. “The Figure 6.” should read “Figure 6”.
11. Line 308. I think “affects” should be “is affected by”.
12. Figure 7 bottom. This x-axis of the graph has no dimensions .

Comments on the Quality of English Language

The English lamguage is adequate with only minor corrections in some places. 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have carefully considered all the suggestions, commnets and corresctions made in the first review and included them accordingly in their revised manuscript. Now the scope and results of the manuscript are more clearely and convinsigly presented. Thus, I suggest its publication in its current form. A minor typo that the authors should treat is the symbols "gm" and "gm0" that still persit in lines 337 and 342 a well as in Figure 5. They should correct it to $\Gamma$ and $\Gamma_0$. 

Author Response

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Author Response File: Author Response.pdf