The Relationship Between Cusp Region Ion Outflows and East‐West Magnetic Field Fluctuations at 4,000‐km Altitude

A number of interdependent conditions and processes contribute to ionospheric‐origin energetic ( ∼ 10 eV to several keV) ion outflows. Due to these interdependences and the associated observational challenges, energetic ion outflows remain a poorly understood facet of atmosphere‐ionosphere‐magnetosphere coupling. Here we demonstrate the relationship between east‐west magnetic field fluctuations ( ΔBEW ) and energetic outflows in the magnetosphere‐ionosphere transition region. We use dayside cusp region FAST satellite observations made near apogee ( ∼ 4,180‐km altitude) near fall equinox and solstices in both hemispheres to derive statistical relationships between ion upflow and ΔBEW spectral power as a function of spacecraft frame frequency bands between 0 and 4 Hz. Identification of ionospheric‐origin energetic ion upflows is automated, and the spectral power PEW in each frequency band is obtained via integration of ΔBEW power spectral density. Derived relationships are of the form J‖,i=J0,iPEWγ for upward ion flux J‖,i at 130‐km altitude, with J0,i the mapped upward ion flux for a nominal spectral power PEW=1 nT 2 . The highest correlation coefficients are obtained for spacecraft frame frequencies ∼ 0.1–0.5 Hz. Summer solstice and fall equinox observations yield power law indices γ≃ 0.9–1.3 and correlation coefficients r≥0.92 , while winter solstice observations yield γ≃ 0.4–0.8 with r≳0.8 . Mass spectrometer observations reveal that the oxygen/hydrogen ion composition ratio near summer solstice is much greater than the corresponding ratio near winter. These results reinforce the importance of ion composition in outflow models. If observed ΔBEW perturbations result from Doppler‐shifted wave structures with near‐zero frequencies, we show that spacecraft frame frequencies ∼ 0.1–0.5 Hz correspond to perpendicular spatial scales of several to tens of kilometers.

Any particular instance of energetic ion outflow therefore represents interplay between a variable number of processes and conditions, which themselves vary over spatial scales ranging from tens to thousands of kilometers, over time scales ranging from seconds to years (Horwitz & Zeng, 2009;Varney et al., 2016), and with altitude (e.g., Bouhram et al., 2004;Fernandes et al., 2016;Nilsson et al., 2006;Nilsson, 2011;Waara et al., 2011).
These empirical relationships, along with a similar set of relationships derived by Zheng et al. (2005) from 37 Polar satellite passes of the dayside Southern Hemisphere (SH), have either been employed directly (Brambles et al., 2010(Brambles et al., , 2011 or otherwise served as points of reference in ion outflow simulations and theoretical works (e.g., Brambles et al., 2011;Horwitz & Zeng, 2009;Kronberg et al., 2014;Moore & Khazanov, 2010;Varney et al., 2016). These works nonetheless all express a need for additional observational studies to validate and expand these empirical relationships. Such studies have largely not been performed, due at least in part to a lack of applicable data sets (i.e., simultaneous electric field, magnetic field, and ion distribution measurements). There are furthermore no studies demonstrating how these statistical relationships might vary with season, local time, or interplanetary magnetic field conditions. There has resultantly been only limited progress in understanding the fundamental causes and processes of ionospheric-origin ion up/outflows during the past decade (Horwitz & Zeng, 2009;Kronberg et al., 2014;Varney et al., 2016).
In this study we consider the relationship between cusp region upward ion fluxes and east-west magnetic field perturbations ΔB EW in nearly arbitrary frequency bands, in both hemispheres during winter and summer. We also show that ion composition is likely an important factor in predicting energetic outflow fluxes. In section 2 we describe FAST satellite ion and magnetic field (B field) measurements and how we process these quantities to calculate average upward ion fluxes and east-west B field fluctuations as a function of spacecraft frame frequency band. We apply our methodology to the FAST observations that S05 and B11 considered and compare our results to theirs. In section 3 we use our methodology, together with four different groups of FAST observations made between December 1996 and January 1999, to obtain statistical relationships between average upward ion flux and ΔB EW for nearly arbitrary spacecraft frame frequencies between 0 and 4 Hz. In section 4 we discuss and summarize the results presented in section 3, including how our methodology could be applied to current satellite missions; we discuss the role of ion composition in these as well as previous results; and we show that if we assume observed field perturbations are spatial rather than temporal, the perpendicular length scales associated with outflow near FAST apogee are of order several to a few tens of kilometers.

