Letter to Referee #1

We thank the referee for a constructive and thoughtful review. The referee has identified our intentions with the study, and their many constructive feedbacks has improved the quality of our research considerably.

In the revised manuscript, we treat the phase fluctuations more faithfully to the state-of-the-art in ionospheric GNSS. The referee’s many suggestions were here useful.

The referee will find in the track-changes PDF that all their suggestions and corrections have been addressed, but the bulk of the changes were made in response to the Referee #2’s critical yet constructive review, which includes the expansion of the Introduction section as well as the introduction of a flow chart (Figure 1 in the revised manuscript).

Sincerely,

Magnus F Ivarsen

Letter to Referee #2

Rebuttal

We thank the referee for a thorough and thoughtful review. The referee has scrutinized our findings and identified the novel contributions, and clarified with greater emphasis than we did in our original manuscript which contributions are not novel. The referee has evaluated our discussions in a clear and systematic manner.

In so doing, the referee cites Parker, Laundal, and paints a picture of the ionosphere-magnetosphere system purely in terms of magnetohydrodynamics (MHD) and steady-state flowing plasma, a well-known view with which the referee encourages familiarization. The referee states that our paper treats the magnetosphere-ionosphere (M-I) system as a ‘lumped element circuit model’, justifying a purely electrostatic description. We strongly disagree.

Idealized MHD versus interconnected fluid and kinetic processes

Contrary to the idealized MHD framework that the referee prefers, the driven M-I system is never in a steady state. Rather, localized and intermittent excursions away from that steady state are in a evolving dynamic equilibrium characterized by various electrostatic and kinetic processes that are electrically connected to the greater MHD flow; this is the energy cascade necessitated by the excursions and whose effect is to restore equilibrium in the flowing plasma.

When the referee states that electrostatic treatments are incompatible with causality they are confusing a system’s state with the sum of its parts. The steady-state MHD flow is always a description of the large-scale behaviour in the interconnected system, but individual processes that affect or are embedded in this flow are not necessarily adhering to the constraining equations of MHD in their primary description. The cumulative effects of these processes can produce behaviour that is otherwise not predicted by the individual processes themselves, wherein an overall MHD-behaviour is assured by nature at all times.

The Referee writes that the “magnetosphere-ionosphere interactions can be understood in terms of the magnetic field and the motion of plasma (the "B, v" paradigm)”. Again, we strongly disagree that this is sufficient to model all interactions within the interconnected system. The referee’s view as expressed in the above quoted sentence holds that particle precipitation is indistinguishable from field-aligned currents, which must flow, and whose vorticity induces strong, perpendicular electric fields in the plasma. It ignores the kinetic and statistical mechanical energy input, the wave-particle interactions that occur in Earth’s radiation belts, and the polarization electric fields that drive responsive currents of electrons and ions. While the physical description, the B, v-paradigm, always holds in the large-scale description of space plasmas it is insufficient as a sole explanation for observed and theorized ionospheric electrodynamics, as the dynamics directly depend on trillions of kinetic wave-particle interactions. 

The referee does however correctly state that unstable MHD wave energy is the source of these kinetic processes; the wave-modes that cause pitch angle scattering of the radiation belt’s hot population of drifting electrons grow in tandem with the Kelvin-Helmholtz waves that drive a cascade of ULF waves in the unstable MHD plasma.

Here, we are very grateful to the referee, as our original manuscript was drastically simplifying the M-I connection through its narrow focus on particle precipitation. In Figure 1 in the revised manuscript, we detail how unstable wave energy departed to the magnetosphere from the solar wind ultimately produce small-scale turbulence through a host of interconnected MHD and kinetic processes.

This narrative is informed by physics, and specifically by the recent literature. Shen et al. (2024) and Ivarsen et al. (2025) show a remarkable 1:1 relation between the evolution of plasma waves near magnetospheric equator and the development of 1km-scale and even <300m plasma turbulence in the ionosphere.

