the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 May 2025
Properties of large-amplitude kilometer-scale field-aligned currents at auroral latitudes, as derived from Swarm satellites
Abstract. High-resolution magnetic field recordings by the Swarm A and C spacecraft have been used to investigate the properties of field-aligned currents (FACs) at auroral latitudes down to their smallest scales (<1 km). Particularly suitable for that purpose are the magnetic field recordings, taken at a rate of 50 Hz, during the two weeks around the quasi-coplanar orbit configuration on 1 October 2021. We have split the recorded signal caused by FACs of along-track wavelengths from 0.3 km to 40 km into 8 quasi-logarithmically spaced ranges. Our investigations revealed that the kilometer-scale FACs (0.3–5 km) show quite different characteristics from those of the small-scale FACs (10–40 km). The kilometer-scale FACs exhibit short-lived (<1 s) randomly appearing large current spikes. They are confined to certain latitude ranges, which depend on local time. Small-scale FAC structures last for longer times (>10 s) and are distributed over larger latitude ranges. Their largest amplitudes are achieved at latitudes that overlap with the kilometer-scale FACs. The small-scale FACs have earlier been identified as Alfvén waves that are partly reflected at the ionosphere, and they can oscillate within the ionospheric Alfvén resonator. When at the same time additional Alfvén waves are launched from the magnetosphere they will interfere with the reflected. We suggest that the interaction between oppositely travelling Alfvén waves, when continuing sufficiently long, is generating the large-amplitude and short-lived kilometer-scale FACs.
Competing interests: The contact author has declared that neither of the authors has any competing interests.
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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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RC1: 'Comment on egusphere-2025-1961', W. Lotko, 02 Jun 2025
Review of “Properties of large-amplitude kilometer-scale field-aligned currents at auroral latitudes, as derived from Swarm satellites” by Y-L Zhou and H. Lühr
This study takes a major step in advancing knowledge of small-scale field-aligned currents (FAC) found at cusp and auroral latitudes with variations on 0.04 to 5 second time scales or 0.3-20 km spatial scales. The results are based on high-resolution, fluxgate magnetometer measurements from a special, two-week campaign in which the SWARM A and C satellites maintain separations of < 2.5 km cross-track and about 2 seconds along-track.
The study is well-motivated. The methodology is clear. The authors present new results pertaining to observed characteristics of small-scale field-aligned currents. Their presentation is well-organized and informative. The discussion of results offers interesting and plausible interpretations that suggest future research directions.
The manuscript will be of interest to the broader scientific community and is publishable. Before accepting it for publication in AG, I recommend implementing minor revisions to include some descriptive clarifications and improvements in language expression and syntax and in the font size in two figures. To facilitate revisions, I have sent a markup of the manuscript directly to the authors via email with embedded comments for their consideration (also attached with referee report).
New and noteworthy scientific methodology and results include:
- Novel and rigorous analysis of two-point, high-resolution time-series from SWARM A and C, including cross-correlation, spectral distributions and polarization characteristics.
- Resolution of spatiotemporal ambiguities using two-point measurements.
- Determination of the preferred length scales for very large-amplitude FACs.
- Characterization of waveform and amplitude persistence as a function of fluctuation length and time scales.
- Analysis of relationships between fast and slowly varying fluctuations.
- Determination of signal polarization, with more slowly varying signals exhibiting mostly elliptical polarization and faster varying signals exhibiting mostly (near) linear polarization.
- MLAT–MLT distributions of signal characteristics.
An intriguing aspect of the study is its plausible interpretation of the data analysis in terms of Alfvénic turbulence. Building on a previous investigation of CHAMP satellite data (Rother et al., 2007) and appealing to results from previous theoretical and modeling studies, the authors assert that the observed magnetic fluctuations and attendant FACs on the dayside are a consequence of magnetopause disturbances that launch Alfvén waves earthward and become trapped in an F-region ionospheric Alfvén resonator (IAR). The guided waves achieve 5-20 km field-perpendicular scales upon reaching the ionosphere, i.e., the longer duration fluctuations in the data. With ongoing magnetopause stimulation of Alfvén waves flowing into the IAR, the resonator modes intensify until their dissipation within it balances the power flowing into it. The authors presume that nonlinear interaction between counterpropagating Alfvén resonator modes produces a turbulent cascade to smaller scales – the short duration, km-scale FACs identified in the data. The dissipation range of the cascade may be attributable to ionospheric Ohmic dissipation of sub-km-scale FACs according to cited modeling studies. Nightside Alfven wave activity originates from magnetotail processes and is more episodic than dayside activity, so its statistical properties differ from those on the dayside. However, the Alfven wave dynamics within the nightside ionosphere should be similar.