Data Set and Methodology
Launched into a polar orbit on 21 August 1996, the FAST satellite covered the range of altitudes between ∼350 and 4,180 km, covering all magnetic local time (MLT) sectors every ∼3 months due to the 83 • inclination of the orbit . The FAST scientific payload included a suite of instruments capable of measuring in situ magnetic and electric fields, two-dimensional electron and ion pitch angle distributions, and three-dimensional distributions of select ion species Ergun et al., 2001;Klumpar et al., 2001 Table 1 summarizes the four groups of FAST orbits that are used in this study. The first consists of the group of 33 NH orbits during September 1998 considered by S05 and B11. The second consists of NH observations during local winter, and the third and fourth consist of SH observations during local summer and local fall, respectively. The latter three groups of orbits were selected based on the following criteria, which mimick the characteristics of the 33 orbits used by S05 and B11: 1. Availability of ion and B field measurements over magnetic latitudes (MLats) between 60 • and 87 • in the NH (−87 • to −60 • in the SH) and over dayside MLTs; 2. Continuous ion and B field measurements at altitudes between 3,800 km and FAST apogee; 3. Satellite trajectory on the dayside that is primarily aligned with the noon-midnight meridian (as opposed to being aligned with, e.g., the dawn-dusk meridian; see Figure 1a).
MLat and MLT are defined at a reference height h r = 130 km in the Modified Apex coordinate system (hereafter MA 130 ) (Laundal & Richmond, 2016;Richmond, 1995), which we obtain from the apexpy Python package (van der Meeren et al., 2018). In our experience, inclusion of FAST observations made under conditions not meeting requirements (1)-(3) renders the intercomparison of analysis results from each orbit group difficult or impossible. In particular relaxing the second and third requirements leads to additional sources of uncertainty/Doppler shifting of the frequencies of field measurements, as well as difference in frames of reference between FAST and ionospheric upflows that lead to sometimes overwhelming spacecraft ram ion signatures in IESA measurements. (See Heelis & Hanson, 1998;Moore et al., 1998, for some discussion of ram ions.) Thus, these requirements are imposed on orbit groups 2-4 in Table 1 to facilitate comparison with Group 1 observations, whose orbit characteristics are the basis of these requirements.

