the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 Nov 2024
Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma
Abstract. This research investigates the impact of temperature anisotropy on Electromagnetic ion cyclotron (EMIC) waves in a multi-ion magneto-plasma environment composed of H+, He+, and O+ ions, with a particular emphasis on the role of the Kappa distribution function. The study delves into how variations in temperature anisotropy influence the behavior and properties of EMIC wave propagation, considering the complex interplay between anisotropic thermal effects and the non-Maxwellian Kappa distribution. Through a comprehensive analysis involving theoretical modeling and numerical simulations, the research elucidates how these factors alter wave dispersion relations, growth rates, and spatial structures of EMIC waves. The results reveal significant deviations from classical Maxwellian predictions, highlighting the necessity to incorporate Kappa distributions for accurate descriptions of wave behavior in realistic plasma conditions. This enhanced understanding has broader implications for space physics, astrophysical phenomena, and laboratory plasma experiments, where non-equilibrium conditions and multiple ion species are prevalent. The results are analyzed in the context of space plasma parameters relevant region within Earth's magnetosphere.
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CC1: 'Insights and Queries on Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma', Sudhir Sawasiya, 24 Nov 2024
This study presents a valuable contribution to the understanding of electromagnetic ion cyclotron (EMIC) waves in a magnetized plasma environment with multiple ion species. The integration of temperature anisotropy and Kappa distribution parameters in analyzing wave behavior is both innovative and essential for advancing theoretical plasma physics. The manuscript’s focus on these aspects fills a critical gap in understanding wave dynamics in conditions akin to the magnetosphere.
The clarity of the presented theoretical framework, supported by detailed numerical simulations and graphical results, is highly commendable. Such an approach not only enhances the comprehensiveness of the analysis but also facilitates better insights into the interaction between plasma parameters and wave properties.
Questions for Discussion:
1.How does temperature anisotropy quantitatively influence the growth rates and damping mechanisms of EMIC waves in a multi-species plasma?
2.What specific challenges are associated with modeling the interactions among different ion species in the magnetosphere, and how effectively does this study overcome them?
3.Can the findings regarding Kappa distribution impacts be extended to extreme astrophysical environments, such as the solar wind or planetary magnetospheres?
Overall, this work sets a strong foundation for future explorations into wave-particle interactions in complex plasma systems.
Citation: https://doi.org/10.5194/angeo-2024-25-CC1 -
AC1: 'Reply on CC1', Rahul Bhaisaniya, 25 Nov 2024
We sincerely appreciate the valuable insights and thought-provoking questions regarding our study. Below are detailed responses to the points raised:
- How does temperature anisotropy quantitatively influence the growth rates and damping mechanisms of EMIC waves in a multi-species plasma?
Temperature anisotropy, defined as the ratio A=T⊥/T∥ directly affects the growth rates of EMIC waves. When T⊥>T∥ (positive anisotropy), the plasma exhibits free energy that drives the wave instability, resulting in enhanced growth rates. Conversely, when T⊥<T∥ (negative anisotropy), damping mechanisms dominate, and wave growth is suppressed. The influence is highly sensitive to ion composition, with heavier ions like He+ and O+ contributing distinct resonance peaks due to their mass-dependent gyrofrequencies. In this study, the integration of the Kappa distribution further modulates the instability thresholds, amplifying growth rates for lower values of kappa (indicating higher non-thermal populations).
- What specific challenges are associated with modeling the interactions among different ion species in the magnetosphere, and how effectively does this study overcome them?
Modeling multi-ion species plasmas introduces challenges such as:
- Resonance Conditions: Each ion species resonates with the EMIC waves at different frequencies, requiring precise solutions.
- Wave Damping and Dispersion: The interplay of multiple ion species complicates the determination of growth and damping rates, particularly when coupled with non-Maxwellian distributions.
- Computational Complexity: Solving fourth-degree dispersion relations in multi-ion plasmas demands robust numerical methods and efficient computation.
This study addresses these challenges effectively by employing numerical techniques to solve the dispersion relation and incorporating the Kappa distribution to account for non-Maxwellian effects. The results provide a comprehensive understanding of multi-ion interactions, particularly highlighting species-specific impacts on wave amplification and propagation.
- Can the findings regarding Kappa distribution impacts be extended to extreme astrophysical environments, such as the solar wind or planetary magnetospheres?
Yes, the findings have significant implications for extreme astrophysical environments:
- Solar Wind: The Kappa distribution is commonly observed in the solar wind, where non-thermal particle populations dominate. The insights from this study can enhance our understanding of wave-particle interactions and energy transfer in the solar wind’s plasma.
- Planetary Magnetospheres: Many planetary magnetospheres, such as Jupiter’s and Saturn’s, contain multi-ion plasmas influenced by ion escape and magnetospheric dynamics. The study’s approach to incorporating temperature anisotropy and non-Maxwellian effects is highly relevant for understanding EMIC wave behavior in such environments.