It is customary in turbulence analysis to determine the power spectral density of the fluctuations and identify a power law spectral index if one exists. An evaluation of the power spectral density and the energetics of the fluctuations across the spectral range might be a useful addition to the paper.
The paper concludes with some unresolved questions for future study. What are the effects of the km-scale Alfven waves on ionosphere-thermosphere heating and neutral gas winds? What is the nature of the electric fields accompanying km-scale FACs? What are the effects on charged-particles, e.g., transverse acceleration of ions and field-aligned electron acceleration?
I would add to this list a key question posed by the authors’ interpretations: If small-scale (5-20 km) and km-scale FACs are causally related, how is the elliptical polarization of small-scale FACs transformed into the linear polarization of km-scale FACs, and by what means do the km-scale FACs achieve much larger amplitudes than the presumed energy-containing population of 5-20 km-scale FACs?
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AC1: 'Reply on RC1', Yunliang Zhou, 20 Jul 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1961/egusphere-2025-1961-AC1-supplement.pdf
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RC2: 'Comment on egusphere-2025-1961', Anonymous Referee #2, 30 Jun 2025
Comments on: “Properties of large-amplitude kilometer-scale field-aligned currents at auroral latitudes, as derived from Swarm satellites,” by Zhou and Luhr
This paper presents observations of field-aligned currents from the Swarm satellite magnetometers. It is well-written and provides very important new results regarding field-aligned currents in the high latitude ionosphere. The use of dual satellites enables new insights regarding the nature of FAC of different scale sizes. There is no question that this work should be published. Provided below are minor comments requesting clarifications and some suggestions to the figures to improve the impact of some of the main points.
Comments
- Large spikes in the FAC data
The paper refers to large current spikes (see line 418 and abstract, for example). Presumably, these are the peaks shown in the enlarged time series plots in Figure 2. The authors should comment if these peaks are well resolved with the 50 s/sec data or would higher sampling reveal even sharper spikes?
Remark: It appears likely that such spikes might be associated with narrow electron beams. Alternatively, they might exhibit steepening of Alfven waves, as reported and modeled by Seyler et al. [1995] in the Freja magnetometer data.
2. Spectrum of FAC and magnetic field variations
The spectrum of the km-scale magnetic field FAC variations is extremely important, particularly because there are not that many examples from other high latitude satellites with 50 s/sec sampling of the magnetometer. (Maybe reference Freja data?).
A few comments: It is well known that a power spectrum of a time series of “spikey” fields appears as a broad spectrum. The authors are asked to comment on whether the spectrum shown at the bottom of Figure 9 might obscure the higher frequencies associated with the spikes in the time series data.
Is the spectrum shown in Figure 9 from Swarm A or C or any average from both satellites? The authors may wish to consider presenting the spectrum in nT for comparison with other measurements or at least comment on how the FAC spectrum represents that of the magnetometer components. It is suggested that a vertical dashed line be placed on the spectrum at 0.2 Hz to immediately inform the reader that there is an instrumental cutoff.
Along these lines, a spectrum of the unfiltered data would be very powerful. Since the paper includes longer-scale FAC, the authors are encouraged to consider including a spectrum that includes the longer scales (i.e., without the filtering.)
3. Scale length instead of wavelength
The paper discusses FACs organized by distance covered along the satellite path. Therefore, it is suggested to use the term “scale length” and not wavelength when referring to the different scales. See use of wavelength in the abstract, for example. Wavelength, in general, refers to a well-defined wave with a k-vector, etc.
4. Cross correlations in Figure 10 are somewhat obscure
Figure 10 also shows cross-correlations and the caption says the format is the same as Figure 1. However, in Figure 10, it is not clear if the cross correlations are between SWARM A and C or between the shorter and longer period waveforms which are shown in the upper panels. This should be clarified.