Ion Measurements and Upflow Identification Algorithm
The IESA sampled full two-dimensional ion pitch angle distributions at cadences between ∼0.4 and 13 Hz, depending on the mode of operation. Figure 1a shows an example pitch angle spectrogram derived from IESA ion measurements on 25 September 1998 during FAST orbit 8276, which is the same orbit represented in Figures 1 and 2 of S05. In Figure 1a the range of pitch angles is adjusted such that "downward" (or earthward) ion measurements are correspond to the lower half (−90 • < < 90 • ) of the pitch angle-time spectrogram. "Upward" or (anti-earthward) ion measurements are those corresponding to the upper half (90 • < < 270 • ) of the pitch angle time spectrogram.
Two ion populations are visible in Figure 1a: (i) an isotropic (i.e., covering all pitch angles) magnetospheric-origin population with mirror points below the altitude of FAST, appearing between ∼00:04:40 and 00:07:50 UT; (ii) an ionospheric-origin intense upflowing ion population appearing between  Figure 1f. The spacecraft frame frequency ranges termed "DC" (0-0.125 Hz) and "AC" (0.125-0.5 Hz) by S05 and B11 are highlighted in orange and blue, respectively, in Figure 1g. To avoid spuriously identifying background noise as upflow, for all energy bins in Figure 1b with upward differential energy fluxes dJ E ∕dE < 5 × 10 5 eV/cm 2 ·s·sr·eV the corresponding up/down ratio is set to zero in Figure 1d and in the upflow identification algorithm.
Figure 1b, which is the "upward ion" energy-time spectrogram that results from averaging over antiearthward pitch angles, shows that the average differential energy fluxes of the lower-energy, ionospheric-origin ion population are intense (dJ E ∕dE ≳ 10 8 eV/cm 2 ·s·sr·eV). This ionospheric population does not appear in the "downward ion" spectrogram ( Figure 1c), which is the ion energy-time spectrogram that results from averaging over all earthward pitch angles | | < 90 • .
We wish to exclude the contribution from magnetospheric ions to the calculated ionospherically sourced upward ion flux. To achieve this, S05 and B11 manually inspected the ion energy spectrogram from each cusp pass and visually determined a cutoff energy. They then integrated the observed ion distributions up to this cutoff energy and over all pitch angles.
Attempting to exactly reproduce the results of S05 and B11 is difficult because they do not state the ion cutoff energies that were used for each orbit. We have alternatively developed the following algorithm for identification of the appropriate upper bound on ion energy.
1. For each point in time, average particle counts in each energy-angle bin over all antiearthward pitch angles to obtain an "upward ion" energy spectrogram (e.g., Figure 1b). Also average particle counts over all Earthward pitch angles to obtain a "downward ion" energy spectrogram (e.g., Figure 1c). 2. Divide the upward ion spectrogram by the downward ion spectrogram to obtain an "up/down ratio" spectrogram ( Figure 1d). 3. To avoid noise, set the up/down ratio to zero for all energy bins with upward differential energy flux dJ E ∕dE < 5 × 10 5 eV/cm 2 ·s·sr·eV. 4. Let the bin with the highest energy for which the up-down ratio is at least 5 be denoted E top . If either (a) no bins have an up/down ratio of at least 5, or (b) less than 75% of energy bins below E top have up/down ratios of at least 1, no upflow is present in this ion distribution. 5. If the ion distribution meets the foregoing criteria, obtain the upward ion flux J ||,up by integrating the original two-dimensional ion distribution over all pitch angles and from the 4 eV lower limit of the IESA detector energy range up to E top .
Following S05 and B11, in this study we have elected to integrate each ion distribution over all pitch angles to obtain the net ion flux. The pink line in Figure 1d indicates E top as identified by this algorithm. The corresponding time series of J ||,up is shown in Figure 1e. All J ||,up are mapped to 130-km altitude (approximately the base of the F region ionosphere) via multiplication by the mapping factor R ≡ D i ∕D FAST > 1. The quantity D = |d 1 × d 2 | is a function of the altitude-dependent basis vectors d 1 and d 2 in the MA 130 coordinate system and is defined such that D i and D FAST are respectively proportional to the main-field magnitudes at 130-km altitude and at FAST altitude (Richmond, 1995). (Thus R > 1 for all FAST observations.) Mapped values of J ||,up are then averaged to obtain a single average upward ion flux.

Magnetic Field Measurements and PSD Estimates
The fluxgate magnetometer sampled all three B field components at rates between 8 and 128 Hz, depending on the mode of operation. Despinning of B field measurements is performed by the ucla_mag_despin routine that is included with SDT software, after which we subtract the International Geomagnetic Reference Field-12 main field model. The quantity ΔB EW = e 1 ·ΔB gives the (approximately) east-west component of the B field perturbation vector ΔB, where e 1 is an MA 130 coordinate system base vector such that ΔB EW is mapped to 130 km.
Via the multitaper method Slepian, 1978;Thomson, 1982), we estimate the power spectral density (PSD) of the portion of the time series that meets the MLat, MLT and altitude criteria given in section 2. We calculate the spectral power in a particular spacecraft frame frequency band by integrating the PSD estimate over all frequencies within that band. For example, a ∼15-min time series of ΔB EW is shown in Figure 1f, with the corresponding multitaper PSD estimate shown in Figure 1g. The spacecraft frame frequency ranges termed "DC" (0-0.125 Hz) and "AC" (0.125-0.5 Hz) by S05 and B11 are respectively highlighted in blue and orange. Integration of the PSD estimate over DC and AC frequency bands thus defined yields spectral powers of 2.88 × 10 5 nT 2 and 6.67 × 10 2 nT 2 , respectively.

