Round 1

Reviewer 1 Report

 

The manuscript presents an analysis of fluid continuity equations for two populations of dust particles (respectively positively and negatively charged) in plasmas, when ion and electron energy populations are described by power-law (kappa) distributions.  

Nonlinear travelling waves solutions are looked for, by a perturbative analysis of the equations around equilibrium constant values. 

The author recovers the well-known equations for propagation of nonlinear disturbances (KdV, etc ...), except that they are written in terms of the parameters of the kappa energy distribution, rather than the standard Maxwell-Boltzmann one. 

 

The mathematical work appears correct although not very original, since this kind of analysis is standard and--furthermore--can nowadays be performed without much effort using a computer algebra software. 

 

Before publishing the manuscript, in my opinion several major issues need be answered. 

 

1) The first major problem with the manuscript is its English. It is often unintelligible and leads to misunderstanding also the physical content. 

It is impossible to point out individually all the errors, since there are too many of them: almost every sentence contains one or several. I just quote the very first sentence, as an example: 

 

"Because definitive role of propagation of dust acoustic waves (DAWs) (vibration of low energetic dusty plasma density) in many applications such as different laboratory and industrial such as plasma devices, semiconductor chips, fusion devices and so on attracted the researchers attention."

 

From the one hand it is not grammatically correct; from the other hand, the meaning of some words does not appear to match the common established one (what does "definitive role of propagation" mean ?) 

 

2) The author states that his target are unmagnetized plasmas. Yet, magnetic fields are present in several environments among those cited by the author himself and quoted in his bibliography. He should therefore better explain the reasons of his choice:

a) Is he intentionally circumscribing his research to environments where magnetic fields are not present ? Or,

b) magnetic fields may be present but he believes are not relevant to the conclusions of his study ? 

 

3) A similar question concerns the issue of non-collisionality. Actually, fluid equations postulate short mean free path, hence collisionality ultimately must be present. It is therefore a matter of time scales: collisions are frequent enough to make valid the fluid approximation, yet scarce enough to be discarded in all other instances. The author should discuss this approximation.   

 

4) As I recalled above, the mathematical analysis performed in the work is quite standard. The only novelty is that the resulting nonlinear evolution equations are parameterized in terms of the ion and electron kappa distribution. In the present form, the work thus amounts just to a mathematical exercise. In my opinion, it seems fairly academical: I am not able to guess which kind of useful information any reader can extract from its reading. This is not a secondary detail at all, given that the manuscript is submitted to an issue of a journal specifically devoted to applications. Therefore, it would be welcome if the author could provide some physically-based justification for his work, say: can the found results be used for inferring kappa-distribution parameters from some kind of measurements?  

Furthermore, in the past years the author has written several papers whose scope and results seem largely to overlap the present one, but for possibly minor differences. E.g., in the paper entitled "Plasma parameters effects on dust acoustic solitary waves..." [Advances in mathematical Physics 2018] the problem addressed seems to me identical to the present one, with a power-law energy distribution for ions and electrons, except that in that case it was referenced to as Tsallis' nonextensive distribution. The author should provide some arguments explaining better any novelty with respect to his previous studies.   

 

Author Response

Reviewer: 1

1. The first major problem with the manuscript is its English. It is often unintelligible and leads to misunderstanding also the physical content. 

It is impossible to point out individually all the errors, since there are too many of them: almost every sentence contains one or several. I just quote the very first sentence, as an example: 

"Because definitive role of propagation of dust acoustic waves (DAWs) (vibration of low energetic dusty plasma density) in many applications such as different laboratory and industrial such as plasma devices, semiconductor chips, fusion devices and so on attracted the researchers attention."

From the one hand it is not grammatically correct; from the other hand, the meaning of some words does not appear to match the common established one (what does "definitive role of propagation" mean ?) 

.

Reply:

These misprinting mistakes and others are considered and corrected.

