the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Apr 2022
Impulse-driven oscillations of the near-Earth’s magnetosphere
Hiroatsu Sato
Jan Trulsen
Per Even Sandholt
Charles Farrugia
Abstract. It is argued that a simple model based on magnetic image arguments suffices to give a convincing insight into both the basic static as well as dynamic properties of the near-Earth’s magnetosphere. Qualitative results can be obtained for the heating due to the compression of the radiation belts. The properties of this simple dynamic model for the solar wind – magnetosphere interaction are discussed and compared to observations. In spite of its simplicity, the model gives convincing results concerning the magnitudes of the near-Earth’s magnetic and electric fields. The database contains ground based results for magnetic field variation in response to shocks in the solar wind. The observations also include satellite data, here from the two Van Allen satellites.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(6663 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(6663 KB) - BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Hiroatsu Sato et al.
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-232', Anonymous Referee #1, 16 May 2022
The paper builds on and analyzes the performance of a simple model of solar wind – Earth’s magnetic field interaction. Consequences of a sudden pressure pulse in the solar wind for the dynamics of the system are then discussed and the respective variations are qualitatively evaluated. These are, in turn, compared with ground-based magnetometer and Van Allen Probes measurements. The claimed reasonable agreement is interpreted in terms of this simple model being, to the lowest order, sufficient to model the near-Earth magnetosphere.
I find the paper rather interesting, as such simple-model approach is quite rarely seen nowadays. On the other hand (or perhaps because of that), I have some doubts/questions concerning the model formulation and its comparison with the measurements.
Detailed comments
- Static limit in equation (1) and around: I feel this argumentation based on the pressure balance is well known. It would be more usual to have the solar wind dynamic pressure units (Figure 3) in nPa and to have the equation (1) in SI units. Also, it is worth noting that the -1/6 scaling resulting from this simple picture is often slightly violated in empirical magnetopause models, so I have some doubts about that “generally accepted” formulation.
- Equation (2) governing the assumed magnetopause oscillations: I believe that this is quite essential for the model formulation and should be better discussed and justified. First, what is the source of the inertia here? What typical values are found/considered? Do the typical speeds of magnetopause obtained here correspond to the observations? (these can be determined experimentally using multi-spacecraft measurements, Cluster was used for that as far as I know). Second, the damping coefficient should be discussed better. It is said that it does not correspond to the dissipation, but is rather a result of the phase-lag in the mathematical formulation. Ok; but I would be hesitant to call this a “physical mechanism” – and the energy should perhaps still go somewhere (?)
- 125-135: People typically consider ExB drift to be negligible for the radiation belts particles, as for high energies grad-B and curvature drifts dominate. I have thus some doubts about the calculation here. How was Figure 10 obtained? For what energies? What pitch angles? The asymmetry of magnetic field should result in some drift-shell splitting. None of this is discussed/described (and considered?).
- 160-165: what are the assumed values of the density here? The relative densities of high-energetic particles will be comparatively very low. Also, the energization of the radiation belt particles is typically due to (inward) radial diffusion, which, in turns, decreases the azimuthal drift velocity.
- Comparison with observations: it remains quite unclear what the model can or cannot predict and how this match or does not match the observations. The sudden change of the magnetic field measured due to the increase of the Chapman-Ferraro current (and magnetopause moving to lower distances) at the time of the pressure pulse is well known. The model might be in principle able to predict the subsequent oscillation period (?) and attenuation of the magnetic field pulsations (?), but these are difficult to see in the data and some more elaborated comparison with the model output is missing. Instead, the shock parameters (not really too relevant for the model evaluation (?)) are described.
- There was recently quite a large number of papers dealing with the shock effects on radiation belts / magnetospheric plasma waves which seem to be quite ignored in the present manuscript (e.g., Sun et al. (2015), doi: 12014JA020754; Foster et al. (2015), doi: doi:10.1002/2014JA020642; Tsuji et al. (2017), doi: 10.1002/2016JA023704; Blum et al. (2021), doi: 10.1029/2021GL092700 – and most likely many others they cite/are cited by).
- 295: This configuration of the three dipoles should be better described already in the beginning, not just here in the conclusions. The claimed “good agreement” between the model and observations is not really demonstrated.
Citation: https://doi.org/10.5194/egusphere-2022-232-RC1 - AC1: 'Reply on RC1', Hans Pecseli, 17 Jun 2022
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RC2: 'Comment on egusphere-2022-232', Takashi Kikuchi, 31 May 2022
Title: Impulse-driven oscillations of the near-Earth’s magnetosphere
Author(s): Hiroatsu Sato et al.