- Astrophysical Shocks: The results can also inform studies of collisionless shocks, where Kappa distributions naturally arise due to energy dissipation mechanisms.
These extensions would require validation against observational data from missions like THEMIS, MMS, or Cassini to confirm the universality of the study's findings.
Citation: https://doi.org/10.5194/angeo-2024-25-AC1
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AC1: 'Reply on CC1', Rahul Bhaisaniya, 25 Nov 2024
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RC1: 'Comment on angeo-2024-25', Anonymous Referee #1, 27 Dec 2024
“Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma.” by Rahul Bhaisaniya and Ganpat Ahirwar
The manuscript presented the impacts of temperature anisotropy (Kapppa distributions) on Electromagnetic ion cyclotron (EMIC) waves in multi-ion plasma environments. In particular, the authors evaluated the wave dispersion relations, growth rates, and spatial structures of EMIC waves by the effects of the temperature anisotropy. These results may be important for a space plasma community, however, these results have already been discussed in the other previous studies. I cannot find the novelty and/or new findings of this manuscript by the effects of Kappa distributions. Therefore, I recommend that the authors should resubmit the manuscript with significant modifications. Please see detailed comments below.
[Major comments]
(1) “RESULT AND DISCUSSION” section
It looks that all the results (resonant energy, linear growth rates etc.) in this manuscript have already been discussed in the other previous studies.
Ahirwar, R. Meda, Effect of parallel electric field on EMIC waves with kappa distribution function, https://doi.org/10.1063/5.0000681
Meda, G. Ahirwar, Effect of kappa distribution function on EMIC instability in cusp region, https://doi.org/10.1063/1.5098751
Lazar, The electromagnetic ion-cyclotron instability in bi-Kappa distributed plasmas, https://doi.org/10.1051/0004-6361/201219861
Sugiyama, H., S. Singh, Y. Omura, M. Shoji, D. Nunn, and D. Summers (2015), Electromagnetic ion cyclotron waves in the Earth's magnetosphere with a kappa-Maxwellian particle distribution, J. Geophys. Res. Space Physics, 120, 8426–8439, doi:10.1002/2015JA021346.
In comparison with these previous studies including the effects of Kappa distributions, the authors must emphasize the novelty and new findings of this manuscript. In the present form, the novelty of this manuscript is very weak.
(2) Effects of nonlinear growth
EMIC wave growth can be essentially characterized by nonlinear effects (e.g., Shoji & Omura, JGR space physics, 2013), but there are no discussions on the nonlinear effects. The authors should discuss in the effects of nonlinear wave growth by Kappa distributions.
[Minor comments]
Line 37: Region24?
Quantitatively mentioning these two important issues regarding the differences with previous studies and the influence of the growth rates of nonlinear waves are necessary for the validation of the new importance of EMIC waves with kappa distributions. We hope that these comments will be useful for your further research.
Citation: https://doi.org/10.5194/angeo-2024-25-RC1 -
AC2: 'Reply on RC1', Rahul Bhaisaniya, 02 Jan 2025
Dear RC ,
I am submitting the response to reviewer comments for the manuscript titled "Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma" (Manuscript ID: angeo-2024-25). The response document addresses the points raised by the RC1, and the necessary revisions have been incorporated into the manuscript.
Please find the response document attached for your review.
Thank you for your attention, and I look forward to your feedback.
Best regards,
Rahul Bhaisaniya
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AC2: 'Reply on RC1', Rahul Bhaisaniya, 02 Jan 2025
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CC2: 'Comment on angeo-2024-25 Comments on Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma', Soniya Patel, 08 Jan 2025
Comments
The present study builds upon foundational research such as Patel et al. (2011), which investigated the role of ion beam velocities and anisotropies on electromagnetic ion cyclotron (EMIC) waves in the auroral acceleration region. By introducing the Kappa distribution and multi-ion species dynamics, this study advances our understanding of wave-particle interactions under more generalized plasma conditions. The inclusion of temperature anisotropy and non-thermal particle effects enhances the theoretical framework for predicting EMIC wave behavior in the magnetosphere and beyond.
The integration of Kappa distribution complements earlier results by addressing non-thermal high-energy populations often present in space plasmas, extending the scope to environments such as the solar wind and planetary magnetospheres. Furthermore, the focus on multi-ion plasmas introduces realistic complexity by accounting for competing resonances from ions like H+, He+, and O+, a significant departure from the single-ion framework adopted in Patel et al. (2011).
Queries for Discussion:
1. How does the integration of the Kappa distribution refine earlier findings on EMIC wave growth driven by ion beam anisotropy?
2. What new insights emerge from the multi-ion plasma approach that were not addressed in single-ion studies like Patel et al. (2011)?
