Ion&rsquo;s ring current: regularities of the energy density distributions on the main phase of geomagnetic storms

Kovtyukh, Alexander

doi:https://doi.org/10.5194/angeo-2023-10

Preprints

https://doi.org/10.5194/angeo-2023-10

Preprints

28 Mar 2023

| 28 Mar 2023

Status: this discussion paper is a preprint. It has been under review for the journal Annales Geophysicae (ANGEO). The manuscript was not accepted for further review after discussion.

Ion’s ring current: regularities of the energy density distributions on the main phase of geomagnetic storms

Alexander Kovtyukh

Abstract. Based on the results of measurements near the equatorial plane a fluxes of H⁺ and O⁺ ions of the ring current (RC) from the Explorer 45, AMPTE/CCE, and Van Allen Probes (A and B) satellites, a systematic analysis of spatial distributions of the energy density for these ions on the main phase of magnetic storms was carried out. The radial profile of the RC ions energy density is characterized by the maximum (L_m) and by the ratio of the energy densities of the ions and the magnetic field at this maximum (ß_m), and at L > L_m this profile is approximated by the function w(L) = w₀exp(–L/L₀). Quantitative dependences of the parameters L_m, ß_m, w₀ and L₀ on the D_st index, ion energy (E), and magnetic local time (MLT) are obtained; these dependences are different for H⁺ and O⁺ ions, as well as for ions of low (E < 60 keV) and higher energies. A strong azimuthal asymmetry of the RC ions with E ~ 1–300 keV at L > L_m was revealed: for H⁺+O⁺ and O⁺ ions, L₀ increases systematically with the increasing MLT from evening to midnight sector, while for H⁺ ions L₀ decreases; energy density of O⁺ ions is more uniformly distributed over MLT compared with H⁺ ions. For O⁺ ions with E ~ 1–300 keV, ß_m ∝ L_m^–6; this result this result shows that a deeper penetration of hot plasma into a geomagnetic trap, during strong storms, requires not only a stronger electric field of convection, but also a significant preliminary accumulation and acceleration of ions (especially O⁺ ions) in the source of the RC. It is shown that the greater |D_st| at the end of the main phase of storms, the smaller the contribution of ions with E < 60 keV and the greater the contribution of higher-energy ions to the RC energy density (the average energy of ions increases); such effect can be associated with increases of the radial diffusion of ions with the increasing the strength of storm and the main phase duration.

Received: 26 Mar 2023 – Discussion started: 28 Mar 2023

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Alexander Kovtyukh

Status: closed

RC1:
'Comment on angeo-2023-10', Anonymous Referee #1, 15 May 2023

Review of Kovtyukh for Annales Geophysicae

The paper presents a study of inner magnetospheric hot ion energy density during storms, searching for patterns as a function of radial distance and local time for different ion energy ranges. The values used are based on other published studies, greatly limiting the robustness of the data set considered. The methodology is flawed. The conclusions are not particular new or significant. I find that the study is not ready for publication.

The introduction has no references to prior work except in two place, one where 10 “reviews” are cited all at once and other where the author’s own prior work (from 2010) is cited. This method of citation is inadequate for justifying and motivating a new study. In fact, this new paper is very similar to their 2010 study, except with slightly different prior publications included.

It only uses 11 storm events, some with repeated entries, to increase the number of entries in Table 1 up to 17. I don’t understand the selection of events and timings for this table, nor the focus on these events. This is not a systematic study of hot ion energy content, but a highly skewed listing based on the author’s selection of previously published studies. There is no way to verify the robustness of the results.

Conducting line fits with fewer than 10 points makes the resulting fit highly susceptible to outliers. It also takes a very high R to reach the traditional p=0.05 level of statistical significance. For example, neither of the R values listed on page 5 (end of section 3.1) reach this p value. That is, even with these seemingly high correlation coefficients, the fit has a decent probability of arising from random chance. In any case, a linear fit of 3 points (the second equation) is almost never a reasonable scientific method.

I have a side comment on visualization in this paper. I greatly dislike the inclusion of points that are then not used in the fits (Figures 1, 2, 5, and 6), or the inclusion of two line fits from subsets of the points on the same graph (Figure 4). This obscures the true connection between points and linear fits. It is fine to show them all together, but then also make a separate plot to show what points go with what fit.

