Chorus Wave Properties From Van Allen Probes: Quantifying the Impact of the Sheath Corrected Electric Field
Abstract
A sheath impedance model has recently been developed to describe how the variable coupling impedance between the Van Allen Probes instrumentation and the ambient plasma affects both the amplitude and phase of electric field wave measurements. Here, the impact of this sheath correction on measured chorus wave properties, including electric field wave power and the Poynting vector, is directly quantified. It is found that the sheathcorrected electric field wave power is typically between two and nine times larger than the uncorrected measurement, depending on wave frequency. The sheath correction typically increases the Poynting flux by a factor of ∼2, and causes the polar angle of the Poynting vector to switch hemisphere from parallel to antiparallel propagation in ∼2% of cases. The uncorrected data exhibit significant deviations from the theoretically predicted relationship between the wave vector and the Poynting vector whereas this relationship is wellreproduced with the sheathcorrected observations.
Key Points

Sheathcorrection results in increase of electric field chorus wave power by a factor of 2–9, and increase in Poynting flux by factor of ∼2

Sheath correction causes the Poynting vector to switch hemispheres, from parallel to antiparallel propagation, in only ∼2% of cases

Theoretically predicted relationship between wave vector and Poynting vector is wellreproduced with sheathcorrected data
Plain Language Summary
The wave electric field on Van Allen Probes has recently been corrected for sheath impedance effects, which can affect both the amplitude and phase of the measurements. Here, for the first time, we directly quantify the impact of this correction factor on chorus wave measurements of electric field wave power. We also investigate the impact on the Poynting vector direction and magnitude, which is itself determined from electric field observations and magnetic field measurements. It is found that after applying the sheath correction to chorus wave observations, the electric field wave power typically increases by a factor between two and nine, whereas the Poynting flux typically increases by a factor of ∼2. The relationship between the wave vector and the Poynting vector is compared to that expected from cold plasma theory, for both the corrected and uncorrected observations. Significant differences between observations and theory are apparent when using the uncorrected measurements, however the sheathcorrected observations agree well with the theoretical predictions.
1 Introduction
Whistlermode chorus waves play an important role in driving radiation belt dynamics (Thorne et al., 2010), including rapid acceleration of electrons (Allison et al., 2021; Thorne et al., 2013) and particle loss to the atmosphere during microbursts (Breneman et al., 2017; Douma et al., 2018; Lorentzen et al., 2001; Mozer et al., 2018; Shumko et al., 2018, 2021) and diffuse auroral precipitation (Newell, 2010; Ni et al., 2011; Nishimura et al., 2010; Thorne et al., 2010). Chorus is typically observed between ∼100 Hz and several kHz (Gurnett & O’Brien, 1964), scaling between 0.05 and 0.90f_{ce}, where f_{ce} is the equatorial electron cyclotron frequency. A minimum in power is often observable at 0.50f_{ce} (Koons & Roeder, 1990; Li et al., 2019; Tsurutani & Smith, 1974).
The Van Allen Probes (Mauk et al., 2012) measure the electric field using spherical double probe sensors. These sensors, part of the Electric Field and Waves (EFW) instrument (Wygant et al., 2013), are electrically coupled to the magnetospheric plasma through a plasma sheath which forms around the sensors. This instrumentplasma coupling can attenuate the measured output voltage and thus leads to a frequencydependent response function which varies with the local plasma environment, affecting both the amplitude and phase of the observations. Due to differences between the electric field instrument for each axis, the instrumentplasma interface is different between the spinplane and spinaxis measurements. Additionally, due to the shorter booms used along the spinaxis, this measurement direction is more susceptible to the electrical shortening that can occur when the Debye length becomes comparable to the antenna length (Califf & Cully, 2016; Cully et al., 2007; Khotyaintsev et al., 2014; Lejosne & Mozer, 2019; Pedersen et al., 1998; Mozer et al., 1974). A model has been developed to correct for these effects (Hartley, Christopher, et al., 2022). Since signals from EFW are passed to the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) Waves instrument for FFT processing (Kletzing et al., 2013), a full sheathcorrected EMFISIS data set was produced for final data archive.
Sheath effects are most prevalent at low density (Hartley, Christopher, et al., 2022; Hartley et al., 2015, 2016, 2017) where chorus is commonly observed, and primarily impact spinaxis measurements. To date, there has been no quantification of how chorus wave properties, including electric field wave power and Poynting vector observations, are impacted by the sheath correction. Here, this is achieved by directly comparing the uncorrected measurements with the sheathcorrected data.