MS No.: egusphere-2022-232
[Comments]
There are major questions as listed below.
- The ground magnetic variations at high latitudes are described as being caused by magnetopause currents. However, ground magnetic variations at high latitudes are caused by ionospheric Hall currents driven by the electric field created by the dynamo in the outer magnetosphere (e.g., Tanaka et al., 2020 JGR, https:// doi.org/10.1029/2019JA027172). Furthermore, the field-aligned currents generated by the dynamo flow to the global ionosphere via the polar ionosphere, resulting in simultaneous occurrence of the preliminary impulse (PI) and main impulse (MI) of SC at high latitude and equator (Araki, 1994 AGU book). The authors are recommended to discuss their results in the context of the current system between the magnetosphere and ionosphere. The dynamos of the PI and MI have also been reproduced by the global simulations (Slinker et al., 1999 JGR; Fujita et al, 2003 JGR).
- Damping of the magnetosphere is attributed to the non-linearity of the equation (4). On the other hand, the FACs flow into the polar ionosphere and further to the global ionosphere, where the energy is consumed by the Pedersen currents (e.g., Kikuchi et al., 2021 EPS). When discussing the damping of the ground magnetic fields, it is advisable to discuss the energy loss in the ionosphere.
- The motion of plasma is described as being earthward, but the calculated and observed electric fields presented in the present paper are directed from the dawn to dusk, which drives sunward motion of plasma. Explanation or comments are required for the difference between the compression of the magnetopause and sunward motion of the magnetospheric plasma.
[Others]
Line 116
The Faraday’s law is equivalent to E=UxB?
Line 124
In Figure 9, the electric field is from the dawn to dusk, which drives sunward motion of plasma in the magnetosphere. If the electric field is induced by the increase in Bz and carried by the compressional MHD wave toward the Earth, the direction of the electric field must be westward, i.e., from the dusk to dawn. How is the dawn-to-dusk electric field generated by the moving magnetopause currents?
Line 147
Draw current vectors on the current lines of the FACs. Previous studies using the global simulations have shown that two kinds of FACs are generated by the compression of the magnetosphere (Slinker et al., 1999 JGR; Fujita et al., 2003 JGR; Tanaka, 2007 SSR), supplying the electric field and currents of the PI and MI of SC. The FAC pair inside the outside pair is also produced by the magnetopause currents?
Line 149
Please specify the energies of radiation belt particles and of particles that work as a generator of the FAC.
Line 157
Please note that the infinite inner impedance does not allow electric currents to flow, since I=V/(r+R) where r and R are the internal and load resistivities.
Line 160
Please note that the FAC is generated by the high-pressure plasma so that the pressure gradient force balances JxB force of the dynamo current J (Tanaka, 2007 SSR).
Lines 160-163
The equations for the current are the same in the warm and cold plasma regions. Please comment on the difference between the nature of the two currents.
Line 209
Ground magnetic disturbances are caused by ionospheric currents, particularly at auroral and subauroral latitudes (e.g., Araki et al., 1997 JGR). At middle and low latitudes, the magnetic fields are caused by magnetopause currents superimposed by weak ionospheric currents. At the dayside equator, the ionospheric Cowling currents work as a major source for the equatorial SC (Araki, 1994 AGU book).
Line 235
Figure 17 shows a typical SC in the morning, composed of positive/negative PI and negative/positive MI at lower/higher latitude part of the IMAGE magnetometer array. These magnetic fields are caused by ionospheric Hall currents surrounding the FACs (e.g., Kikuchi et al., 2022 Frontiers, doi: 10.3389/fspas.2022.879314). Note that the onset of PI at higher latitude (NAL, BJN) is simultaneous with those at lower latitude (NUR,,,,), because the ionospheric currents flow at the speed of light to the global ionosphere, including the equator (Kikuchi et al., 2021 EPS, DOI: 10.1186/s40623-020-01350-8). Magnetopause currents cause magnetic fields at low latitude, which is DL according to Araki (1994) model.
Line 248
Which part of the data is believed to have been caused by FAC?
Line 253
The electric fields measured by the satellites are from the dawn to dusk (Fig. 21), same as in the model calculation (Fig.9). The ExB drift velocity is sunward, which is opposite to the earthward motion of the magnetopause. The electric field observed in the ionosphere at middle latitude is also directed from the dawn to dusk, which lifts up the dayside ionosphere (Kikuchi et al., 2016 JGR, doi:10.1002/2015JA022166).