3. How do temperature anisotropy and Kappa indices jointly influence the growth length and resonant energy transfer in EMIC waves?Citation: https://doi.org/10.5194/angeo-2024-25-CC2 -
AC3: 'Reply on CC2', Rahul Bhaisaniya, 08 Jan 2025
We sincerely appreciate the valuable insights and thought-provoking questions regarding our study. Below are detailed responses to the points raised:
- How does the integration of the Kappa distribution refine earlier findings on EMIC wave growth driven by ion beam anisotropy?
Response -The integration of the Kappa distribution refines earlier findings by accounting for the presence of high-energy, non-thermal particles commonly found in space plasmas. These particles significantly influence the energy transfer and wave-particle interaction mechanisms, which were not addressed in studies using Maxwellian distributions, such as Patel et al. (2011). Specifically:
- Wave Growth Enhancement: The Kappa distribution allows for a higher concentration of suprathermal particles, which enhances the resonant energy transfer between particles and EMIC waves. This leads to an increased growth rate compared to Maxwellian models under similar anisotropy conditions.
- Modified Resonance Dynamics: Non-thermal populations in the Kappa framework shift the resonant frequencies and broaden the range of wave-particle resonance, providing a more generalized picture of EMIC wave propagation.
- Temperature Dependence: The interplay between the ion beam anisotropy and the suprathermal particle density (characterized by lower Kappa indices) results in more accurate predictions of wave growth rates in regions with varying plasma densities, such as the plasmapause or auroral zones.
- What new insights emerge from the multi-ion plasma approach that were not addressed in single-ion studies like Patel et al. (2011)?
Response - The multi-ion plasma approach introduces the following new insights that were absent in single-ion studies like Patel et al. (2011):
- Competing Resonances: The inclusion of multiple ion species (H+, He+, and O+) reveals the interplay of competing cyclotron resonances. Each ion species contributes to wave growth and damping in distinct frequency ranges, creating a more realistic representation of magnetospheric plasmas.
- Ion Mass and Charge Effects: Heavier ions like He+ and O+ amplify EMIC wave growth due to their higher mass, which lowers their gyrofrequency and modifies the wave dispersion characteristics. This effect is particularly pronounced near the plasmapause, where heavy ion concentrations are higher.
- Cross-Species Interactions: The presence of multiple ion species introduces cross-species interactions that can lead to hybrid modes, which are not observed in single-ion studies. This provides a better understanding of wave behavior in complex plasma environments, such as the auroral acceleration region or planetary magnetospheres.
- Space Weather Implications: Multi-ion plasmas better capture the dynamics of geomagnetic storms and substorms, where ion compositions vary due to solar wind influx or ionospheric outflows.
- How do temperature anisotropy and Kappa indices jointly influence the growth length and resonant energy transfer in EMIC waves?
Response - The combined effects of temperature anisotropy and Kappa indices significantly influence the growth length and energy transfer in EMIC waves:
- Growth Length Reduction: Lower Kappa indices (e.g., = 2) represent higher populations of suprathermal particles, which enhance wave-particle interactions. This leads to a shorter growth length, as more energy is rapidly transferred from particles to the wave. Conversely, higher Kappa indices ( > 6) result in weaker interactions and longer growth lengths, resembling Maxwellian conditions.
- Energy Transfer Efficiency: Temperature anisotropy (T⊥/T∥ > 1) provides the free energy required for wave amplification. When combined with a low Kappa index, the availability of suprathermal particles further enhances the energy transfer efficiency, increasing the wave growth rate.
- Non-Maxwellian Effects: The inclusion of the Kappa distribution modifies the velocity distribution function, broadening the range of resonant velocities. This enables the wave to interact with a wider population of particles, particularly in plasmas with significant temperature anisotropies.
- Localized Dynamics: In regions such as the plasmapause or auroral acceleration zone, where strong temperature anisotropies coexist with non-thermal populations, the combined effects predict more intense and localized wave growth compared to traditional Maxwellian models.
These refinements collectively advance the understanding of EMIC wave propagation in realistic space plasma conditions, extending beyond the scope of earlier studies like Patel et al. (2011).
Citation: https://doi.org/10.5194/angeo-2024-25-AC3
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AC3: 'Reply on CC2', Rahul Bhaisaniya, 08 Jan 2025
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CC3: 'Comment on angeo-2024-25 Comments on Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma', Soniya Patel, 08 Jan 2025
Dear Sir
I am sending the reply of Community comments of ANGEO Preprint:
Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma
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AC4: 'Reply on CC3', Rahul Bhaisaniya, 08 Jan 2025
We sincerely appreciate the valuable insights and thought-provoking questions regarding our study. Below are detailed responses to the points raised:
- How does the integration of the Kappa distribution refine earlier findings on EMIC wave growth driven by ion beam anisotropy?