2. The author states that his target are unmagnetized plasmas. Yet, magnetic fields are present in several environments among those cited by the author himself and quoted in his bibliography. He should therefore better explain the reasons of his choice:
3. a) Is he intentionally circumscribing his research to environments where magnetic fields are not present ? Or,
4. b) magnetic fields may be present but he believes are not relevant to the conclusions of his study ? 
5. A similar question concerns the issue of non-collisionality. Actually, fluid equations postulate short mean free path, hence collisionality ultimately must be present. It is therefore a matter of time scales: collisions are frequent enough to make valid the fluid approximation, yet scarce enough to be discarded in all other instances. The author should discuss this approximation.

Reply:

In this paper author interested in his study to environments where the effect of magnetic field can be neglected, and in future work the effect of magnetic field and collisionality will be studied with my group.   

 

4. As I recalled above, the mathematical analysis performed in the work is quite standard. The only novelty is that the resulting nonlinear evolution equations are parameterized in terms of the ion and electron kappa distribution. In the present form, the work thus amounts just to a mathematical exercise. In my opinion, it seems fairly academical: I am not able to guess which kind of useful information any reader can extract from its reading. This is not a secondary detail at all, given that the manuscript is submitted to an issue of a journal specifically devoted to applications. Therefore, it would be welcome if the author could provide some physically-based justification for his work, say: can the found results be used for inferring kappa-distribution parameters from some kind of measurements? 

 

Furthermore, in the past years the author has written several papers whose scope and results seem largely to overlap the present one, but for possibly minor differences. E.g., in the paper entitled "Plasma parameters effects on dust acoustic solitary waves..." [Advances in mathematical Physics 2018] the problem addressed seems to me identical to the present one, with a power-law energy distribution for ions and electrons, except that in that case it was referenced to as Tsallis' nonextensive distribution. The author should provide some arguments explaining better any novelty with respect to his previous studies.  

Reply:

In this work author has been

• used the kappa distribution because, the velocity population functions in space plasmas show non-Maxwellian super-thermal tails, which taking the formula as a power law of the velocity.
• introduced the effect of viscosity for both positive and negative dust species.

derived some nonlinear partial differential equations as KdV, Burgers', KdV Burgers', modified KdV, modified Burgers', modified KdV-Burgers', and Further(Gardener) Burgers using modified form for reductive perturbation technique by introducing three parameters which are controlled the strength of nonlinearity, dispersion and dissipation in system.    

Reviewer 2 Report

Reviewer comments

Ms title: The fully nonlinear small amplitude dynamical waves for multi-component complex plasma with kappa distributed electrons and ions.

Ms ID: applsci-1874212

Author: Abeer A. Mahmoud

In this investigation, the author used a reductive perturbation method to study the behavior of probable propagated waves in four component dusty plasma system with kappa distributed electrons and ions. The manuscript seems mathematically good but the following points should be considered before I recommend publication

1-    The language must be revised and improved.

2-    The whole manuscript loses many meanings and physical discussions, and the author must discuss its results physically

3-     The abstract must be rephrased and contained the answer to the following question: what are the motivations of this study?  

4-    The word 'mutli-components' must be changed to 'multicomponent'. But multiions must be replaced by multi-ions

5-    In this paper author study the small but finite amplitude, so why did the author use fully nonlinear in the title, the title should be rephrased because the authors did not reduce their fluid equations to Sagdeev potential in order to say fully nonlinear.

6-    The author used the reductive perturbation method for reducing the fluid equations of the plasma model to the family of the KdV equation including the KdV equation with quadratic nonlinearity, the mKdV equation with cubic nonlinearity, and the Gardner/Extended KdV equation with both quadratic and cubic nonlinearities,  in order to study the characteristics of the unmodulated (not envelope) structures such as solitons, shock, cnoidal waves. My question here, why did the author use the word 'envelope'? He/she did not reduce their fluid equations to the NLSE to say envelope structures.

7-    Some full-stop and commas are missed at the end of some equations.