Comparison With S05 and B11
In summary, the methodology of S05 and B11 is based on manual identification of an ion cutoff energy for each cusp pass and average Poynting flux calculated from time series of B field and electric field measurements. In contrast, our methodology is based on automated identification of ion outflows for each cusp pass and a spectral representation of B field measurements. We now compare analysis results using each methodology to determine whether our methodology, which excludes electric field measurements and uses frequency-domain (instead of time-domain) calculations of average B field fluctuations, yields correlation coefficients that are similar to those yielded by the S05 and B11 methodology.  From the comparison of methodologies shown in Figure 2, we conclude that our methodology yields correlation values that are comparable to or higher than those resulting from the S05 and B11 methodologies.
While our methodology provides no information about which processes or possibly wave modes may be operating in association with the observed outflows, it nevertheless makes apparent that electric field measurements are not necessary for determination of an empirical relationship between field perturbations and energetic ion outflow. We now apply our methodology to four groups of orbits to investigate the relationship between J ||,up and ΔB EW as a function of season, hemisphere, and frequency band.

Statistical Relationships Between Ion Outflow and B EW
The AC and DC frequency bands defined by S05 arose in connection with the interpolation and the series of decimations and smoothings that they applied to the time series of field measurements (Appendix A in S05). In contrast the spectral method we use allows for analysis of an arbitrary frequency band, up to the frequency resolution of each PSD (typically less than 0.01 Hz).
In this section we perform the same type of correlation and fitting shown in Figure 2 for the 19,900 possible frequency bands between 0 and 4 Hz with spectral resolution 0.02 Hz, for the four groups of orbits indicated in Table 1. We hypothesize that the inferred relationship between average ion outflow and B field fluctuations varies as a function of season and hemisphere. To test this hypothesis we analyze each group of orbits separately. Figure 3 shows the results of analysis of 19,900 frequency bands between 0 and 4 Hz for the 33 NH cusp region passes considered by S05 and B11. Figure 3a shows the portion of each pass that meets the three criteria in section 2 (60-87 • MLat, 6-18 MLT, and at or above 3,800-km altitude), with thick lines indicating observations of ion outflow. Except during storms, the geomagnetic cusp is typically observed at 70 • < MLat < 80 • (Zhang et al., 2013;Zhou et al., 2000). The observation of ion outflows at MLat < 70 • during several passes is therefore indicative of the geomagnetic storm that occurred during 24-25 September 1998. Figure 3b shows the PSD estimate for each ΔB EW time series as well as the median PSD (orange line). The median PSD ranges over nearly seven orders of magnitud, and decreases by roughly 4 orders of magnitude between 0 and ∼0.2 Hz. (The two spikes that reach ∼10 1.5 nT 2 /Hz at ∼3.7 and 3.9 Hz are artifacts related to the ucla_mag_despin routine, whereas the troughs at ∼1.1, 2.35, and 3.45 Hz are related to the recursive filter of the fluxgate magnetometer (Elphic et al., 2001). Similar artifacts are visible in the PSDs shown in Figures 4b, 5b, and 6b.) Figure 3c displays the correlation coefficient r resulting from a least squares linear fit to the logarithm of the average mapped upward ion flux and the logarithm of ΔB EW spectral power within the frequency bands given by the x and axes. The x axis gives the upper bound ("stop frequency") of the frequency band top , and the axis gives the lower bound ("start frequency") of the frequency band bot . Each linear fit is of the form