Response -The integration of the Kappa distribution refines earlier findings by accounting for the presence of high-energy, non-thermal particles commonly found in space plasmas. These particles significantly influence the energy transfer and wave-particle interaction mechanisms, which were not addressed in studies using Maxwellian distributions, such as Patel et al. (2011). Specifically:
- Wave Growth Enhancement: The Kappa distribution allows for a higher concentration of suprathermal particles, which enhances the resonant energy transfer between particles and EMIC waves. This leads to an increased growth rate compared to Maxwellian models under similar anisotropy conditions.
- Modified Resonance Dynamics: Non-thermal populations in the Kappa framework shift the resonant frequencies and broaden the range of wave-particle resonance, providing a more generalized picture of EMIC wave propagation.
- Temperature Dependence: The interplay between the ion beam anisotropy and the suprathermal particle density (characterized by lower Kappa indices) results in more accurate predictions of wave growth rates in regions with varying plasma densities, such as the plasmapause or auroral zones.
- What new insights emerge from the multi-ion plasma approach that were not addressed in single-ion studies like Patel et al. (2011)?
Response - The multi-ion plasma approach introduces the following new insights that were absent in single-ion studies like Patel et al. (2011):
- Competing Resonances: The inclusion of multiple ion species (H+, He+, and O+) reveals the interplay of competing cyclotron resonances. Each ion species contributes to wave growth and damping in distinct frequency ranges, creating a more realistic representation of magnetospheric plasmas.
- Ion Mass and Charge Effects: Heavier ions like He+ and O+ amplify EMIC wave growth due to their higher mass, which lowers their gyrofrequency and modifies the wave dispersion characteristics. This effect is particularly pronounced near the plasmapause, where heavy ion concentrations are higher.
- Cross-Species Interactions: The presence of multiple ion species introduces cross-species interactions that can lead to hybrid modes, which are not observed in single-ion studies. This provides a better understanding of wave behavior in complex plasma environments, such as the auroral acceleration region or planetary magnetospheres.
- Space Weather Implications: Multi-ion plasmas better capture the dynamics of geomagnetic storms and substorms, where ion compositions vary due to solar wind influx or ionospheric outflows.
- How do temperature anisotropy and Kappa indices jointly influence the growth length and resonant energy transfer in EMIC waves?
Response - The combined effects of temperature anisotropy and Kappa indices significantly influence the growth length and energy transfer in EMIC waves:
- Growth Length Reduction: Lower Kappa indices (e.g., = 2) represent higher populations of suprathermal particles, which enhance wave-particle interactions. This leads to a shorter growth length, as more energy is rapidly transferred from particles to the wave. Conversely, higher Kappa indices ( > 6) result in weaker interactions and longer growth lengths, resembling Maxwellian conditions.
- Energy Transfer Efficiency: Temperature anisotropy (T⊥/T∥ > 1) provides the free energy required for wave amplification. When combined with a low Kappa index, the availability of suprathermal particles further enhances the energy transfer efficiency, increasing the wave growth rate.
- Non-Maxwellian Effects: The inclusion of the Kappa distribution modifies the velocity distribution function, broadening the range of resonant velocities. This enables the wave to interact with a wider population of particles, particularly in plasmas with significant temperature anisotropies.
- Localized Dynamics: In regions such as the plasmapause or auroral acceleration zone, where strong temperature anisotropies coexist with non-thermal populations, the combined effects predict more intense and localized wave growth compared to traditional Maxwellian models.
These refinements collectively advance the understanding of EMIC wave propagation in realistic space plasma conditions, extending beyond the scope of earlier studies like Patel et al. (2011).
Citation: https://doi.org/10.5194/angeo-2024-25-AC4 -
AC3: 'Reply on CC2', Rahul Bhaisaniya, 08 Jan 2025
We sincerely appreciate the valuable insights and thought-provoking questions regarding our study. Below are detailed responses to the points raised:
- How does the integration of the Kappa distribution refine earlier findings on EMIC wave growth driven by ion beam anisotropy?
Response -The integration of the Kappa distribution refines earlier findings by accounting for the presence of high-energy, non-thermal particles commonly found in space plasmas. These particles significantly influence the energy transfer and wave-particle interaction mechanisms, which were not addressed in studies using Maxwellian distributions, such as Patel et al. (2011). Specifically:
- Wave Growth Enhancement: The Kappa distribution allows for a higher concentration of suprathermal particles, which enhances the resonant energy transfer between particles and EMIC waves. This leads to an increased growth rate compared to Maxwellian models under similar anisotropy conditions.
- Modified Resonance Dynamics: Non-thermal populations in the Kappa framework shift the resonant frequencies and broaden the range of wave-particle resonance, providing a more generalized picture of EMIC wave propagation.
- Temperature Dependence: The interplay between the ion beam anisotropy and the suprathermal particle density (characterized by lower Kappa indices) results in more accurate predictions of wave growth rates in regions with varying plasma densities, such as the plasmapause or auroral zones.
