Particle Production in Strong Electromagnetic Fields and Local Approximations

Round 1

Reviewer 1 Report

In this article, the authors are looking theoretically at electron-positron pair production in the strong field regime. They are assessing the effect of quantum statistics when quantum interference takes place. This is performed by comparing two theoretical approaches: one based on the numerical calculations of kinetic equations and the second based on the locally constant approximation. Their main conclusion is that the LCFA can be invalid due to these statistical effects and this occurs when interference takes place.

In my view, this article is very well written. The context of the work is described clearly and there is enough details on the theoretical methods to understand the calculations. The results are interpreted physically and properly, while the conclusion is supported by the numerical work. Overall, I thought it was a very nice piece of theory. For these reasons, I am recommending this article for publication, without reserve.

My only suggestion for a minor change is the following. In the abstract and introduction, it is mentioned that the calculations are performed in the ''strong-coupling'' regime. Personally, I would rather say in the ''strong-field'' regime, because the coupling (alpha, the fine structure constant) is still small, even though the combination alpha*A (where A is the potential strength) is not.

Author Response

We thank the reviewer for reading our manuscript and providing the report. We are also happy to receive a positive response. We agree that the term “strong-field regime” is more appropriate, so we made the corresponding change.

Reviewer 2 Report

Report on “Particle production in strong electromagnetic fields and local approximations” by Aleksandrov et al.

The authors report on theoretical simulations of particle production in overcritical fields, employing both the QKE (quantum kinetic equation) and the LCFA (local constant field approximation). The main result is that in two temporally separated electric field pulses, an interference pattern in the momentum distribution of the created particles appears, which is not captured by the LCFA.

I think that the manuscript is well written, and the results appear to be, as far as I can judge, solid. The results may be of some importance in planning future experiments demonstrating pair production from vacuum using ultrastrong electromagnetic fields. I therefore recommend the manuscript for publication. Before publishing the manuscript, I have however a few comments which the authors may want to address.

1.    I think it would be helpful for the reader if a plot of the electric fields used (defined in Eq. (1)) could be shown. In particular it would be nice to have a clear picture of the difference between the field configurations with positive sigma compared to negative sigma, because this difference is important later in the results section.

2.    I would appreciate some more comments on the relevance of the field configuration considered in the manuscript for a realistic experimental setup employing strong laser pulses. Something is written in the conclusions, but a bit longer discussion would be helpful. For example, could the field defined in Eq. (1) be a (crude) approximation of a single-cycle laser pulse? Could a real laser pulse be modeled by a sum of many Sauter pulses?

3.    As far I as can see, “E_c” is never defined in the manuscript. It stands for the critical field, I guess, but it should still be defined.

4.    What determines the period (or frequency) of the oscillation in the momentum spectrum in Fig. 2?

5.    In Eqs. (19-21), please state the physical meaning of the quantities u and v.

Author Response

We thank the reviewer for reading our manuscript and providing the report. Below we address the reviewer’s comments and criticism:
1) We totally agree that this kind of scheme should significantly improve the presentation. We added the corresponding figure.
2) This important issue is now discussed in Section 2 (see p. 2, “A spatially homogeneous...”).
3) We now define this quantity on p. 2.
4) The frequency is proportional to tau and delta. We added the corresponding comment on p. 9.
5) We added a comment after Equations (19)-(21) (p. 6).
Having performed these amendments, we hope now that the revised version of the paper can be accepted for publication.