Northern Hemisphere, September 1998 (Local Fall)
where J ||,i is the predicted upward ion flux after mapping to 130-km altitude, is the power law index (Figure 3d), P EW is the spectral power within the selected frequency band, and J 0,i is the mapped upward ion flux (in cm −2 s −1 ) for nominal spectral power P EW = 1 nT 2 .
As an aid in the interpretation of Figure 3c, The highest correlation coefficients (r ≥ 0.9) correspond to frequency bands such that 0.08 Hz ≲ bot ≲ 0.3 Hz and bot < top ≲ 4 Hz. In particular the frequency band 0.2-0.34 Hz (indicated by the transparent black star in Figure 3c) yields the highest correlation coefficient r = 0.932, with a best fit relationship J ||,i = 2.28 × 10 7 P 1.20 EW . Figure 4 shows the results of analysis of 19,900 frequency bands between 0 and 4 Hz for 38 NH cusp region passes occurring between 30 December 1996 and 7 January 1997, corresponding to local winter. The layout identical to that of Figure 3. Figure 4a shows that observed ion outflows are confined to MLat ≳ 70 • during these passes, with the majority observed at MLat ≳ 75 • . Outflows at these latitudes are indicative of the geomagnetic quiescence that prevails throughout the 9-day period. Figure 4b shows that the individual PSD estimates (transparent black lines) and median PSD (orange line) vary less overall than the PSD estimates shown in Figure 3b. The median PSD ranges over fewer than 6 orders of magnitude, decreasing by roughly 2 orders of magnitude over 0-0.2 Hz.

Northern Hemisphere, December 1996 (Local Winter)
In Figure 4c, the highest correlation coefficients (r ≥ 0.75) correspond to spacecraft frame frequency bands such that 0.25 Hz≤ bot ≤0.7 Hz and 0.6 Hz≤ top ≤1.5 Hz. In particular the frequency band 0.62-0.8 Hz yields the highest correlation coefficient r = 0.792, with a best-fit relationship J ||,i = 4.47 × 10 8 P 0.83 EW .  Figure 5 shows the results of analysis of 19,900 frequency bands between 0 and 4 Hz for 32 SH cusp region passes occurring between 8 and 15 January 1999, corresponding to local summer. The layout is identical to that of Figure 3. Figure 5a shows that ion outflows are mostly observed at MLat ≳ 70 • during these passes. The relatively small number of outflow observations made below these magnetic latitudes correspond to the portion of the 8-day observational period that coincides with a geomagnetic storm (Dst min = −110 nT) during 13-17 January. Figure 5b shows that the individual PSD estimates (transparent black lines) and median PSD (orange line) are comparable to the PSD estimates and median PSD shown in Figure 3b. The median PSD ranges over ∼7 orders of magnitude and decreases by more than 3 orders of magnitude between 0 and ∼0.2 Hz. Similar to the artifacts visible in Figure 3b, the spiked spectral features at ≳3.5 Hz are also artifacts related to the ucla_mag_despin routine. The troughs at ∼1.25, 2.35, and 3.45 Hz are related to the recursive filter of the fluxgate magnetometer.