- What new insights emerge from the multi-ion plasma approach that were not addressed in single-ion studies like Patel et al. (2011)?
Response - The multi-ion plasma approach introduces the following new insights that were absent in single-ion studies like Patel et al. (2011):
- Competing Resonances: The inclusion of multiple ion species (H+, He+, and O+) reveals the interplay of competing cyclotron resonances. Each ion species contributes to wave growth and damping in distinct frequency ranges, creating a more realistic representation of magnetospheric plasmas.
- Ion Mass and Charge Effects: Heavier ions like He+ and O+ amplify EMIC wave growth due to their higher mass, which lowers their gyrofrequency and modifies the wave dispersion characteristics. This effect is particularly pronounced near the plasmapause, where heavy ion concentrations are higher.
- Cross-Species Interactions: The presence of multiple ion species introduces cross-species interactions that can lead to hybrid modes, which are not observed in single-ion studies. This provides a better understanding of wave behavior in complex plasma environments, such as the auroral acceleration region or planetary magnetospheres.
- Space Weather Implications: Multi-ion plasmas better capture the dynamics of geomagnetic storms and substorms, where ion compositions vary due to solar wind influx or ionospheric outflows.
- How do temperature anisotropy and Kappa indices jointly influence the growth length and resonant energy transfer in EMIC waves?
Response - The combined effects of temperature anisotropy and Kappa indices significantly influence the growth length and energy transfer in EMIC waves:
- Growth Length Reduction: Lower Kappa indices (e.g., = 2) represent higher populations of suprathermal particles, which enhance wave-particle interactions. This leads to a shorter growth length, as more energy is rapidly transferred from particles to the wave. Conversely, higher Kappa indices ( > 6) result in weaker interactions and longer growth lengths, resembling Maxwellian conditions.
- Energy Transfer Efficiency: Temperature anisotropy (T⊥/T∥ > 1) provides the free energy required for wave amplification. When combined with a low Kappa index, the availability of suprathermal particles further enhances the energy transfer efficiency, increasing the wave growth rate.
- Non-Maxwellian Effects: The inclusion of the Kappa distribution modifies the velocity distribution function, broadening the range of resonant velocities. This enables the wave to interact with a wider population of particles, particularly in plasmas with significant temperature anisotropies.
- Localized Dynamics: In regions such as the plasmapause or auroral acceleration zone, where strong temperature anisotropies coexist with non-thermal populations, the combined effects predict more intense and localized wave growth compared to traditional Maxwellian models.
These refinements collectively advance the understanding of EMIC wave propagation in realistic space plasma conditions, extending beyond the scope of earlier studies like Patel et al. (2011).
Citation: https://doi.org/10.5194/angeo-2024-25-AC3
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AC4: 'Reply on CC3', Rahul Bhaisaniya, 08 Jan 2025
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RC2: 'Comment on angeo-2024-25', Anonymous Referee #2, 25 Feb 2025
Review of “Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma” by Bhaisaniya et al.
Summary:
The authors address the combined effects of temperature anisotropy along with Kappa ion distributions on the EMIC wave dispersion relation. The study is significant as the inclusion of a bi-Maxwellian (temperature anisotropy) alone will not always describe the realistic plasma conditions and there is a need to incorporate Kappa distributions for accurate description EMIC waves in space plasmas. However, there have been few studies who have attempted this in the past and the reviewer is unable to find any novelty in the results. In general, the manuscript presentation is not clear and needs a lot of improvement in language and scientific explanation of the results. The manuscript may be encouraged for a resubmission after additional work and significant modifications.
A few major comments are as follows:
- What is the novelty in the work? How is the results different from the past similar works reported? For example, Sugiyama et al., 2015 talks about in detail how the dispersion relation and EMIC wave properties are impacted by a kappa-Maxwellian distribution function. Few other works which addresses similar study are listed below for the author’s reference.
- There is a need to rewrite the whole introduction section. Authors start to introduce EMIC waves and suddenly talk about auroral acceleration regions (see Lines 30-37).
- The referencing is not proper throughout the paper: sometimes it appears as numbered (Lines 29, 37 etc.), sometimes just as author name (Lines 30, 32, etc.), or sometimes not citation (Line 167, 174 etc.,) . Please use proper referencing format. The authors may also want to quote the correct references: for instance, the reviewer could not find the reference “Anderson, B. J., and Williams, D. J.: The electromagnetic ion cyclotron wave and its interaction with the magnetosphere, Space Sci. Rev., 89(1–2), 253–268, 1999.”
- What is tanh, tano etc? They are not defined in the manuscript or in the equations.
- Different terms need to be defined and described before they are used in the equations and in the text. How you obtain an equation, steps to reach there or if it is taken from another paper, proper referencing is required.