5. Use of the term “small scale” is somewhat counter-intuitive when compared to the term “km-scale,” since small scale is really larger than km-scale, at least in this paper
A main thrust of this paper is to compare two groups of FACs: those with km-scales and those with 10’s of km scales. The authors have chosen to call the longer scale FACs “small scale”. This is extremely confusing, as this group of data refers to FACs that are longer scale than the km-scale FACs, even though they are referred to as short scale. Suggestion: Why not refer to the two groups as either: “10’s km scale and km scale FACs” or “medium scale and small scale FACs” in which the shorter, km scale FACs are designated as “small scale”.
The entire paper would then be easier to read, from the title and abstract through to the summary and conclusions. In the summary, line 526, might then read, “For medium scale FACs (5-20 km) whereas line 532 would remain as is, “The km-scale FACs (0.5-5 km size)…”. The title refers simply to “km-scale FACs” and this would then be appropriate as is. Sentences such as line 519 that refer to the “smallest scale” FACs which are confusing, at least to this reviewer, could be left as is.
This may appear as a very minor point, but the authors are urged to reconsider their nomenclature.
6. Typo
Line 61: suggest remove the comma before “these narrow FACs” and perhaps put: “…large amplitudes that these narrow FACs…”
Suggestions
- Time series showing combined medium scale and short scale data
This paper underscores that there are two populations of FACs characterized by different scales whose appearances in the data are highly related to each other. The paper would be well served if there was a simple time series example showing the juxtaposition of the superimposed scales. Here it would be important to not filter the data. In other words, perhaps show 30 seconds or so of data that will clearly show the large-scale variations upon which are superimposed the km-scale variations? Maybe before Figure 1? Since the km-scale variations have the larger amplitude, this would be very powerful. Maybe leave in nT instead of nT/s so the waveform can be readily compared with other high latitude magnetometer data from other satellites?
2. Cross correlation curves on Figure 1
This suggestion follows the suggestion above.
The “overview” examples in Figure 1 are very powerful. However, these are just for the km scale data. Although the figure is somewhat busy with two examples, including a panel (for each example) of the longer scale length data would be highly desirable, particularly as Figure 1 introduces the reader to what the paper is all about. (Perhaps have a Figure 1a and 1b on separate pages?)
Since the cross correlations of km-scale variations show low correlations in the regions of km scale FACs, the reader does not immediately grasp that the longer scales have high correlations. Although this will become apparent later in the text, given the fact that this is such a unique data set with two SWARM satellites, it is suggested to have two cross correlation line plots (in different colors?) in which the 10-40 km FACs are included. It seems that this is a golden opportunity to show the different cross correlations in a pair of line plots in this introductory figure that clearly shows off the beauty of having two SWARM satellite.
Citation: https://doi.org/10.5194/egusphere-2025-1961-RC2 -
AC2: 'Reply on RC2', Yunliang Zhou, 20 Jul 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1961/egusphere-2025-1961-AC2-supplement.pdf
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-1961', W. Lotko, 02 Jun 2025
Review of “Properties of large-amplitude kilometer-scale field-aligned currents at auroral latitudes, as derived from Swarm satellites” by Y-L Zhou and H. Lühr
This study takes a major step in advancing knowledge of small-scale field-aligned currents (FAC) found at cusp and auroral latitudes with variations on 0.04 to 5 second time scales or 0.3-20 km spatial scales. The results are based on high-resolution, fluxgate magnetometer measurements from a special, two-week campaign in which the SWARM A and C satellites maintain separations of < 2.5 km cross-track and about 2 seconds along-track.
The study is well-motivated. The methodology is clear. The authors present new results pertaining to observed characteristics of small-scale field-aligned currents. Their presentation is well-organized and informative. The discussion of results offers interesting and plausible interpretations that suggest future research directions.
The manuscript will be of interest to the broader scientific community and is publishable. Before accepting it for publication in AG, I recommend implementing minor revisions to include some descriptive clarifications and improvements in language expression and syntax and in the font size in two figures. To facilitate revisions, I have sent a markup of the manuscript directly to the authors via email with embedded comments for their consideration (also attached with referee report).
New and noteworthy scientific methodology and results include:
- Novel and rigorous analysis of two-point, high-resolution time-series from SWARM A and C, including cross-correlation, spectral distributions and polarization characteristics.