Evaluating this impact is important as numerous studies have investigated the electric field chorus wave power (Li et al., 2016; Tyler et al., 2019), in part, because the highamplitude parallel electric field associated with oblique chorus (Cattell et al., 2008) can drive nonlinear electron acceleration through Landau resonance (Agapitov et al., 2014; Artemyev et al., 2012, 2013). Additionally, the Poynting vector (which requires electric field observations to compute) describes the propagation of wave energy, and is a crucial quantity for determining the location, size, and dynamics of the chorus source region (LeDocq et al., 1998; Nagano et al., 1996; Parrot et al., 2003; Santolik et al., 2004, 2005; Taubenschuss et al., 2016; Teng et al., 2018), as well as for describing chorus propagation (Cattell et al., 2015; Chen et al., 2021; Colpitts et al., 2020; Demekhov et al., 2017; Hartley, Chen, et al., 2022; Santolik et al., 2006, 2009).
2 Chorus Wave Identification
As in previous studies (Bingham et al., 2018; Hartley et al., 2015, 2016, 2019; Li et al., 2014; Wang et al., 2019), waves are identified as chorus if they, (a) occur between 0.05f_{ce} and 0.90f_{ce}, (b) occur when the plasma density (Kurth et al., 2015) is less than 10 × (6.6/L)^{4} or 30 cm^{−3}, whichever is smaller, (c) have planarity (Santolík et al., 2003) exceeding 0.6, and ellipticity (Santolík et al., 2002) and 2D degree of coherence in the polarization plane (Santolík & Gurnett, 2002) exceeding 0.5, and (d) have magnetic field wave power larger than the greater of 10^{−9} nT^{2}/Hz or 5× the instrument background levels.
These thresholds ensure righthanded waves which are approximately circularly polarized and meet the plane wave approximation. Note that these selection criteria are based on magnetic field observations only and are therefore unaffected by sheath effects, meaning that the same events are selected for both the uncorrected and sheathcorrected data. Note also that this selection procedure is not affected by the timefrequency structure on timescales below a few seconds, meaning the selected data contains not only chorus with discrete elements, but also “hisslike” chorus (Li et al., 2012) and any hiss or exohiss (Zhu et al., 2015) that may be coherent (Summers et al., 2014; Tsurutani et al., 2015), all of which may exist without clear timefrequency signatures. For simplicity, waves that meet the above described selection procedure are referred to as chorus waves throughout this paper.
Figure 1 provides an example of this wave identification procedure showing (a) plasma density (blue) and L shell (red), (b) power spectral density of the magnetic field, B_{w}, and (c) the chorus wave flag. For waves flagged as chorus, the power spectral density (SD) of the electric field is shown for (d) uncorrected measurements, $$, and (e) sheathcorrected measurements $$. The Poynting flux is shown for (f) uncorrected observations, S^{uncor}, and (g) sheathcorrected observations, S^{cor}. The polar and azimuthal angles of the Poynting vector are shown in (h) and (j) for the uncorrected data, $$ and $$, and (i) and (k) for the sheathcorrected data, $$ and $$. All sheathcorrected values are based on the correction provided by Hartley, Christopher, et al. (2022).
It is immediately evident that differences exist between the uncorrected and sheathcorrected observations, with both $$ and S^{cor} > S^{uncor}, as well as differences between $$ and $$. This chorus identification procedure is applied to measurements from both Van Allen Probes spacecraft over the full mission duration, resulting in a database containing 14,815,703 individual frequencytime observations across 3,635,626 unique time intervals. This allows us to conduct direct comparisons between the uncorrected and sheathcorrected observations in a statistical analysis and to quantify the differences.
