Hamiltonian Model for Electron Heating by Electromagnetic Waves during Magnetic Reconnection with a Strong Guide Field

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript studied electron heating by electromagnetic waves during magnetic reconnection with a strong guide field. Based on the Magnetic Reconnection eXperiment (MRX) conditions and results as two works (J.Yoo et al, Phys. Rev. Lett. 132, 145101 (2024); S. Bose, et al, Phys. Rev.Lett. 132, 205102 (2024)), the authors use the Hamiltonian model to simulate the electrons heated by a monochromatic electromagnetic wave during the magnetic reconnection. They found that a positive correlation of the electron temperature dependence on the amplitude of the electric field fluctuation, which is consistent with the experiment data from the MRX, and indicate that the heating mechanisms that convert from magnetic energy to plasma kinetic one. The manuscript presents some interesting results, however I suggest a major revision for these main issues outlined below before the manuscript can be accepted for publication.

 

1.      In present version, the manuscript and the Supplemental Material of a video just show the theoretic process of the electrons moving in the guide field, and the main process such as how the monochromatic electromagnetic wave exited during the magnetic reconnection is missed, which are not helpful for the reader to understand the whole physical process. Line 74, the wave is directed added in the text, however, it should be excited by the certain condition during the magnetic reconnection. I suggest that the author has to simulate the magnetic reconnection and add figures to show the reconnection and the wave excitation.

2.      Figure 1 show the main result of this manuscript, and please give the way how to calculate the electron temperature for different amplitude of the electric field.

3.      Figure 2 gives an example of time trace of one simulation with an Ew = 170 V/m. If the electromagnetic wave is shown, it is helpful for reader to understand why the kinetic energy is increased during the interval between 5000-15000.

4.      Figure 3 shows the distribution of the initial and final momentum, and their middle values of momentum are same as zero. Should the final momentum distribution shift to the right than the initial distribution due to with a higher energy after the heating.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Referee report on manuscript entitled “Hamiltonian model for electron heating by electromagnetic waves during magnetic reconnection with a strong guide field” by Fabio Sattin:

This paper investigates electron heating via interaction with low-frequency high-amplitude transient electromagnetic waves generated during a reconnection event with a strong guide field. It is directly related to experimental results presented in two previous works by other authors. The subject is interesting and has important astrophysical ramifications, thus I believe that this work deserves publication. Before expressing my final recommendation, I would like the author to address a couple of points listed below:

1)     This paper is heavily based on two previous works. Nevertheless, it should also stand as an independent publication. The author should add a cartoon of the electric and magnetic field configuration that he is considering. It is not clear what the x,y,z coordinates represent.

2)     The argument of a moving separatrix in phase space that brakes the adiabaticity of the motion and allows for an irreversible transfer of energy is very interesting. Unfortunately, the reader has no idea of what this is all about. The author must add diagrams with evolving surfaces of section in phase space to show the presence of a separatrix and its evolution with time.

3)     There is a mention of a separatrix in line 47. Is this the same as the separatrix in phase space (line 102)? Without a diagram of the reconnection configuration, and a diagram of the particle phase space, the reader is confused.

4)     I do not understand figure 3. What are the grey histogram bars? Where are the initial and final momentum distribution? Something is not quite right.

5)     I would like to see a comparison between the wave acceleration mechanism and the direct electric field parallel acceleration. Which one is more efficient?

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper, the author proposes a mechanism for electron heating during magnetic reconnection in the presence of a strong guide magnetic field. The characterization of electron heating is done by adapting the standard stochastic particle heating mechanism to the MRX, with emphasize on the contribution of electromagnetic waves to the energization of electrons during reconnection. Also, the author analyzes the processes through which magnetic energy is converted into kinetic energy of electrons. The paper presents a Hamiltonian model of wave-particle interaction from which the measured levels of electron heating observed in MRX experiments can be recovered. The results obtained from the proposed model are in agreement with some experimental data. 

The paper seems correct from the mathematical point of view, although the Mathematica routines have not been included for crosschecking.

As the author states, the paper is an exercise in the MRX, but with non-trivial results. 

As pointed out in the final part of the paper, some conclusions are speculative. There are several reasons for which we may think of different outcomes: 1) The model is based on a simplified Hamiltonian to describe wave-particle interactions, which overlooks more complex dynamics in plasma, such as non-linear effects, multi-scale interactions and the contribution of plasma species. 2) The limited frequency range considered in the paper. 3) Dependence of MRX plasma parameters which in different experimental setup or astrophysical conditions may lead to different outcomes. 4) The use of a just heating mechanism which may downplay other processes that contributes to electron energization during reconnection, such as turbulence of wave interactions. 5) Comparison with a more extensive range of data.

It would be helpful to have these points stated in the paper and I leave it to the author's discretion to clarify these limiting points to the conclusions of this work, possibly as a comment in the final section.

I have also detected some minor misprints:

Page 2, line 54: extra dot in front of references [7-20].

Page 3, line 96: "n\"{a}ively" should be replaced by "naively".

Page 5, line 166: "n Fig. (4)" should be corrected to "In Fig. (4)".

Page 7, line 215: a dot is missing after [21].

 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This version has already considered and revised what I mentioned in the comments, and I recommend that the manuscript could be accepted,

Reviewer 2 Report

Comments and Suggestions for Authors

I am happy with the author's response over my queries. I now like the paper very much. The new figures really helped me appreciate this small but interesting and honest piece of work. I wholeheartedly recommend publication!