- Conclusions are written in much generalized way, rather than focusing on the results obtained in the paper. A summary section may be included which can list major results from this work.
Suggested References:
Cattaert, T., M. A. Hellberg, and R. L. Mace (2007), Oblique propagation of electromagnetic waves in a kappa-Maxwellian plasma, Phys. Plasmas, 14(8), 082111, doi:10.1063/1.2766647.
M. A. Hellberg, R. L. Mace; Generalized plasma dispersion function for a plasma with a kappa-Maxwellian velocity distribution. Phys. Plasmas 1 May 2002; 9 (5): 1495–1504, https://doi.org/10.1063/1.1462636
Lazar, M. (2012), The electromagnetic ion-cyclotron instability in bi-kappa distributed plasmas, Astron. Astrophys., 547, A94, doi:10.1051/0004-6361/201219861.
Omura, Y., J. Pickett, B. Grison, O. Santolik, I. Dandouras, M. Engebretson, P. M. E. Decreau, and A. Masson (2010), Theory and observation of electromagnetic ion cyclotron triggered emissions in the magnetosphere, J. Geophys. Res., 115, A07234, doi:10.1029/2010JA015300
Sugiyama, H., S. Singh, Y. Omura, M. Shoji, D. Nunn, and D. Summers (2015), Electromagnetic ion cyclotron waves in the Earth's magnetosphere with a kappa-Maxwellian particle distribution, J. Geophys. Res. Space Physics, 120, 8426–8439, doi:10.1002/2015JA021346.
Xiao, F., Q. Zhou, H. He, H. Zheng, and S. Wang (2007), Electromagnetic ion cyclotron waves instability threshold condition of suprathermal protons by kappa distribution, J. Geophys. Res., 112, A07219, doi:10.1029/2006JA012050.
Xue, S., R. M. Thorne, and D. Summers (1993), Electromagnetic ion-cyclotron instability in space plasmas, J. Geophys. Res., 98(A10), 17,475–17,484, doi:10.1029/93JA00790.
Xue, S., R. M. Thome, and D. Summers (1996a), Growth and damping of oblique electromagnetic ion cyclotron waves in the Earth's magnetosphere, J. Geophys. Res., 101(A7), 15,457–15,466, doi:10.1029/96JA01088.
Xue, S., R. M. Thorne, and D. Summers (1996b), Parametric study of electromagnetic ion cyclotron instability in the Earth's magnetosphere, J. Geophys. Res., 101, 15,467–15,474, doi:10.1029/96JA01087.
Citation: https://doi.org/10.5194/angeo-2024-25-RC2 -
AC5: 'Reply on RC2', Rahul Bhaisaniya, 01 Mar 2025
We sincerely appreciate the reviewer's time and valuable feedback on our manuscript, "Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma." We have carefully considered the comments and made significant revisions to improve the manuscript's clarity, scientific explanations, and novelty. Below, we address each comment in detail.
Major Comments and Responses
- Novelty of the Work
We acknowledge the reviewer's concern regarding the novelty of our study. Our research presents a distinctive contribution by examining the combined effects of temperature anisotropy and the Kappa distribution function on the dispersion properties and growth rates of EMIC waves. While previous studies, such as Sugiyama et al. (2015), have analysed aspects of the Kappa-Maxwellian distribution, they do not comprehensively explore the interaction between temperature anisotropy and Kappa-distributed plasmas in a multi-ion environment.
Our study introduces the following novel aspects:
- Impact of multi-ion plasma composition (H⁺, He⁺, O⁺) under varying Kappa parameters :
Multi-Species Plasma: This study uniquely investigates EMIC wave growth in a multi-ion plasma environment (H+, He+, O+) more complexity compared to single-ion studies, a more realistic representation of space plasma compared to the predominantly single-ion focus of previous studies. This multi-species approach allows us to quantify the distinct contributions of each ion species to wave growth under varying Kappa distributions, a crucial aspect previously unexplored in this context.
- Temperature anisotropy effects coupled with Kappa distribution:
We go beyond previous studies by analyzing the combined influence of temperature anisotropy and Kappa distributions on EMIC wave properties. While some studies have examined these factors individually or with General loss cone distribution, their synergistic effects in a multi-ion environment have not been comprehensively investigated before. This approach highlights the interplay between these two factors and their impact on wave-particle interactions, a critical aspect absents in the cited studies.
- Implications for plasmapause and auroral regions:
Our results extend the understanding of EMIC wave growth to regions where multi-ion compositions dominate, such as near the plasmapause and in auroral acceleration zones particularly during space weather events like geomagnetic storms. We believe these specific environmental conditions have not been thoroughly discussed in the cited studies.