- Resolution of spatiotemporal ambiguities using two-point measurements.
- Determination of the preferred length scales for very large-amplitude FACs.
- Characterization of waveform and amplitude persistence as a function of fluctuation length and time scales.
- Analysis of relationships between fast and slowly varying fluctuations.
- Determination of signal polarization, with more slowly varying signals exhibiting mostly elliptical polarization and faster varying signals exhibiting mostly (near) linear polarization.
- MLAT–MLT distributions of signal characteristics.
An intriguing aspect of the study is its plausible interpretation of the data analysis in terms of Alfvénic turbulence. Building on a previous investigation of CHAMP satellite data (Rother et al., 2007) and appealing to results from previous theoretical and modeling studies, the authors assert that the observed magnetic fluctuations and attendant FACs on the dayside are a consequence of magnetopause disturbances that launch Alfvén waves earthward and become trapped in an F-region ionospheric Alfvén resonator (IAR). The guided waves achieve 5-20 km field-perpendicular scales upon reaching the ionosphere, i.e., the longer duration fluctuations in the data. With ongoing magnetopause stimulation of Alfvén waves flowing into the IAR, the resonator modes intensify until their dissipation within it balances the power flowing into it. The authors presume that nonlinear interaction between counterpropagating Alfvén resonator modes produces a turbulent cascade to smaller scales – the short duration, km-scale FACs identified in the data. The dissipation range of the cascade may be attributable to ionospheric Ohmic dissipation of sub-km-scale FACs according to cited modeling studies. Nightside Alfven wave activity originates from magnetotail processes and is more episodic than dayside activity, so its statistical properties differ from those on the dayside. However, the Alfven wave dynamics within the nightside ionosphere should be similar.
It is customary in turbulence analysis to determine the power spectral density of the fluctuations and identify a power law spectral index if one exists. An evaluation of the power spectral density and the energetics of the fluctuations across the spectral range might be a useful addition to the paper.
The paper concludes with some unresolved questions for future study. What are the effects of the km-scale Alfven waves on ionosphere-thermosphere heating and neutral gas winds? What is the nature of the electric fields accompanying km-scale FACs? What are the effects on charged-particles, e.g., transverse acceleration of ions and field-aligned electron acceleration?
I would add to this list a key question posed by the authors’ interpretations: If small-scale (5-20 km) and km-scale FACs are causally related, how is the elliptical polarization of small-scale FACs transformed into the linear polarization of km-scale FACs, and by what means do the km-scale FACs achieve much larger amplitudes than the presumed energy-containing population of 5-20 km-scale FACs?
-
AC1: 'Reply on RC1', Yunliang Zhou, 20 Jul 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1961/egusphere-2025-1961-AC1-supplement.pdf
-
RC2: 'Comment on egusphere-2025-1961', Anonymous Referee #2, 30 Jun 2025
Comments on: “Properties of large-amplitude kilometer-scale field-aligned currents at auroral latitudes, as derived from Swarm satellites,” by Zhou and Luhr
This paper presents observations of field-aligned currents from the Swarm satellite magnetometers. It is well-written and provides very important new results regarding field-aligned currents in the high latitude ionosphere. The use of dual satellites enables new insights regarding the nature of FAC of different scale sizes. There is no question that this work should be published. Provided below are minor comments requesting clarifications and some suggestions to the figures to improve the impact of some of the main points.
Comments
- Large spikes in the FAC data
The paper refers to large current spikes (see line 418 and abstract, for example). Presumably, these are the peaks shown in the enlarged time series plots in Figure 2. The authors should comment if these peaks are well resolved with the 50 s/sec data or would higher sampling reveal even sharper spikes?
Remark: It appears likely that such spikes might be associated with narrow electron beams. Alternatively, they might exhibit steepening of Alfven waves, as reported and modeled by Seyler et al. [1995] in the Freja magnetometer data.
2. Spectrum of FAC and magnetic field variations
The spectrum of the km-scale magnetic field FAC variations is extremely important, particularly because there are not that many examples from other high latitude satellites with 50 s/sec sampling of the magnetometer. (Maybe reference Freja data?).
A few comments: It is well known that a power spectrum of a time series of “spikey” fields appears as a broad spectrum. The authors are asked to comment on whether the spectrum shown at the bottom of Figure 9 might obscure the higher frequencies associated with the spikes in the time series data.