For Table 2, the peak energy density column has values given to one or two significant figures. The beta values are then given to 3 significant figures, which is unjustified. They should all be reported only to one significant digit. The uncertainty on all of the beta values is, therefore, large. This most liinvalidates the linear fits found from the plots of beta versus 3 parameters in Figure 2. While the R values of the two fits reach the p=0.05 level, this extra uncertainty makes them not meaningful.

The analysis at the beginning of section 3.3, built around Table 3 and Figure 3, appear to be based on exponential curve parameter values from only two L value energy densities. This chosen functional form is not justified with only two points. This analysis does not defend the “well described” word choice in the text.

I have the same complaints about Figures 4, 5, and 6 as I do about Figures 1 and 2. There are too few points, chosen by an unsystematic selection of storm events, to make the results meaningful.

I think that the issues with the methodology of section 3 invalidate any conclusions drawn from the discussion in section 4.

The conclusions drawn are not new. That the ions should move closer to the Earth during larger storm events is well known. A maximum energy density in the pre-midnight sector is expected based on drift physics. The same can be said about the energy dependence of MLT features.

The only suggestion that I can make to raise the robustness: download the data for many more storms and calculate these dependences with a systematic approach to all possible observations. Instead of relying on other studies to identify storms and do the initial analysis, calculate the energy densities directly from the data.

Citation: https://doi.org/10.5194/angeo-2023-10-RC1
- AC1: 'Reply on RC1', Alexander Kovtyukh, 21 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC1
- AC2:
  'Reply on RC1', Alexander Kovtyukh, 21 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC2-supplement.zip
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC2
  - AC3: 'Reply on AC2', Alexander Kovtyukh, 24 May 2023
    
    The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC3-supplement.pdf
    
    Citation: https://doi.org/10.5194/angeo-2023-10-AC3
    
    AC4: 'Reply on AC3', Alexander Kovtyukh, 24 May 2023
    
    The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC4-supplement.pdf
    
    Citation: https://doi.org/10.5194/angeo-2023-10-AC4
RC2:
'Comment on angeo-2023-10', Anonymous Referee #2, 25 May 2023

Review of a paper entitled:
Ion's ring current: regularities of the energy density distributions on the main phase of geomagnetic storms
Submitted by Alexander S. Kovtyukh to Annales Geophysicae

GENERAL COMMENT:
The author aims to determine the characteristics of the ring current, by analyzing the spatial distributions of the energy density of energetic ions during the main phase of magnetic storms. According to Table 1 of this manuscript, the data used in this study are obtained from those presented in published papers. It seems to me that the author has read the data values (Universal time, Magnetic local time, L-value, and Dst index, all of which correspond to the satellite observation time of the maximum energy density) from the figures in the papers. However, the manuscript does not adequately describe from which figure the author extracted the data values (see Specific Comments #1 below). It is difficult for me to evaluate the author’s analysis and interpretations until the data values used in the manuscript are enough reliable.
SPECIFIC COMMENTS:
1. The author should mention about the figures and/or tables that she/he used to extract all the data values, UT, MLT, Lm, and |Dst|, listed in Table 1.
I have checked two of the listed references: Yue et al, 2018 and Keika et al., 2018; and found it difficult for me to extract the data and even find some data.
For example, in the paper by Yue et al., 2018, pressure was at maximum at ~13:30 UT, which is different from UT in Table 1. The SYM-H index is presented in the paper, but the Dst index is not presented. The L value is not presented in the paper; Lm (L for the maximum energy density) is not mentioned.
In the paper by Keika et al., 2018, Lm is presented, but the corresponding UT and MLT are not presented/mentioned.
If the author obtained those data partly from the published figures/tables and partly by her/himself from the original data files provided by the mission teams, please elaborate on the processes.

2. The early part of Introduction (Lines 30-46) and latter part (lines 66-72) have not cited any published papers, although the paragraphs contain our current understanding based on a large number of previous studies.

3. The dipole magnetic field is used to calculate w_Bd, but it is well accepted that the magnetic field configuration on the night side is significantly deviated from the dipole during a storm, particularly during the main phase. In addition, magnetic field data are available at the time of the maximum energy density (i.e., at Lm) for most of the storms listed in Table 1. The author should use either a better magnetic field model or in-situ observations.