- This study delves deeper into the effects of Kappa distributions on EMIC wave growth by providing a quantitative evaluation. We systematically examine how variations in the Kappa parameter ( ) – for instance, comparing =2 (representing a significantly non-Maxwellian distribution) to =6 (approaching a Maxwellian distribution) – influence key wave characteristics such as growth rates, resonant energies, and spatial profiles. This level of quantitative analysis surpasses the scope of some previous studies, such as Sugiyama et al. (2015), which primarily focused on qualitative assessments of Kappa-Maxwellian particle distributions. By meticulously comparing these variations, our study unveils a crucial finding: low values significantly enhance EMIC wave growth, particularly for heavy ions, due to a pronounced increase in wave-particle resonances.
Comparison with Previous Work
Study
Focus
Limitation
Novelty of Our Work
Ahirwar & Meda (2020)
Effect of parallel electric fields on EMIC waves with Kappa distributions
Focuses on single-ion (H+) plasmas with effect of parallel electric fields
Our study extends previous research by investigating EMIC wave growth in multi-ion plasmas (H+, He+, O+), while also analyzing the combined effects of temperature anisotropy and κ values
Meda & Ahirwar (2019)
EMIC instability in cusp regions with Kappa distributions
Primarily studies wave growth near the cusp
Our work targets plasmapause and auroral zones, emphasizing relevance to diverse space environments
Lazar (2012)
Electromagnetic ion-cyclotron instability in bi-Kappa plasmas
Limited to bi-Kappa distributions in homogeneous plasmas
We study multi-ion plasmas with varying kappa and anisotropy in non-homogeneous environments.
Sugiyama et al. (2015)
EMIC waves with Kappa-Maxwellian distributions in the Earth's magnetosphere
Lacks detailed multi-ion analysis and does not quantify the role of heavy ions and use Kappa-Maxwellian distributions
We analyze how Kappa distributions influence the roles of H+, He+, and O+ in EMIC wave growth
To clearly highlight these contributions, we will revise the introduction and discussion sections, providing a detailed comparison with past literature, including Sugiyama et al. (2015).
Additionally, our study stands out from the cited references by reviewer in several key aspects:
- Multi-Species Plasma Composition
- Many of the cited references focus on single-ion species plasmas (e.g., hydrogen-dominated plasmas). Our study explicitly examines multi-species plasmas (H⁺, He⁺, O⁺) and their combined influence on EMIC wave propagation.
- Influence of Temperature Anisotropy
- Our research uniquely quantifies the role of temperature anisotropy in different ion species, determining its effect on EMIC wave growth.
- While Lazar (2012), Xue et al. (1996a, 1996b), and Xiao et al. (2007) discuss temperature anisotropy, they primarily focus on its impact in single-ion species plasmas or assume Maxwellian distributions.
- Our study provides a comprehensive analysis of anisotropy effects in multi-ion environments, which is crucial for understanding wave-particle interactions in space plasmas.
iii. Specific Focus on Kappa Distributions
- While Hellberg & Mace (2002) and Cattaert et al. (2007) examine kappa-Maxwellian distributions, they do so primarily in the context of generalized dispersion functions and oblique propagation.
- Our study directly links the value of kappa to EMIC wave growth rates in a multi-ion plasma, making it more application-oriented for space weather studies.
- Additionally, Our work provides quantitative comparisons between different kappa values (e.g., = 2 vs. = 6), whereas prior studies often treat kappa distributions as a general assumption.
- Growth Rate Analysis and Plasma Instability Thresholds
- While Xiao et al. (2007), Xue et al. (1993), and Sugiyama et al. (2015) discuss EMIC wave growth in various plasma conditions, they do not systematically compare how different kappa distributions affect instability thresholds.
- Our research contributes a detailed parametric study on the combined effects of kappa distributions and temperature anisotropy on wave growth rates, instability conditions, and wave-particle interactions.
- Introduction Section Requires Rewriting
We will extensively revise the Introduction to enhance clarity and logical flow:
- Introduction to EMIC Waves: The revised section now begins with a clear and concise explanation of EMIC waves, their role in space plasmas, and their significance in magnetospheric dynamics.
- Research Gap and Motivation: We will explicitly outline the limitations of previous studies, particularly the lack of a combined analysis of temperature anisotropy and Kappa-distributed plasmas. Despite extensive research on EMIC wave propagation, many previous studies have primarily focused on single-ion plasmas or assumed Maxwellian velocity distributions. However, space plasmas are often characterized by multi-ion compositions (H⁺, He⁺, and O⁺) and non-Maxwellian particle distributions, particularly the Kappa distribution, which better represents suprathermal particles. While some studies have investigated temperature anisotropy effects and Kappa distributions separately, a comprehensive analysis of their combined impact on EMIC wave growth in multi-ion plasmas remains limited. This gap in knowledge motivates our study, which systematically examines how temperature anisotropy and Kappa-distributed plasmas jointly influence the growth and dispersion of EMIC waves.
