the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Jan 2024
The dynamic of ion Bernstein-Greene-Kruskal holes in plasmas with regularized κ-distributed electrons
Abstract. The dynamics of ion holes (IHs) in plasmas where electrons follow the regularized Kappa distribution (RKD) and ions follow the Maxwellian distribution (MD) are investigated based on the Bernstein-Greene-Kruskal (BGK) method. The results show that the depth of the IHs, the allowed combination of width and amplitude to support physically plausible IHs equilibrium depend on the spectral index κe and cut-off parameter α of the distribution function. That is, with increasing values of the spectral index κe and cut-off parameter α, the IHs formed become deeper and allow a larger permissible region of width and amplitude. In contrast, with decreasing values of the spectral index κe and cut-off parameter α, the IHs formed become shallower and have a smaller allowed range of width and amplitude. The present work may contribute to the comprehension of the nonlinear structures in plasmas system where non-thermal particles are found.
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RC1: 'Comment on npg-2023-25', Anonymous Referee #1, 15 Jan 2024
The manuscript presents a study on ion Bernstein-Greene-Kruskal (BGK) modes in the context of regularized kappa distributions (RKD). This offers a significant contributions to our understanding of characterestics of BGK modes and its effects on distribution function. The exploration of ion BGK modes under the framework of RKD is both timely and relevant, given the growing importance of non-Maxwellian distributions in space plasma research.
I recommend the manuscript for publication, subject to the following revisions which I believe will greatly enhance its impact and clarity:
Please consider these points:
- Observational Evidence of RKD: It is crucial for the manuscript to include specific observational results that substantiate the physical existence of conditions where kappa less than or equal to 1.5. While the mathematical premise stands, empirical evidence would solidify the paper's relevance. For instance, statistical surveys of the solar wind and magnetosphere have revealed kappa values between 2-6, but intervals with k < 2 are not uncommon during dynamic processes like magnetic reconnection. Referencing such observations is essential to substantiate the regimes where their model is applicable. The authors should also discuss whether there are specific instances in space plasma environments where this condition is observed? Providing such observational instances would significantly elevate the paper's practical implications in the field.
- While the focus on unmagnetized and collisionless electron-ion plasmas using the BGK method with RKD electrons is commendable, considering both ions and electrons as suprathermal (following RKD) could enhance the model’s generalizability. This approach allows the model to address various plasma contexts by adjusting the spectral indices kappa_i and kappa_e, alpha_e, and alpha_i. I recommend revising the model to incorporate RKD for both species.
- An explicit analytical representation of RKD is crucial for clarity. Please define and explain terms such as the kappa index, alpha, and their implications on the distribution. For example, a high kappa index suggests proximity to thermal equilibrium. Include references for RKD formulation.
- To enhance the manuscript's credibility, outline the derivation steps or provide references for the RKD expression used. Adding an appendix for this purpose would be beneficial. For example, please explain how the authors obtaianed equation 5.
- Also, provide a reference to Kummer function such that the reader who are interested could learn more about the function.
- You mentioned that “Nevertheless, the distribution of electrons with the SKD in the potential field will be valid within the region where κe is greater than 0 and alpha not equal to 0. In this paper, we extended the SKD to the range of κ > 0 to demonstrate the impact of the cut-off parameter α on the properties of ion BGK holes”- In the case of RKD to be come SKD the kappa indedx should be greater than 3/2 and alpha should be almost 0. Given this is the case, your statement lacks precision.
- In the section 3, the authors talk about equations 19, and 20. I did not see any equations 19 and 20.
- Another important factor that the authors should take into account is that when you make the figures all the axis should be fixed, then only the readers can understand the effects of various parameters. Please fix the axes of figures 1,2 and 3.
- I completely agree with the physical explanation that you provided for the figures 1,2,3. But it should clearly mentioned that this clearly depends on the shape of the potential. So it should be written in such a way that for a fixed potential, …..
- Please check the caption of figure 4. It is always better if you keep the legends similar. I dont see any pink dashed or black line in fig 4 (b). So I encourage the authors to verify and modify the caption accordingly.
- Also please explain the limits of alpha that appears in RKD. What happens if the value of alpha is large.
In summary, the manuscript presents promising contributions to the field. However, for it to reach its full potential, it is imperative that the authors address the highlighted concerns. Enhancements in observational substantiation, model generalization, and clarifications in mathematical and physical terms are needed. Further, refinement in presentation, including plot standardization and a detailed discussion on parameter limits, will considerably strengthen the manuscript's clarity, rigor, and overall impact. These revisions, I believe, are crucial for transforming this study into a robust and impactful publication.
Citation: https://doi.org/10.5194/npg-2023-25-RC1 -
AC1: 'Reply on RC1', Qiuping Lu, 27 Feb 2024
The comment was uploaded in the form of a supplement: https://npg.copernicus.org/preprints/npg-2023-25/npg-2023-25-AC1-supplement.pdf
-
RC2: 'Comment on npg-2023-25', Anonymous Referee #2, 28 Mar 2024
Although the paper title and abstract are about “The dynamic of ion Bernstein-Greene-Kruskal holes”, this paper does not consider any dynamical properties and entirely focuses on construction of the stationary solutions of ion holes. There are multiple such solutions already published for different plasma distributions, and all these solutions may be important only in context of comparison with observations or investigation of hole dynamics and stability analysis. It’s quite hard, if possible, to justify construction of 1D electrostatic equilibrium without any analysis of applicability of this equilibrium to some realistic (observed in space or laboratory) structures. Therefore, the motivation for this study, and importance of obtained results are unclear.
