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
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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
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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
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“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
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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
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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
reply
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
reply
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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
reply
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
reply
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
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AC4: 'Reply on CC3', Rahul Bhaisaniya, 08 Jan 2025
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