Line 259
RBSP spacecrafts are located deep inside the magnetosphere, not close to the magnetopause. The location of spacecrafts should be explicitly mentioned in the discussion.
Line 300
Phase relationships among the ground magnetic variations should be mentioned. If the magnetic variations are caused solely by the magnetopause currents, we would see coherent variations in multiple locations.
- AC2: 'Reply on RC2', Hans Pecseli, 30 Jun 2022
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-232', Anonymous Referee #1, 16 May 2022
The paper builds on and analyzes the performance of a simple model of solar wind – Earth’s magnetic field interaction. Consequences of a sudden pressure pulse in the solar wind for the dynamics of the system are then discussed and the respective variations are qualitatively evaluated. These are, in turn, compared with ground-based magnetometer and Van Allen Probes measurements. The claimed reasonable agreement is interpreted in terms of this simple model being, to the lowest order, sufficient to model the near-Earth magnetosphere.
I find the paper rather interesting, as such simple-model approach is quite rarely seen nowadays. On the other hand (or perhaps because of that), I have some doubts/questions concerning the model formulation and its comparison with the measurements.
Detailed comments
- Static limit in equation (1) and around: I feel this argumentation based on the pressure balance is well known. It would be more usual to have the solar wind dynamic pressure units (Figure 3) in nPa and to have the equation (1) in SI units. Also, it is worth noting that the -1/6 scaling resulting from this simple picture is often slightly violated in empirical magnetopause models, so I have some doubts about that “generally accepted” formulation.
- Equation (2) governing the assumed magnetopause oscillations: I believe that this is quite essential for the model formulation and should be better discussed and justified. First, what is the source of the inertia here? What typical values are found/considered? Do the typical speeds of magnetopause obtained here correspond to the observations? (these can be determined experimentally using multi-spacecraft measurements, Cluster was used for that as far as I know). Second, the damping coefficient should be discussed better. It is said that it does not correspond to the dissipation, but is rather a result of the phase-lag in the mathematical formulation. Ok; but I would be hesitant to call this a “physical mechanism” – and the energy should perhaps still go somewhere (?)
- 125-135: People typically consider ExB drift to be negligible for the radiation belts particles, as for high energies grad-B and curvature drifts dominate. I have thus some doubts about the calculation here. How was Figure 10 obtained? For what energies? What pitch angles? The asymmetry of magnetic field should result in some drift-shell splitting. None of this is discussed/described (and considered?).
- 160-165: what are the assumed values of the density here? The relative densities of high-energetic particles will be comparatively very low. Also, the energization of the radiation belt particles is typically due to (inward) radial diffusion, which, in turns, decreases the azimuthal drift velocity.
- Comparison with observations: it remains quite unclear what the model can or cannot predict and how this match or does not match the observations. The sudden change of the magnetic field measured due to the increase of the Chapman-Ferraro current (and magnetopause moving to lower distances) at the time of the pressure pulse is well known. The model might be in principle able to predict the subsequent oscillation period (?) and attenuation of the magnetic field pulsations (?), but these are difficult to see in the data and some more elaborated comparison with the model output is missing. Instead, the shock parameters (not really too relevant for the model evaluation (?)) are described.
- There was recently quite a large number of papers dealing with the shock effects on radiation belts / magnetospheric plasma waves which seem to be quite ignored in the present manuscript (e.g., Sun et al. (2015), doi: 12014JA020754; Foster et al. (2015), doi: doi:10.1002/2014JA020642; Tsuji et al. (2017), doi: 10.1002/2016JA023704; Blum et al. (2021), doi: 10.1029/2021GL092700 – and most likely many others they cite/are cited by).
- 295: This configuration of the three dipoles should be better described already in the beginning, not just here in the conclusions. The claimed “good agreement” between the model and observations is not really demonstrated.
Citation: https://doi.org/10.5194/egusphere-2022-232-RC1 - AC1: 'Reply on RC1', Hans Pecseli, 17 Jun 2022
-
RC2: 'Comment on egusphere-2022-232', Takashi Kikuchi, 31 May 2022
Title: Impulse-driven oscillations of the near-Earth’s magnetosphere
Author(s): Hiroatsu Sato et al.
MS No.: egusphere-2022-232
[Comments]
There are major questions as listed below.