8-    The resolution of all figures is not good and needs to improve, the author can use eps format for all figures.

9-    It is noted that all Refs. are very old. The author should update the whole refs by inserting some Refs related to this topic and should be new.

10- All evolution equations should be written in a new fashion and the author should remove (x,t) from all dependent quantities.

 

I want to see the revised version. 

Author Response

Reviewer: 2

 

1-    The language must be revised and improved.

.

Reply:

These misprinting mistakes and others are considered and corrected.

2 The whole manuscript loses many meanings and physical discussions, and the author must discuss its results physically.

The whole manuscript has been improved.

Reply:

3. The abstract must be rephrased and contained the answer to the following question: what are the motivations of this study? 

Reply:

The abstract has been improved.

4. The word 'mutli-components' must be changed to 'multicomponent'. But multiions must be replaced by multi-ions

.

Reply:

The word 'mutli-components' changed to 'multicomponent', and multiions  replaced by multi-ions.

 

5. In this paper author study the small but finite amplitude, so why did the author use fully nonlinear in the title, the title should be rephrased because the authors did not reduce their fluid equations to Sagdeev potentialin order to say fully nonlinear.

Reply:

In sagdeev potential the most probable large amplitude propagated waves have been studied. Similarly, in this paper author was interested to study the most probable small amplitude nonlinear waves which may be appeared in the system under consideration, by using reductive perturbation method through using three parameters which are adjustment the strength of nonlinearity, dispersion and dissipation.

  

6- The author used the reductive perturbation method for reducing the fluid equations of the plasma model to the family of the KdV equation including the KdV equation with quadratic nonlinearity, the mKdV equation with cubic nonlinearity, and the Gardner/Extended KdV equation with both quadratic and cubic nonlinearities,  in order to study the characteristics of the unmodulated (not envelope) structures such as solitons, shock, cnoidal waves. My question here, why did the author use the word 'envelope'? He/she did not reduce their fluid equations to the NLSE to say envelope structures.

Reply:

The word 'enveloped' has been cancelled from paper.

7- Some full-stop and commas are missed at the end of some equations.

Reply:

The full-stop and commas are revised.

8- The resolution of all figures is not good and needs to improve, the author can use eps format for all figures.

Reply:

A file for all figures in postscript format will be submitted with the revised form.

9- It is noted that all Refs. are very old. The author should update the whole refs by inserting some Refs related to this topic and should be new.

Reply:

Some refs are updated.

 

10- All evolution equations should be written in a new fashion and the author should remove (x,t) from all dependent quantities.

Reply:

All evolution equations have been written in a new fashion and the (x,t) have been removed from all dependent quantities.

 

 

 

Round 2

Reviewer 1 Report

 

Second report

 

Regretfully, the revised version of the manuscript still contains the same issues signalled in the reviewers' reports.

 

1) The language. Both reviewers complained about the poor English. Despite the claims of the author, there are not improvements in the revised version. I believe that there must be some basic problem with the author's knowledge of English. To quote just the very first instance: the first lines of the abstract

"Most equations which described the probable dust acoustic waves propagated in an unmagnetized collisionless four components complex plasma system. This plasma system contains two differ in charge dust species and kappa distributed electrons and ions."

 

- According to my dictionary, "probable" stands for "likely to happen". What does it mean according to the author ? 

- Why using the past in the first sentence, and the present in the second one ?

- Which is the subject of the first sentence ? "Most equations" ? In this case, which is the verb associated to it ? "described" or "propagated" ?

- The last sentence "This plasma system contains ..." is completely unintelligible. It is likely that some word is missing, since I do not understand to which term "two" and "differ" are referring to.  

- ... and we may continue a long way along the same tune.

 

2) The motivation for the work. Both reviewers' reports stress that the manuscript is not sufficiently justified. It looks like a mathematical exercise without any serious physical motivation. Furthermore, its originality is dubious since, to some extent, its content overlaps previous studies by the same author. Despite the author' claims, I could not see any improvement under this regard in the revised version. 