3 The Impact on Electric Field Observations
Figure 2a shows the median power spectral density of $$ (blue) and $$ (red) as a function of normalized wave frequency, f/f_{ce}. These median power spectral density values are expressed as $$ and $$ hereafter, with M denoting the median of the value in parenthesis. Both the ratio of these median values $$ and the median of the ratios $$ are calculated. Figure 2b (solid line) shows the ratio between these median spectra, $$. For waves near 0.05f_{ce}, $$ is a factor of ∼2 larger than $$. This factor increases with increasing wave frequency up to a local maximum of ∼6 near 0.40f_{ce}, decreases down to ∼4 near 0.60f_{ce}, before increasing again to a factor of ∼9 by 0.90f_{ce}. For context, Figure 2b also shows the distribution formed by taking the ratio between $$ and $$ for each individual observation (color), with the median ratio, $$ (dashed line) and corresponding 25th and 75th percentiles (dotted lines) also shown. The median of the ratios, $$, exhibits a similar behavior to the ratio of the medians, $$, albeit with some deviations occurring for 0.35–0.55f_{ce}, likely attributable to skew in the underlying distributions. The number of data points (colors) indicate a sharp lower cutoff at a ratio ∼1–2 and a long tail up to high ratio values (>10). The 25th and 75th percentiles (dotted lines) indicate that, despite this long tail, the majority of data are relatively tightly bound to the median.
Electric field observations are then sorted into wave power that is perpendicular to, E_{w⊥} (Figures 2c and 2d), and parallel to, E_{w‖} (Figures 2e and 2f), the background magnetic field, B_{0}. The median spectra of $$ and $$ look largely similar to those for $$ and $$. The ratio of the median spectra, $$ (solid line in Figure 2d), is ∼2 for the lowest frequencies, increases to ∼7 at 0.40f_{ce}, decreases to ∼5 at 0.60f_{ce}, and increases to almost 10 for the highest frequencies. However, the median spectra of E_{w‖} show some differences, with $$ at frequencies below ∼0.25f_{ce}. For frequencies greater than ∼0.25f_{ce}, $$. This is quantified by the ratio of the median spectra, $$ (solid line in Figure 2f), which is less than unity for frequencies below 0.25f_{ce} with a minimum near 0.6 at the lowest frequencies. It then rises to ∼3–4 near 0.40f_{ce}, where it remains for frequencies up to 0.80f_{ce}, before increasing to values between ∼4 and 6 for the highest frequencies. For both E_{w⊥} and E_{w‖}, the median of the ratio values (dashed lines) exhibit a very similar behavior to the ratios of the respective medians (solid line).
This analysis reveals that the sheath correction generally has a larger impact on E_{w⊥} than E_{w‖}. This is attributable to the spacecraft orientation, which results in the spin axis antenna, which has a larger correction factor, more frequently measuring E_{w⊥} than E_{w‖}. It should be noted that there are occurrences where the ratios can deviate substantially from the median values. However, the direct comparison between the sheathcorrected and uncorrected values presented here is important given that E_{w‖} and E_{w⊥} can accelerate electrons through Landau and cyclotron resonances (e.g., Agapitov et al., 2015, 2016; Artemyev et al., 2016; Chen et al., 2019; Min et al., 2014; Omura et al., 2019).
4 The Impact on Poynting Vector Direction and Magnitude
In a similar manner to the electric field analysis presented above, the median Poynting flux spectra is determined from the uncorrected, S^{uncor}, and sheathcorrected, S^{cor}, observations, denoted as M(S^{uncor}) and M(S^{cor}), respectively. These spectra are shown in Figure 3a with M(S^{uncor}) in blue and M(S^{cor}) in red, with the ratio between them, M(S^{cor})/M(S^{uncor}), shown in Figure 3b (solid line). In contrast to the electric field observations, M(S^{cor})/M(S^{uncor}) is relatively constant for all frequencies, with M(S^{cor}) a factor of ∼2 greater than M(S^{uncor}), with actual values varying between 1.30 and 2.55. The ratio of the median values, M(S^{cor})/M(S^{uncor}) (solid line), is equivalent to the median of the ratios, M(S^{cor}/S^{uncor}) (dashed line), with both lines almost completely overlapping. The 25th and 75th percentiles (dotted lines) remain within ∼15% of the median value. The Poynting flux ratio distribution (colors) exhibits a larger spread toward higher ratio values than it does toward lower ratio values.