Is the spectrum shown in Figure 9 from Swarm A or C or any average from both satellites? The authors may wish to consider presenting the spectrum in nT for comparison with other measurements or at least comment on how the FAC spectrum represents that of the magnetometer components. It is suggested that a vertical dashed line be placed on the spectrum at 0.2 Hz to immediately inform the reader that there is an instrumental cutoff.
Along these lines, a spectrum of the unfiltered data would be very powerful. Since the paper includes longer-scale FAC, the authors are encouraged to consider including a spectrum that includes the longer scales (i.e., without the filtering.)
3. Scale length instead of wavelength
The paper discusses FACs organized by distance covered along the satellite path. Therefore, it is suggested to use the term “scale length” and not wavelength when referring to the different scales. See use of wavelength in the abstract, for example. Wavelength, in general, refers to a well-defined wave with a k-vector, etc.
4. Cross correlations in Figure 10 are somewhat obscure
Figure 10 also shows cross-correlations and the caption says the format is the same as Figure 1. However, in Figure 10, it is not clear if the cross correlations are between SWARM A and C or between the shorter and longer period waveforms which are shown in the upper panels. This should be clarified.
5. Use of the term “small scale” is somewhat counter-intuitive when compared to the term “km-scale,” since small scale is really larger than km-scale, at least in this paper
A main thrust of this paper is to compare two groups of FACs: those with km-scales and those with 10’s of km scales. The authors have chosen to call the longer scale FACs “small scale”. This is extremely confusing, as this group of data refers to FACs that are longer scale than the km-scale FACs, even though they are referred to as short scale. Suggestion: Why not refer to the two groups as either: “10’s km scale and km scale FACs” or “medium scale and small scale FACs” in which the shorter, km scale FACs are designated as “small scale”.
The entire paper would then be easier to read, from the title and abstract through to the summary and conclusions. In the summary, line 526, might then read, “For medium scale FACs (5-20 km) whereas line 532 would remain as is, “The km-scale FACs (0.5-5 km size)…”. The title refers simply to “km-scale FACs” and this would then be appropriate as is. Sentences such as line 519 that refer to the “smallest scale” FACs which are confusing, at least to this reviewer, could be left as is.
This may appear as a very minor point, but the authors are urged to reconsider their nomenclature.
6. Typo
Line 61: suggest remove the comma before “these narrow FACs” and perhaps put: “…large amplitudes that these narrow FACs…”
Suggestions
- Time series showing combined medium scale and short scale data
This paper underscores that there are two populations of FACs characterized by different scales whose appearances in the data are highly related to each other. The paper would be well served if there was a simple time series example showing the juxtaposition of the superimposed scales. Here it would be important to not filter the data. In other words, perhaps show 30 seconds or so of data that will clearly show the large-scale variations upon which are superimposed the km-scale variations? Maybe before Figure 1? Since the km-scale variations have the larger amplitude, this would be very powerful. Maybe leave in nT instead of nT/s so the waveform can be readily compared with other high latitude magnetometer data from other satellites?
2. Cross correlation curves on Figure 1
This suggestion follows the suggestion above.
The “overview” examples in Figure 1 are very powerful. However, these are just for the km scale data. Although the figure is somewhat busy with two examples, including a panel (for each example) of the longer scale length data would be highly desirable, particularly as Figure 1 introduces the reader to what the paper is all about. (Perhaps have a Figure 1a and 1b on separate pages?)
Since the cross correlations of km-scale variations show low correlations in the regions of km scale FACs, the reader does not immediately grasp that the longer scales have high correlations. Although this will become apparent later in the text, given the fact that this is such a unique data set with two SWARM satellites, it is suggested to have two cross correlation line plots (in different colors?) in which the 10-40 km FACs are included. It seems that this is a golden opportunity to show the different cross correlations in a pair of line plots in this introductory figure that clearly shows off the beauty of having two SWARM satellite.
Citation: https://doi.org/10.5194/egusphere-2025-1961-RC2 -
AC2: 'Reply on RC2', Yunliang Zhou, 20 Jul 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1961/egusphere-2025-1961-AC2-supplement.pdf
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Hermann Lühr
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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