 

3) In my first report, I stressed that the author had not provided justifications for neglecting the role of the magnetic field and of the collisions in his study. The author did not provide a satisfactory reply to this issue, too. Besides this, I point out to a possible inconsistency in his study, about this point. Actually, the author does not account for collisionality in his model, but includes viscosity. Now, in a unmagnetized plasma, viscosity and collisionality are not independent: ultimately, both arise from electrostatic interactions between particles. Indeed, the very use of a fluid model is justified if interactions are not weak and the mean free path is short. Mathematically, one can always switch on or off any kind of interaction, but should wonder if he is doing something physically sound, and this leads us again to the problem that this study appears just a (quite standard) mathematical exercise without a clear physical rationale.

 

I do not judge the present manuscript suitable for publication but, since it looks technically correct, I do not wish to reject it either. I am ready to consider another revision but it must be carefully checked by someone mother-tongue or, at least, very proficient in English.  

 

Author Response

Reply on Reviewers Comments

 

Manuscript: applsci-1874212

Title: The fully nonlinear small amplitude dynamical waves for multi-component complex plasma with kappa distributed electrons and ions.

By: Abeer A. Mahmoud

 

Regretfully, the revised version of the manuscript still contains the same issues signalled in the reviewers' reports.

 

1) The language. Both reviewers complained about the poor English. Despite the claims of the author, there are not improvements in the revised version. I believe that there must be some basic problem with the author's knowledge of English. To quote just the very first instance: the first lines of the abstract

"Most equations which described the probable dust acoustic waves propagated in an unmagnetized collisionless four components complex plasma system. This plasma system contains two differ in charge dust species and kappa distributed electrons and ions."

 

- According to my dictionary, "probable" stands for "likely to happen". What does it mean according to the author ? 

- Why using the past in the first sentence, and the present in the second one ?

- Which is the subject of the first sentence ? "Most equations" ? In this case, which is the verb associated to it ? "described" or "propagated" ?

- The last sentence "This plasma system contains ..." is completely unintelligible. It is likely that some word is missing, since I do not understand to which term "two" and "differ" are referring to.  

- ... and we may continue a long way along the same tune.

Reply

 The language is revised and the introduction, abstract, and conclusion are rewritten.

2) The motivation for the work. Both reviewers' reports stress that the manuscript is not sufficiently justified. It looks like a mathematical exercise without any serious physical motivation. Furthermore, its originality is dubious since, to some extent, its content overlaps previous studies by the same author. Despite the author's claims, I could not see any improvement in this regard in the revised version. 

Reply

 The motivation for the work is explained after we rewrote both the introduction and conclusion.

3) In my first report, I stressed that the author had not provided justifications for neglecting the role of the magnetic field and of the collisions in his study. The author did not provide a satisfactory reply to this issue, too. Besides this, I point out a possible inconsistency in his study, about this point. Actually, the author does not account for collisionality in his model but includes viscosity. Now, in an unmagnetized plasma, viscosity and collisionality are not independent: ultimately, both arise from electrostatic interactions between particles. Indeed, the very use of a fluid model is justified if interactions are not weak and the mean free path is short. Mathematically, one can always switch on or off any kind of interaction but should wonder if he is doing something physically sound. This leads us again to the problem that this study appears just a (quite standard) mathematical exercise without a clear physical rationale.

Reply

In this paper, the chosen magnetized plasma system is relevant to different areas of space science such as Jupiter’s magnetosphere, Earth’s mesosphere, and cometary tails [33-35]. In this paper, the viscosity effect is very small, and we take the values of viscosity parameters as normalized parameters value, and we liked to focus our work on the effect of viscosity. So we neglect the effect of collision. 

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

The revised manuscript is still written in fairly poor English, but I was informed by the journal that this kind of problems should be fixed by their editing service, hence will not consider language issues.  

Regarding the other concerns, I believe that the author has done sufficient improvements. 

In my opinion, the paper may be published.