The sheath correction also affects the direction of the Poynting vector, which is defined by two angles: the polar angle, θ_{S}, (angle between S and B_{0}), and the azimuthal angle, ϕ_{S} (angle around B_{0} with respect to the antiEarthward direction). Here, we first investigate how the sheath correction impacts θ_{S}. Figure 3c shows the distribution of $$ as a function of f/f_{ce}, with colors indicating the number of data. Black lines show the median θ_{S} value for both θ_{S} < 90° and θ_{S} > 90°. Figure 3c demonstrates that S^{uncor} is typically oriented either quasiparallel (θ_{S} < 30°) or quasiantiparallel (θ_{S} > 150°). The median value is typically ∼12°–30° from fieldaligned (or antifieldaligned). Figure 3d is in the same format as Figure 3c but shows $$. The median $$ value varies from ∼5°–20°, demonstrating that the sheath correction typically causes the Poynting vector to become more closely aligned with B_{0}.
Figure 3e shows the absolute value of the difference between $$ and $$ as a function of f/f_{ce}. This difference is often small, but can be substantial in some instances. $$ is less than 10° for 64% of observations, between 10° and 20° for 27% of observations, between 20° and 30° for 5% of observations, and greater than 30° for 4% of observations.
Singular Value Decomposition (SVD) is used to determine the wave vector direction (Santolík et al., 2003), resulting in two possible solutions, one with a component of the wave vector parallel to the background magnetic field, and one with a component antiparallel to the background field. θ_{S} is used to remove this ambiguity and correctly define the wave vector direction, since the Poynting vector must exist in the same hemisphere as the wave vector. As such, the crucial quantity is whether θ_{S} < 90° or θ_{S} > 90°.
It is evident in Figure 3e that $$° in some instances. This means that applying the sheath correction must result in the Poynting vector switching hemisphere, although we note that for oblique θ_{S} values a difference less than 90° may also result in the Poynting vector changing hemisphere. As such, we directly compute the percentage of observations where the sheath correction results in the Poynting vector switching hemisphere, as shown in Figure 3f as a function of f/f_{ce}. At low frequency, this can be as high as 5.4%, but for frequencies above 0.125f/f_{ce} the percentage drops below 1%, and is typically only a few tenths of a percent. Overall, for all frequencies, it is found that S^{cor} is in the same hemisphere as S^{uncor} (parallel or antiparallel to the background magnetic field) in ∼98% of cases. That is, the sheath correction causes the Poynting vector to flip hemispheres in only ∼2% of cases, with most of these cases at low frequency. As such, previous studies which used θ_{S} to determine the location, scale size, and dynamics of the chorus source region and chorus wave propagation characteristics are likely to achieve very similar results if repeated using the sheathcorrected data.
5 Comparison Between Wave Vector and Poynting Vector
For whistlermode waves in a cold plasma, a theoretical relationship exists between the relative directions of the wave vector and the Poynting vector (Taubenschuss et al., 2016). Figure 4a shows the refractive index surface in a cold plasma in the fieldaligned coordinate system where the f = 1.5 kHz, f_{ce} = 10 kHz, and f_{pe} = 20 kHz. The resonance cone and the Gendrin angle, θ_{G} (Gendrin, 1961), are shown by dashed and dotted lines, respectively. For each wave vector direction, the Poynting vector is normal to the refractive index surface. Here, we consider two wave vector directions defined by k_{1} (red) and k_{2} (blue). For k_{1}, θ_{k1} < θ_{G}, which results in both k_{1}, and the Poynting vector, S_{1}, oriented in the positive n_{⊥} direction. For k_{2}, θ_{k2} > θ_{G}, resulting in k_{2} being oriented in the positive n_{⊥} direction, but the Poynting vector, S_{2}, being oriented in the negative n_{⊥} direction. As such, the absolute value of azimuthal wave vector angle subtracted from the azimuthal angle of the Poynting vector, ϕ_{S} − ϕ_{k}, is equal to 0° in the case of k_{1} and S_{1}, but equal to 180° in the case of k_{2} and S_{2}. This theoretical relationship should remain true for all wave vector directions. That is, ϕ_{S} − ϕ_{k} = 0° for θ_{k} < θ_{G}, and ϕ_{S} − ϕ_{k} = 180° for θ_{k} > θ_{G}. Here, we explore the validity of this relationship using both the uncorrected and sheathcorrected observations.