Methodological caveats

On the same note, the referee criticized our simplified analysis of the particles using the “Fang equations”, and here we concede the deficiency in largely ignoring the variation of specific chemistry, simplifying the collision frequencies, refraining from the detailed models of plasma production and loss that exists in the field. However, while such detailed models are merited when predicting the state of the ionosphere, our method of simplifying the chemistry does isolate a specific and characteristic statistical behaviour in the core dataset: the precipitating particle flux. A comprehensive modeling of the phenomenon is outside the scope of the present investigation. We have clarified the issue in the revised manuscript  

Conclusion

While we disagree both with the sentiment and conclusion expressed by the referee, we concede that some of the criticism raised was valid and called-for, and the referee pointed out areas where our treatment of the subject could be strengthened considerably. As a result, we have made extensive revisions to the manuscript, including a complete re-writing of the Introduction and a chart that simplifies and explains the energy cascade of unstable wave energy in the auroral ionosphere (see the revised manuscript and below in the present document for a description and justification).

We thank the referee for the constructive review of our paper, which has strengthened the presentation considerably. The referee’s many helpful minor points have likewise been corrected in the revised manuscript.

A note on the flowchart

As mentioned, the revised manuscript contains a rather busy flowchart that summarizes the energy cascade of unstable wave energy contained in the magnetosphere. Anticipating a discussion of its validity, what follows is a justification and description.

 

1.    The flow chart starts at the top with a cascade from solar wind pushing against the magnetosphere, which generates Kelvin-Helmholtz waves along the various boundaries that feature velocity shear. This interaction generates a variety of large-scale ULF waves, which serve as the primary carriers of energy from the outer magnetosphere toward the high-latitude ionosphere. This cascade is highly simplified in the chart for reasons of brevity.

2.    The energy may be transported downwards directly through waves. Here, the interchange instability typically triggers, structuring the density and producing “seeds”. The cascade end in kinetic Alfvén waves, which accelerate electrons and modulate the ionospheric (“convection”) electric field, often through Alfvén wave resonators set up by the boundary conditions.

3.    Another route for the energy is through the powering of plasma waves near the radiation belts, which scatter with hot electrons at certain angles, causing particle precipitation and diffuse aurorae. This route is known to dominate the total energy budget of the particle precipitation observed by DMSP (Newell et al., 2009, 2010).

4.    Both routes of energy expenditure move through ionospheric electrodynamics (the nodes Conductance, Density gradients, and Electric field modulation), which conduct electricity, facilitating the Joule heating that eventually expands the thermosphere, dissipating the initial unstable wave energy. The three nodes feature very high connectivity with the rest of the chart and are crucial for both Joule heating rates and the production of small-scale turbulence. Especially ionospheric conductance, which affects the most nodes in the chart, has, historically and at present, been considered a vital variable in geospace, regulating the entire process of energy dissipation (Wiltberger et al., 2017).

5.    In the chart, there are several connecting routes to the node Small-scale turbulence, and among them, we find several that directly embed a turbulent pattern or structure into the plasma from the wave organization of the magnetic field- lines (Ivarsen et al., 2024). On the other hand, the node Plasma instabilities has traditionally been considered to be an important cause of structuring in the auroral ionosphere, and may dominate structuring during conditions favourable to their triggering.

6.    The blue-colored nodes and arrows are explicitly expressed as waves and other multi-scale oscillatory variations in plasma density, highlighting the critical role of unstable wave energy in the M-I coupling.

7.    The red-colored arrows represent dampening effects, and correspond to the fact that conductance regulates the energy expenditure (and therefore causal purpose) of the M-I system.