- Connection to Space Plasma and Auroral Acceleration Regions: We will strengthen the link between EMIC waves and auroral acceleration regions, emphasizing their interaction mechanisms. EMIC waves play a significant role in magnetospheric plasma dynamics, particularly in regions such as the plasmapause and auroral acceleration zones, where interactions with energetic ions can lead to wave amplification. These waves contribute to the loss of energetic ring current particles via pitch-angle scattering, affecting radiation belt dynamics. The presence of non-Maxwellian suprathermal ions, described by the Kappa distribution, alters wave-particle interactions, making it essential to investigate how these distributions modify EMIC wave characteristics in auroral and near-Earth plasma environments.
- Referencing Issues
We will address all referencing inconsistencies by:
- Ensuring uniformity in citation style throughout the manuscript.
- Verifying accuracy of all references and ensuring proper citation of previously published works.
- Correcting the Anderson and Williams citation (1999) and properly formatting missing references.
- Adding missing citations at critical points (e.g., lines 167, 174, and other relevant sections).
- Definition of Terms (tanh, tano, etc.)
We acknowledge the oversight in defining key terms such as "tano." In the revised manuscript, we have:
- Clearly defined all terms when first introduced in the text.
- Explained mathematical functions such as tanh and tano, ensuring they are used correctly.
- Provided references or derivations for equations that rely on these terms.
- Clarification of Equations and Their Derivation
We will provide additional explanations and derivations for key equations, ensuring:
- All equations are properly introduced and referenced, with explicit derivations where applicable.
- Clear descriptions of physical significance accompany the equations, helping contextualize their role in our analysis.
- Proper citations are included if an equation is taken from previous literature.
- Generalized Conclusions
To enhance the manuscript's impact, we will refine the conclusion section by:
- Focusing on key findings, specifically:
- The influence of temperature anisotropy on EMIC wave dispersion.
- The role of Kappa distribution in modifying wave growth rates.
- The combined effect of these parameters in determining wave stability.
- Adding a summary section that explicitly highlights the main contributions and their significance for space weather research.
- Discussing practical implications, particularly in relation to wave-particle interactions in Earth's magnetosphere and their effects on geomagnetic storms.
- Incorporation of Suggested References
We appreciate the reviewer's recommendations for additional references. We will incorporated relevant citations, including:
- Cattaert et al. (2007) and Hellberg & Mace (2002) for discussions on non-Maxwellian distributions in plasma physics.
- Lazar (2012) and Omura et al. (2010) for wave-particle interactions and Kappa-distributed plasmas.
- Sugiyama et al. (2015) for direct comparisons with previous studies on EMIC waves.
- Xiao et al. (2007) for additional context on magnetospheric wave propagation. These references are now integrated into the literature review and discussion sections to strengthen the study’s foundation and comparative analysis.
We thank the reviewer for their constructive feedback, which has significantly improved the quality of our manuscript. By addressing all concerns, we will enhance the manuscript’s clarity, scientific rigor, and overall presentation. We hope that these revisions satisfactorily resolve the issues raised and that our manuscript is now suitable for publication. We look forward to further feedback and hope for a positive consideration of our revised manuscript.
Citation: https://doi.org/10.5194/angeo-2024-25-AC5
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AC6: 'Final Author Response for Manuscript MS No.: angeo-2024-25', Rahul Bhaisaniya, 02 Mar 2025
Dear Prof. Yoshizumi Miyoshi, Handling topic editor
We sincerely appreciate the valuable feedback provided by the reviewers and community members during the interactive discussion of our manuscript:
Title: Study of Temperature Anisotropy and Kappa Distribution Impacts on EMIC Waves in Multi-Species Magnetized Plasma
MS No.: angeo-2024-25We have carefully addressed all Referee Comments (RCs) and Community Comments (CCs), providing detailed explanations and justifications. The key concerns regarding theoretical aspects, methodology, and result interpretations have been thoroughly clarified in our responses.
Key Improvements Based on Review Feedback:
- Enhanced theoretical explanations on temperature anisotropy and the Kappa distribution function in multi-ion plasma for improved clarity and accessibility.
- Strengthened discussion on the implications of our findings for space plasma environments, particularly within the Earth's magnetosphere.
- Improved referencing to ensure completeness, accuracy, and stronger contextual support for key arguments.
The review process has been invaluable in refining the manuscript’s clarity, coherence, and scientific depth. The revised version has been carefully prepared in accordance with the journal’s guidelines, incorporating key refinements such as an expanded discussion on EMIC wave growth in multi-ion plasma, enhanced clarity in methodological explanations, and precise citation formatting.
As per the journal’s instructions, we are not submitting the revised manuscript at this stage but are prepared to do so upon confirmation.
We remain available for any further clarifications if needed. Thank you for your time and thoughtful evaluation of our work.
Best regards,
Rahul Bhaisaniya & Ganpat AhirwarCitation: https://doi.org/10.5194/angeo-2024-25-AC6
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