As previously mentioned, θ_{S} is used to place the wave vector in the appropriate hemisphere and correctly define the wave vector direction. Once this adjustment to ϕ_{k} has been performed, we consider the probability distribution of ϕ_{k}, which is shown in Figure 4b for cases where θ_{k} < θ_{G} (red) and θ_{k} > θ_{G} (blue). Here, probability is defined as the number of occurrences in each bin divided by the total number of occurrences. For both θ_{k} < θ_{G} and θ_{k} > θ_{G}, the distribution is peaked near ϕ_{k} = 0° (antiEarthward). For θ_{k} < θ_{G} the wave vector is more fieldaligned, meaning there is intrinsically more scatter in the distribution of ϕ_{k}, as small variations in the direction of k can result in large changes in ϕ_{k}. For θ_{k} > θ_{G} the distribution is very strongly peaked in the antiEarthward direction. In these cases, ϕ_{k} is welldefined due to the more oblique propagation. This feature of ϕ_{k}, being peaked in the antiEarthward direction, has been previously reported (Taubenschuss et al., 2016; Hartley, Chen, et al., 2022; Hartley et al., 2019) and is a propagation effect that is wellmodeled by ray tracing (e.g., Chum and Santolik (2005); Santolik et al. (2006)).
Given the strongly peaked distribution of ϕ_{k} in the antiEarthward direction, it is expected that ϕ_{S} will present a distribution predominantly peaked antiEarthward direction if θ_{k} < θ_{G}, and Earthward direction if θ_{k} > θ_{G}. Here, we compute the difference between the azimuthal wave vector angle and the azimuthal Poynting vector angle, ϕ_{S} − ϕ_{k}, for each chorus wave observation. These distributions are shown for both the uncorrected (blue) and sheathcorrected (red) data in Figure 4c for cases when θ_{k} < θ_{G}, and in Figure 4d for cases when θ_{k} > θ_{G}.
For θ_{k} < θ_{G} (Figure 4c), the uncorrected observations (blue) show a bimodal structure in the distribution of ϕ_{S} − ϕ_{k}, with one peak near −45° and another near −145°. Overall, the distribution is quite broad around the two peaks. Given that θ_{S} generally becomes more fieldaligned in the sheathcorrected data (as demonstrated in Figure 2), one might expect the distribution of ϕ_{S} − ϕ_{k} to become broader when using the sheathcorrected data set. In fact, the opposite is true, with the corrected observations (red) presenting a narrower, singlepeaked distribution centered near 0°. This is much closer to the expected relation of ϕ_{S} − ϕ_{k} = 0°, as shown by the vertical dashed black line in Figure 4c. The mean of each distribution is also found by calculating $$, where the sum is over the total number of observations. These mean values are shown in Figure 4c for the uncorrected (blue) and sheathcorrected (red) distributions by vertical dashed lines. The mean of the uncorrected distribution is −72°, whereas the mean of the corrected distribution is −1°. This demonstrates that the uncorrected data display significant differences to the expected relationship between k and S, which are almost entirely rectified when using the sheathcorrected data.
For θ_{k} > θ_{G}, as shown in Figure 4d, both the uncorrected data (blue) and sheathcorrected observations (red) exhibit a singlepeaked distribution in ϕ_{S} − ϕ_{k}. We center the plot around the expected peak of 180° (vertical dashed black line). It should be noted that the uncorrected and sheathcorrected distributions are offset from each other. To quantify this offset, the mean of each distribution is determined yielding 192° for the uncorrected data, and 174° for the sheathcorrected data, which are shown by vertical dashed blue and red lines, respectively. The mean of 192° in the uncorrected data means that, on average, there is a 12° offset from the expected value. This offset is only 6° for the corrected observations, again demonstrating that the sheath correction results in the relationship between k and S being more in line with what is expected from Figure 4a.
To explore the frequency dependence of the relationship between k and S we consider the mean difference between ϕ_{S} and ϕ_{k} as a function of wave normal angle, θ_{k}, and f/f_{ce}. We take the absolute value of this difference, so values of −45° and 45° are considered to be the same deviation from the expected value, and also limit ϕ_{S} − ϕ_{k} values to be between 0° and 180°. These mean ϕ_{S} − ϕ_{k} values are shown in Figures 4e and 4f for the uncorrected and sheathcorrected observations, respectively. The solid black line represents the resonance cone and the dotdash line represents θ_{G}. For the uncorrected observations shown in Figure 4e, it is evident that for the majority of upper band chorus (0.5 < f/f_{ce} < 0.9), the difference between ϕ_{S} and ϕ_{k} is near, but not exactly, 180°. In general, values deviate further from 180° for frequencies near 0.5f_{ce}. The corrected observations shown in Figure 4f present average values of ϕ_{S} − ϕ_{k} very close to 180° for upper band chorus, with little variation with frequency. This relationship between k and S is expected, since all upper band chorus propagates with θ_{k} > θ_{G} (θ_{G} = 0° above 0.5f_{ce}).