Sincerely,

Magnus F Ivarsen

References:

Ivarsen, M. F., Miyashita, Y., St-Maurice, J.-P., Hussey, G. C., Pitzel, B., Galeschuk, D., Marei, S., Horne, R. B., Kasahara, Y., Matsuda, S., Kasahara, S., Keika, K., Miyoshi, Y., Yamamoto, K., Shinbori, A., Huyghebaert, D. R., Matsuoka, A., Yokota, S., & Tsuchiya, F. (2025). Characteristic E-Region Plasma Signature of Magnetospheric Wave-Particle Interactions. Physical Review Letters, 134(14), 145201. https://doi.org/10.1103/PhysRevLett.134.145201 

Ivarsen, M. F., Gillies, M. D., Huyghebaert, D. R., St-Maurice, J.-P., Lozinsky, A., Galeschuk, D., Donovan, E., & Hussey, G. C. (2024). Turbulence Embedded Into the Ionosphere by Electromagnetic Waves. Journal of Geophysical Research: Space Physics, 129(8), e2023JA032310. https://doi.org/10.1029/2023JA032310

Newell, P. T., Sotirelis, T., & Wing, S. (2009). Diffuse, monoenergetic, and broadband aurora: The global precipitation budget. Journal of Geophysical Research: Space Physics, 114(A9). https://doi.org/10.1029/2009JA014326 

Newell, P. T., Sotirelis, T., & Wing, S. (2010). Seasonal variations in diffuse, monoenergetic, and broadband aurora. Journal of Geophysical Research: Space Physics, 115(A3). https://doi.org/10.1029/2009JA014805 

Wiltberger, M., Merkin, V., Zhang, B., Toffoletto, F., Oppenheim, M., Wang, W., Lyon, J. G., Liu, J., Dimant, Y., Sitnov, M. I., & Stephens, G. K. (2017). Effects of electrojet turbulence on a magnetosphere-ionosphere simulation of a geomagnetic storm. Journal of Geophysical Research: Space Physics, 122(5), 5008–5027. https://doi.org/10.1002/2016JA023700

Shen, Y., Verkhoglyadova, O. P., Artemyev, A., Hartinger, M. D., Angelopoulos, V., Shi, X., & Zou, Y. (2024). Magnetospheric Control of Ionospheric TEC Perturbations via Whistler-Mode and ULF Waves. AGU Advances, 5(6), e2024AV001302. https://doi.org/10.1029/2024AV001302 

Letter to Referee #2

Rebuttal

We thank the referee for a thorough and thoughtful review. The referee has scrutinized our findings and identified the novel contributions, and clarified with greater emphasis than we did in our original manuscript which contributions are not novel. The referee has evaluated our discussions in a clear and systematic manner.

In so doing, the referee cites Parker, Laundal, and paints a picture of the ionosphere-magnetosphere system purely in terms of magnetohydrodynamics (MHD) and steady-state flowing plasma, a well-known view with which the referee encourages familiarization. The referee states that our paper treats the magnetosphere-ionosphere (M-I) system as a ‘lumped element circuit model’, justifying a purely electrostatic description. We strongly disagree.

Idealized MHD versus interconnected fluid and kinetic processes

Contrary to the idealized MHD framework that the referee prefers, the driven M-I system is never in a steady state. Rather, localized and intermittent excursions away from that steady state are in a evolving dynamic equilibrium characterized by various electrostatic and kinetic processes that are electrically connected to the greater MHD flow; this is the energy cascade necessitated by the excursions and whose effect is to restore equilibrium in the flowing plasma.

When the referee states that electrostatic treatments are incompatible with causality they are confusing a system’s state with the sum of its parts. The steady-state MHD flow is always a description of the large-scale behaviour in the interconnected system, but individual processes that affect or are embedded in this flow are not necessarily adhering to the constraining equations of MHD in their primary description. The cumulative effects of these processes can produce behaviour that is otherwise not predicted by the individual processes themselves, wherein an overall MHD-behaviour is assured by nature at all times.