4. The author says that the ring current ion energy density is well approximated by an exponential function. It is important to present quantitatively to what extent it can be approximated.

5. An important storm that occurred on March 17, 2013 is missing. The storm was extensively analyzed by Gkioulidou et al., 2014.

Citation: https://doi.org/10.5194/angeo-2023-10-RC2
- AC5: 'Reply on RC2', Alexander Kovtyukh, 30 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC5-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC5
- AC6: 'Reply on RC2', Alexander Kovtyukh, 30 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC6-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC6
- AC7: 'Reply on RC2', Alexander Kovtyukh, 30 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC7-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC7
AC8: 'Comment on angeo-2023-10', Alexander Kovtyukh, 31 May 2023

The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC8-supplement.pdf

Citation: https://doi.org/10.5194/angeo-2023-10-AC8

Status: closed

RC1:
'Comment on angeo-2023-10', Anonymous Referee #1, 15 May 2023

Review of Kovtyukh for Annales Geophysicae

The paper presents a study of inner magnetospheric hot ion energy density during storms, searching for patterns as a function of radial distance and local time for different ion energy ranges. The values used are based on other published studies, greatly limiting the robustness of the data set considered. The methodology is flawed. The conclusions are not particular new or significant. I find that the study is not ready for publication.

The introduction has no references to prior work except in two place, one where 10 “reviews” are cited all at once and other where the author’s own prior work (from 2010) is cited. This method of citation is inadequate for justifying and motivating a new study. In fact, this new paper is very similar to their 2010 study, except with slightly different prior publications included.

It only uses 11 storm events, some with repeated entries, to increase the number of entries in Table 1 up to 17. I don’t understand the selection of events and timings for this table, nor the focus on these events. This is not a systematic study of hot ion energy content, but a highly skewed listing based on the author’s selection of previously published studies. There is no way to verify the robustness of the results.

Conducting line fits with fewer than 10 points makes the resulting fit highly susceptible to outliers. It also takes a very high R to reach the traditional p=0.05 level of statistical significance. For example, neither of the R values listed on page 5 (end of section 3.1) reach this p value. That is, even with these seemingly high correlation coefficients, the fit has a decent probability of arising from random chance. In any case, a linear fit of 3 points (the second equation) is almost never a reasonable scientific method.

I have a side comment on visualization in this paper. I greatly dislike the inclusion of points that are then not used in the fits (Figures 1, 2, 5, and 6), or the inclusion of two line fits from subsets of the points on the same graph (Figure 4). This obscures the true connection between points and linear fits. It is fine to show them all together, but then also make a separate plot to show what points go with what fit.

For Table 2, the peak energy density column has values given to one or two significant figures. The beta values are then given to 3 significant figures, which is unjustified. They should all be reported only to one significant digit. The uncertainty on all of the beta values is, therefore, large. This most liinvalidates the linear fits found from the plots of beta versus 3 parameters in Figure 2. While the R values of the two fits reach the p=0.05 level, this extra uncertainty makes them not meaningful.

The analysis at the beginning of section 3.3, built around Table 3 and Figure 3, appear to be based on exponential curve parameter values from only two L value energy densities. This chosen functional form is not justified with only two points. This analysis does not defend the “well described” word choice in the text.

I have the same complaints about Figures 4, 5, and 6 as I do about Figures 1 and 2. There are too few points, chosen by an unsystematic selection of storm events, to make the results meaningful.

I think that the issues with the methodology of section 3 invalidate any conclusions drawn from the discussion in section 4.

The conclusions drawn are not new. That the ions should move closer to the Earth during larger storm events is well known. A maximum energy density in the pre-midnight sector is expected based on drift physics. The same can be said about the energy dependence of MLT features.

The only suggestion that I can make to raise the robustness: download the data for many more storms and calculate these dependences with a systematic approach to all possible observations. Instead of relying on other studies to identify storms and do the initial analysis, calculate the energy densities directly from the data.