For lower band chorus (0.05 < f/f_{ce} < f0.50), the uncorrected observations (Figure 4e) present a strong frequency dependence in the relationship between k and S. At frequencies near 0.05f_{ce}, the azimuthal difference between k and S is near the expected value of 0°. But with increasing frequency, ϕ_{S} − ϕ_{k} shifts away from 0° and by 0.20f_{ce} is close to 90°, even for θ_{k} values not near θ_{G}. For approximately fieldaligned waves, between 0.25 and 0.50f_{ce} and θ_{k} < θ_{G} the azimuthal difference between k and S is near 180°. In this region, there may be substantial scatter, as small fluctuations in the direction of k can result in large changes in ϕ_{k}. However, this relationship of ϕ_{S} − ϕ_{k} being close to 180° remains apparent even for θ_{k} > 30° above 0.30f_{ce} and with θ_{k} < θ_{G}. This is in conflict with the expected relationship shown in Figure 4a.
For the sheathcorrected observations shown in Figure 4f, the relationship between k and S is much closer to that expected, with ϕ_{S} − ϕ_{k} being near 0° for θ_{k} < θ_{G} and being near 180° for θ_{k} > θ_{G}, with the transition being welldefined by the θ_{k} = θ_{G} boundary. We do note some deviation from this expected relationship between 0.40 and 0.50f_{ce} for θ_{k} < 30°. This may be attributable to multiple factors, including (a) the assumption of a dipole field when determining the equatorial f_{ce} value from local observations, (b) ϕ_{k} not being welldefined for small θ_{k}, (c) the discrete frequency bins in the EMFISIS survey data leading to blurring across the f/f_{ce} = 0.50 boundary, or (d) some other yet unknown effect.
Considering how sheath corrections can impact the direction of S in the context of previous works, we note that Taubenschuss et al. (2016) reported some deviations from the expected relationship between k and S which affected a few instances of lower band chorus and the majority of upper band chorus. Whilst their analysis was conducted using different instrumentation (THEMIS), sheath effects are universal to all electric field wave instruments and are therefore a possible explanation for the reported deviations.
Overall, comparison between Figures 4e and 4f demonstrates that the expected relationship between k and S, as shown in Figure 4a, is generally wellreproduced by the sheathcorrected data, whereas significant deviations from the expected relationship exist in the uncorrected observations.
6 Summary and Conclusions

The sheathcorrected electric field chorus wave power is between two and nine times larger than the uncorrected observations, depending on wave frequency.

In general, the sheath correction has a larger impact on the electric field wave power in the perpendicular direction, and less so in the parallel direction. This is due to the spacecraft orientation.

The sheath correction results in the chorus wave Poynting flux being around a factor of 2 larger than in the uncorrected observations.

The sheath correction causes the polar angle of the Poynting vector, θ_{S} to switch hemisphere in only ∼2% of chorus wave observations.

The theoretically predicted relationship between the wave vector, k, and the Poynting vector, S, is wellreproduced by the sheathcorrected data (ϕ_{k} − ϕ_{S} = 0° for θ_{k} < θ_{G} and ϕ_{k} − ϕ_{S} = 180° for θ_{k} > θ_{G}), whereas the uncorrected observations show significant deviations from these expected values.
Overall, this study provides the first direct comparison between the sheathcorrected electric field observations and the uncorrected data product, quantifying the impact that the sheath correction has on chorus wave observations. These results help frame the context of previous studies based on uncorrected electric field wave observations by providing the community with statistically averaged values describing the impact of the sheath correction on chorus wave properties.
Acknowledgments
DPH, IWC, MRA and NA acknowledge that this material is based upon work supported by the National Aeronautics and Space Administration under Grant 80NSSC21K0519 issued through the Heliophysics Guest Investigators  Open 2020 Program. OS and IK acknowledge funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 870452 and acknowledge support from MSMT Grant LUAUS23152.
Open Research
Data Availability Statement
All data used in this analysis is freely available and may be obtained from http://emfisis.physics.uiowa.edu/data/index or http://spdf.gsfc.nasa.gov/pub/data/rbsp/.