- The ground magnetic variations at high latitudes are described as being caused by magnetopause currents. However, ground magnetic variations at high latitudes are caused by ionospheric Hall currents driven by the electric field created by the dynamo in the outer magnetosphere (e.g., Tanaka et al., 2020 JGR, https:// doi.org/10.1029/2019JA027172). Furthermore, the field-aligned currents generated by the dynamo flow to the global ionosphere via the polar ionosphere, resulting in simultaneous occurrence of the preliminary impulse (PI) and main impulse (MI) of SC at high latitude and equator (Araki, 1994 AGU book). The authors are recommended to discuss their results in the context of the current system between the magnetosphere and ionosphere. The dynamos of the PI and MI have also been reproduced by the global simulations (Slinker et al., 1999 JGR; Fujita et al, 2003 JGR).
- Damping of the magnetosphere is attributed to the non-linearity of the equation (4). On the other hand, the FACs flow into the polar ionosphere and further to the global ionosphere, where the energy is consumed by the Pedersen currents (e.g., Kikuchi et al., 2021 EPS). When discussing the damping of the ground magnetic fields, it is advisable to discuss the energy loss in the ionosphere.
- The motion of plasma is described as being earthward, but the calculated and observed electric fields presented in the present paper are directed from the dawn to dusk, which drives sunward motion of plasma. Explanation or comments are required for the difference between the compression of the magnetopause and sunward motion of the magnetospheric plasma.
[Others]
Line 116
The Faraday’s law is equivalent to E=UxB?
Line 124
In Figure 9, the electric field is from the dawn to dusk, which drives sunward motion of plasma in the magnetosphere. If the electric field is induced by the increase in Bz and carried by the compressional MHD wave toward the Earth, the direction of the electric field must be westward, i.e., from the dusk to dawn. How is the dawn-to-dusk electric field generated by the moving magnetopause currents?
Line 147
Draw current vectors on the current lines of the FACs. Previous studies using the global simulations have shown that two kinds of FACs are generated by the compression of the magnetosphere (Slinker et al., 1999 JGR; Fujita et al., 2003 JGR; Tanaka, 2007 SSR), supplying the electric field and currents of the PI and MI of SC. The FAC pair inside the outside pair is also produced by the magnetopause currents?
Line 149
Please specify the energies of radiation belt particles and of particles that work as a generator of the FAC.
Line 157
Please note that the infinite inner impedance does not allow electric currents to flow, since I=V/(r+R) where r and R are the internal and load resistivities.
Line 160
Please note that the FAC is generated by the high-pressure plasma so that the pressure gradient force balances JxB force of the dynamo current J (Tanaka, 2007 SSR).
Lines 160-163
The equations for the current are the same in the warm and cold plasma regions. Please comment on the difference between the nature of the two currents.
Line 209
Ground magnetic disturbances are caused by ionospheric currents, particularly at auroral and subauroral latitudes (e.g., Araki et al., 1997 JGR). At middle and low latitudes, the magnetic fields are caused by magnetopause currents superimposed by weak ionospheric currents. At the dayside equator, the ionospheric Cowling currents work as a major source for the equatorial SC (Araki, 1994 AGU book).
Line 235
Figure 17 shows a typical SC in the morning, composed of positive/negative PI and negative/positive MI at lower/higher latitude part of the IMAGE magnetometer array. These magnetic fields are caused by ionospheric Hall currents surrounding the FACs (e.g., Kikuchi et al., 2022 Frontiers, doi: 10.3389/fspas.2022.879314). Note that the onset of PI at higher latitude (NAL, BJN) is simultaneous with those at lower latitude (NUR,,,,), because the ionospheric currents flow at the speed of light to the global ionosphere, including the equator (Kikuchi et al., 2021 EPS, DOI: 10.1186/s40623-020-01350-8). Magnetopause currents cause magnetic fields at low latitude, which is DL according to Araki (1994) model.
Line 248
Which part of the data is believed to have been caused by FAC?
Line 253
The electric fields measured by the satellites are from the dawn to dusk (Fig. 21), same as in the model calculation (Fig.9). The ExB drift velocity is sunward, which is opposite to the earthward motion of the magnetopause. The electric field observed in the ionosphere at middle latitude is also directed from the dawn to dusk, which lifts up the dayside ionosphere (Kikuchi et al., 2016 JGR, doi:10.1002/2015JA022166).
Line 259
RBSP spacecrafts are located deep inside the magnetosphere, not close to the magnetopause. The location of spacecrafts should be explicitly mentioned in the discussion.
Line 300
Phase relationships among the ground magnetic variations should be mentioned. If the magnetic variations are caused solely by the magnetopause currents, we would see coherent variations in multiple locations.
- AC2: 'Reply on RC2', Hans Pecseli, 30 Jun 2022
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Hiroatsu Sato et al.
Hiroatsu Sato et al.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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