Citation: https://doi.org/10.5194/angeo-2023-10-RC1
- AC1: 'Reply on RC1', Alexander Kovtyukh, 21 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC1
- AC2:
  'Reply on RC1', Alexander Kovtyukh, 21 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC2-supplement.zip
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC2
  - AC3: 'Reply on AC2', Alexander Kovtyukh, 24 May 2023
    
    The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC3-supplement.pdf
    
    Citation: https://doi.org/10.5194/angeo-2023-10-AC3
    
    AC4: 'Reply on AC3', Alexander Kovtyukh, 24 May 2023
    
    The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC4-supplement.pdf
    
    Citation: https://doi.org/10.5194/angeo-2023-10-AC4
RC2:
'Comment on angeo-2023-10', Anonymous Referee #2, 25 May 2023

Review of a paper entitled:
Ion's ring current: regularities of the energy density distributions on the main phase of geomagnetic storms
Submitted by Alexander S. Kovtyukh to Annales Geophysicae

GENERAL COMMENT:
The author aims to determine the characteristics of the ring current, by analyzing the spatial distributions of the energy density of energetic ions during the main phase of magnetic storms. According to Table 1 of this manuscript, the data used in this study are obtained from those presented in published papers. It seems to me that the author has read the data values (Universal time, Magnetic local time, L-value, and Dst index, all of which correspond to the satellite observation time of the maximum energy density) from the figures in the papers. However, the manuscript does not adequately describe from which figure the author extracted the data values (see Specific Comments #1 below). It is difficult for me to evaluate the author’s analysis and interpretations until the data values used in the manuscript are enough reliable.
SPECIFIC COMMENTS:
1. The author should mention about the figures and/or tables that she/he used to extract all the data values, UT, MLT, Lm, and |Dst|, listed in Table 1.
I have checked two of the listed references: Yue et al, 2018 and Keika et al., 2018; and found it difficult for me to extract the data and even find some data.
For example, in the paper by Yue et al., 2018, pressure was at maximum at ~13:30 UT, which is different from UT in Table 1. The SYM-H index is presented in the paper, but the Dst index is not presented. The L value is not presented in the paper; Lm (L for the maximum energy density) is not mentioned.
In the paper by Keika et al., 2018, Lm is presented, but the corresponding UT and MLT are not presented/mentioned.
If the author obtained those data partly from the published figures/tables and partly by her/himself from the original data files provided by the mission teams, please elaborate on the processes.

2. The early part of Introduction (Lines 30-46) and latter part (lines 66-72) have not cited any published papers, although the paragraphs contain our current understanding based on a large number of previous studies.

3. The dipole magnetic field is used to calculate w_Bd, but it is well accepted that the magnetic field configuration on the night side is significantly deviated from the dipole during a storm, particularly during the main phase. In addition, magnetic field data are available at the time of the maximum energy density (i.e., at Lm) for most of the storms listed in Table 1. The author should use either a better magnetic field model or in-situ observations.

4. The author says that the ring current ion energy density is well approximated by an exponential function. It is important to present quantitatively to what extent it can be approximated.

5. An important storm that occurred on March 17, 2013 is missing. The storm was extensively analyzed by Gkioulidou et al., 2014.

Citation: https://doi.org/10.5194/angeo-2023-10-RC2
- AC5: 'Reply on RC2', Alexander Kovtyukh, 30 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC5-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC5
- AC6: 'Reply on RC2', Alexander Kovtyukh, 30 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC6-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC6
- AC7: 'Reply on RC2', Alexander Kovtyukh, 30 May 2023
  
  The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC7-supplement.pdf
  
  Citation: https://doi.org/10.5194/angeo-2023-10-AC7
AC8: 'Comment on angeo-2023-10', Alexander Kovtyukh, 31 May 2023

The comment was uploaded in the form of a supplement: https://angeo.copernicus.org/preprints/angeo-2023-10/angeo-2023-10-AC8-supplement.pdf

Citation: https://doi.org/10.5194/angeo-2023-10-AC8

Alexander Kovtyukh

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Short summary

To construct realistic models of the RC that describes its structure during magnetic storms of different intensity, quantitative patterns of the variations of the main parameters of the radial profile of the RC energy density are necessary. Such patterns are of high importance both for theoretical studies and mathematical modeling of the dynamics of the magnetosphere, and for many applied problems.


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