The Referee writes that the “magnetosphere-ionosphere interactions can be understood in terms of the magnetic field and the motion of plasma (the "B, v" paradigm)”. Again, we strongly disagree that this is sufficient to model all interactions within the interconnected system. The referee’s view as expressed in the above quoted sentence holds that particle precipitation is indistinguishable from field-aligned currents, which must flow, and whose vorticity induces strong, perpendicular electric fields in the plasma. It ignores the kinetic and statistical mechanical energy input, the wave-particle interactions that occur in Earth’s radiation belts, and the polarization electric fields that drive responsive currents of electrons and ions. While the physical description, the B, v-paradigm, always holds in the large-scale description of space plasmas it is insufficient as a sole explanation for observed and theorized ionospheric electrodynamics, as the dynamics directly depend on trillions of kinetic wave-particle interactions. 

The referee does however correctly state that unstable MHD wave energy is the source of these kinetic processes; the wave-modes that cause pitch angle scattering of the radiation belt’s hot population of drifting electrons grow in tandem with the Kelvin-Helmholtz waves that drive a cascade of ULF waves in the unstable MHD plasma.

Here, we are very grateful to the referee, as our original manuscript was drastically simplifying the M-I connection through its narrow focus on particle precipitation. In Figure 1 in the revised manuscript, we detail how unstable wave energy departed to the magnetosphere from the solar wind ultimately produce small-scale turbulence through a host of interconnected MHD and kinetic processes.

This narrative is informed by physics, and specifically by the recent literature. Shen et al. (2024) and Ivarsen et al. (2025) show a remarkable 1:1 relation between the evolution of plasma waves near magnetospheric equator and the development of 1km-scale and even <300m plasma turbulence in the ionosphere.

Methodological caveats

On the same note, the referee criticized our simplified analysis of the particles using the “Fang equations”, and here we concede the deficiency in largely ignoring the variation of specific chemistry, simplifying the collision frequencies, refraining from the detailed models of plasma production and loss that exists in the field. However, while such detailed models are merited when predicting the state of the ionosphere, our method of simplifying the chemistry does isolate a specific and characteristic statistical behaviour in the core dataset: the precipitating particle flux. A comprehensive modeling of the phenomenon is outside the scope of the present investigation. We have clarified the issue in the revised manuscript  

Conclusion

While we disagree both with the sentiment and conclusion expressed by the referee, we concede that some of the criticism raised was valid and called-for, and the referee pointed out areas where our treatment of the subject could be strengthened considerably. As a result, we have made extensive revisions to the manuscript, including a complete re-writing of the Introduction and a chart that simplifies and explains the energy cascade of unstable wave energy in the auroral ionosphere (see the revised manuscript and below in the present document for a description and justification).

We thank the referee for the constructive review of our paper, which has strengthened the presentation considerably. The referee’s many helpful minor points have likewise been corrected in the revised manuscript, highlighted in the attached "bluetext" PDF.

A note on the flowchart

As mentioned, the revised manuscript contains a rather busy flowchart that summarizes the energy cascade of unstable wave energy contained in the magnetosphere. Anticipating a discussion of its validity, what follows is a justification and description.

 

1.    The flow chart starts at the top with a cascade from solar wind pushing against the magnetosphere, which generates Kelvin-Helmholtz waves along the various boundaries that feature velocity shear. This interaction generates a variety of large-scale ULF waves, which serve as the primary carriers of energy from the outer magnetosphere toward the high-latitude ionosphere. This cascade is highly simplified in the chart for reasons of brevity.

2.    The energy may be transported downwards directly through waves. Here, the interchange instability typically triggers, structuring the density and producing “seeds”. The cascade end in kinetic Alfvén waves, which accelerate electrons and modulate the ionospheric (“convection”) electric field, often through Alfvén wave resonators set up by the boundary conditions.

