We sincerely appreciate the valuable insights and thought-provoking questions regarding our study. Below are detailed responses to the points raised:

1. 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).

1. 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.

1. 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.

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

We sincerely appreciate the valuable insights and thought-provoking questions regarding our study. Below are detailed responses to the points raised:

1. 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.

1. 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.

1. 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).

We sincerely appreciate the valuable insights and thought-provoking questions regarding our study. Below are detailed responses to the points raised:

1. 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.

1. 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.

1. 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).

We sincerely appreciate the valuable insights and thought-provoking questions regarding our study. Below are detailed responses to the points raised:

1. 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.

1. 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.

1. 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).

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

1. 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:

1. 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.

1. 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.

1. 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.

1. 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

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:

1. 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.

1. 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.

1. 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.

1. 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.

1. 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).

1. 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.

1. 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.

1. 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.

1. 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.