A few specific comments:
* Figures 2, 3 show absolutely identical structures that are different only by color bars…
* Section 2 ends by Eq. (18), whereas Section 3 starts with “…BGK holes are examined by analyzing Eqs.(19) and (20).” I did not find these equations in the text…
Citation: https://doi.org/10.5194/npg-2023-25-RC2 -
AC2: 'Reply on RC2', Qiuping Lu, 02 Apr 2024
The comment was uploaded in the form of a supplement: https://npg.copernicus.org/preprints/npg-2023-25/npg-2023-25-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Qiuping Lu, 02 Apr 2024
Status: closed
-
RC1: 'Comment on npg-2023-25', Anonymous Referee #1, 15 Jan 2024
The manuscript presents a study on ion Bernstein-Greene-Kruskal (BGK) modes in the context of regularized kappa distributions (RKD). This offers a significant contributions to our understanding of characterestics of BGK modes and its effects on distribution function. The exploration of ion BGK modes under the framework of RKD is both timely and relevant, given the growing importance of non-Maxwellian distributions in space plasma research.
I recommend the manuscript for publication, subject to the following revisions which I believe will greatly enhance its impact and clarity:
Please consider these points:
- Observational Evidence of RKD: It is crucial for the manuscript to include specific observational results that substantiate the physical existence of conditions where kappa less than or equal to 1.5. While the mathematical premise stands, empirical evidence would solidify the paper's relevance. For instance, statistical surveys of the solar wind and magnetosphere have revealed kappa values between 2-6, but intervals with k < 2 are not uncommon during dynamic processes like magnetic reconnection. Referencing such observations is essential to substantiate the regimes where their model is applicable. The authors should also discuss whether there are specific instances in space plasma environments where this condition is observed? Providing such observational instances would significantly elevate the paper's practical implications in the field.
- While the focus on unmagnetized and collisionless electron-ion plasmas using the BGK method with RKD electrons is commendable, considering both ions and electrons as suprathermal (following RKD) could enhance the model’s generalizability. This approach allows the model to address various plasma contexts by adjusting the spectral indices kappa_i and kappa_e, alpha_e, and alpha_i. I recommend revising the model to incorporate RKD for both species.
- An explicit analytical representation of RKD is crucial for clarity. Please define and explain terms such as the kappa index, alpha, and their implications on the distribution. For example, a high kappa index suggests proximity to thermal equilibrium. Include references for RKD formulation.
- To enhance the manuscript's credibility, outline the derivation steps or provide references for the RKD expression used. Adding an appendix for this purpose would be beneficial. For example, please explain how the authors obtaianed equation 5.
- Also, provide a reference to Kummer function such that the reader who are interested could learn more about the function.
- You mentioned that “Nevertheless, the distribution of electrons with the SKD in the potential field will be valid within the region where κe is greater than 0 and alpha not equal to 0. In this paper, we extended the SKD to the range of κ > 0 to demonstrate the impact of the cut-off parameter α on the properties of ion BGK holes”- In the case of RKD to be come SKD the kappa indedx should be greater than 3/2 and alpha should be almost 0. Given this is the case, your statement lacks precision.
- In the section 3, the authors talk about equations 19, and 20. I did not see any equations 19 and 20.
- Another important factor that the authors should take into account is that when you make the figures all the axis should be fixed, then only the readers can understand the effects of various parameters. Please fix the axes of figures 1,2 and 3.
- I completely agree with the physical explanation that you provided for the figures 1,2,3. But it should clearly mentioned that this clearly depends on the shape of the potential. So it should be written in such a way that for a fixed potential, …..
- Please check the caption of figure 4. It is always better if you keep the legends similar. I dont see any pink dashed or black line in fig 4 (b). So I encourage the authors to verify and modify the caption accordingly.
- Also please explain the limits of alpha that appears in RKD. What happens if the value of alpha is large.
In summary, the manuscript presents promising contributions to the field. However, for it to reach its full potential, it is imperative that the authors address the highlighted concerns. Enhancements in observational substantiation, model generalization, and clarifications in mathematical and physical terms are needed. Further, refinement in presentation, including plot standardization and a detailed discussion on parameter limits, will considerably strengthen the manuscript's clarity, rigor, and overall impact. These revisions, I believe, are crucial for transforming this study into a robust and impactful publication.
Citation: https://doi.org/10.5194/npg-2023-25-RC1 -
AC1: 'Reply on RC1', Qiuping Lu, 27 Feb 2024
The comment was uploaded in the form of a supplement: https://npg.copernicus.org/preprints/npg-2023-25/npg-2023-25-AC1-supplement.pdf
-
RC2: 'Comment on npg-2023-25', Anonymous Referee #2, 28 Mar 2024
Although the paper title and abstract are about “The dynamic of ion Bernstein-Greene-Kruskal holes”, this paper does not consider any dynamical properties and entirely focuses on construction of the stationary solutions of ion holes. There are multiple such solutions already published for different plasma distributions, and all these solutions may be important only in context of comparison with observations or investigation of hole dynamics and stability analysis. It’s quite hard, if possible, to justify construction of 1D electrostatic equilibrium without any analysis of applicability of this equilibrium to some realistic (observed in space or laboratory) structures. Therefore, the motivation for this study, and importance of obtained results are unclear.
A few specific comments:
* Figures 2, 3 show absolutely identical structures that are different only by color bars…
* Section 2 ends by Eq. (18), whereas Section 3 starts with “…BGK holes are examined by analyzing Eqs.(19) and (20).” I did not find these equations in the text…
Citation: https://doi.org/10.5194/npg-2023-25-RC2 -
AC2: 'Reply on RC2', Qiuping Lu, 02 Apr 2024
The comment was uploaded in the form of a supplement: https://npg.copernicus.org/preprints/npg-2023-25/npg-2023-25-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Qiuping Lu, 02 Apr 2024
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