3.    Another route for the energy is through the powering of plasma waves near the radiation belts, which scatter with hot electrons at certain angles, causing particle precipitation and diffuse aurorae. This route is known to dominate the total energy budget of the particle precipitation observed by DMSP (Newell et al., 2009, 2010).

4.    Both routes of energy expenditure move through ionospheric electrodynamics (the nodes Conductance, Density gradients, and Electric field modulation), which conduct electricity, facilitating the Joule heating that eventually expands the thermosphere, dissipating the initial unstable wave energy. The three nodes feature very high connectivity with the rest of the chart and are crucial for both Joule heating rates and the production of small-scale turbulence. Especially ionospheric conductance, which affects the most nodes in the chart, has, historically and at present, been considered a vital variable in geospace, regulating the entire process of energy dissipation (Wiltberger et al., 2017).

5.    In the chart, there are several connecting routes to the node Small-scale turbulence, and among them, we find several that directly embed a turbulent pattern or structure into the plasma from the wave organization of the magnetic field- lines (Ivarsen et al., 2024). On the other hand, the node Plasma instabilities has traditionally been considered to be an important cause of structuring in the auroral ionosphere, and may dominate structuring during conditions favourable to their triggering.

6.    The blue-colored nodes and arrows are explicitly expressed as waves and other multi-scale oscillatory variations in plasma density, highlighting the critical role of unstable wave energy in the M-I coupling.

7.    The red-colored arrows represent dampening effects, and correspond to the fact that conductance regulates the energy expenditure (and therefore causal purpose) of the M-I system.

Sincerely,

Magnus F Ivarsen

References:

Ivarsen, M. F., Miyashita, Y., St-Maurice, J.-P., Hussey, G. C., Pitzel, B., Galeschuk, D., Marei, S., Horne, R. B., Kasahara, Y., Matsuda, S., Kasahara, S., Keika, K., Miyoshi, Y., Yamamoto, K., Shinbori, A., Huyghebaert, D. R., Matsuoka, A., Yokota, S., & Tsuchiya, F. (2025). Characteristic E-Region Plasma Signature of Magnetospheric Wave-Particle Interactions. Physical Review Letters, 134(14), 145201. https://doi.org/10.1103/PhysRevLett.134.145201 

Ivarsen, M. F., Gillies, M. D., Huyghebaert, D. R., St-Maurice, J.-P., Lozinsky, A., Galeschuk, D., Donovan, E., & Hussey, G. C. (2024). Turbulence Embedded Into the Ionosphere by Electromagnetic Waves. Journal of Geophysical Research: Space Physics, 129(8), e2023JA032310. https://doi.org/10.1029/2023JA032310

Newell, P. T., Sotirelis, T., & Wing, S. (2009). Diffuse, monoenergetic, and broadband aurora: The global precipitation budget. Journal of Geophysical Research: Space Physics, 114(A9). https://doi.org/10.1029/2009JA014326 

Newell, P. T., Sotirelis, T., & Wing, S. (2010). Seasonal variations in diffuse, monoenergetic, and broadband aurora. Journal of Geophysical Research: Space Physics, 115(A3). https://doi.org/10.1029/2009JA014805 

Wiltberger, M., Merkin, V., Zhang, B., Toffoletto, F., Oppenheim, M., Wang, W., Lyon, J. G., Liu, J., Dimant, Y., Sitnov, M. I., & Stephens, G. K. (2017). Effects of electrojet turbulence on a magnetosphere-ionosphere simulation of a geomagnetic storm. Journal of Geophysical Research: Space Physics, 122(5), 5008–5027. https://doi.org/10.1002/2016JA023700

Shen, Y., Verkhoglyadova, O. P., Artemyev, A., Hartinger, M. D., Angelopoulos, V., Shi, X., & Zou, Y. (2024). Magnetospheric Control of Ionospheric TEC Perturbations via Whistler-Mode and ULF Waves. AGU Advances, 5(6), e2024AV001302. https://doi.org/10.1029/2024AV001302