Southern Hemisphere, January 1999 (Local Summer)
In Figure 5c, the correlation coefficient r ≥ 0.9 for nearly 50% of all spacecraft frame frequency bands considered. Correlation coefficients r ≥ 0.90 correspond to frequency bands given by either 1 Hz ≤ bot ≤ 1.6 Hz and bot ≤ top ≤ 2.6 Hz, or 0.1 Hz ≤ bot ≤ 0.6 Hz and 0.2 Hz ≤ top ≤ 4 Hz. In particular the spacecraft frame frequency band 1.6-1.74 Hz yields the highest correlation coefficient r = 0.927, with a best fit relationship J ||,i = 2.05 × 10 9 P 0.99 EW . Figure 6 shows the results of analysis of 19,900 frequency bands between 0 and 4 Hz for 29 SH cusp region passes occurring between 24 May and 5 June 1999, corresponding to late fall. The layout is identical to that 10.1029/2019JA027454 of Figure 3. Figure 6a shows that ion outflows are mostly observed at MLat ≳ 70 • during these passes. The two regions of outflow over 14-15.5 MLT and near or below 70 • MLat were observed during periods of weak geomagnetic activity (Dst min = −34 nT) that occurred intermittently during the 13-day observational period. Figure 6b shows that the individual PSD estimates (transparent black lines) and median PSD (orange line) vary less overall than the PSD estimates shown in Figure 3b. The median PSD ranges over more than 6 orders of magnitude overall and decreases by more than 3 orders of magnitude over 0-0.2 Hz. The two spikes that reach ∼10 nT 2 /Hz at ∼3.7 and 3.85 Hz are artifacts related to the ucla_mag_despin routine, whereas the deep troughs at ∼1.2, 2.35, and 3.45 Hz are related to the recursive filter of the fluxgate magnetometer. Figure 6c shows that the highest correlation coefficients (r ≥ 0.85) correspond to spacecraft frame frequency bands such that 0.2 Hz ≤ bot ≤ 0.4 Hz, 0.25 Hz ≤ top ≤ 4 Hz. The frequency band 0.26-0.36 Hz yields the highest correlation coefficient r = 0.909, with a best fit relationship J ||,i = 1.26 × 10 8 P 0.68 EW .

Discussion and Summary
Two primary goals of this study are validation of the spectral method for studying the relationship between field fluctuations and upward ion fluxes, and expansion of the original data set considered by S05 and B11 to the Southern Hemisphere and other seasons. Results in Figures 2-6 demonstrate that empirical relationships very similar to those reported by S05 and B11 arise without inclusion of electric field measurements, and without recourse to visual determination of the cutoff energy (see sections 2.1 and 2.3). While we believe these aspects are significant, our methodology and data sets are nevertheless subject to their own limitations.
First, the algorithm for automated identification of ion outflows presented in section 2.1 is well suited to cusp region energetic ion outflows, but likely misses other forms of energetic ion up/outflows that are more typical at other local times, such as nightside ion beams (Kondo et al., 1990). We have elsewhere developed and employed an algorithm for automated identification of ion beams (Hatch, Chaston et al. 2018), which could be employed in possible future work dealing with the relationship between ion beams and field fluctuations.
Second, throughout this study we have relied on the assumption of S05 and B11 that the relationship between upward ion flux and field fluctuations is of the form of a power law. The scatter plots shown in the b panels of Figures 2-6 provide clear evidence that such a relationship could be derived from first principles for the presented ranges of spectral powers and outflow fluxes, but leave as an open question whether a power law relationship is valid for fluxes and spectral powers outside the observed ranges. Existing attempts in the literature (Horwitz & Zeng, 2009;Moore & Khazanov, 2010;Varney et al., 2016) to theoretically reproduce the observations presented by S05 and B11 represent important steps toward a full theoretical description, but each study points to a need for more observational data.
Third, regarding field measurements, we have not used FAST electric field measurements to estimate the field-aligned Poynting flux, as did S05 and B11. Two disadvantages of this approach, noted in section 2.3, are that it does not provide information about input electromagnetic energy, nor does it allow for inference of the relevant processes on the basis of techniques involving analysis of the perturbation electric and magnetic field ratio or plasma density perturbations (e.g., Wahlund et al., 1998; Figure A1 in S05). On the other hand this approach opens the exploitation of magnetic field measurements as a possibly powerful alternative to Poynting flux measurements in studies of energetic ion outflows, and could yield a significant contribution to filling the knowledge gaps mentioned in section 1. This approach is the planned subject of future work.
Fourth, we have exclusively considered the east-west component of the measured magnetic field. This component yields overall higher correlation coefficients than those yielded when we instead use the north-south component of the measured magnetic field, though in many cases the differences are slight. Our choice is also motivated by the preferential east-west orientation of Alfvénic magnetic field perturbations, as already discussed in section 1.
Fifth, the dayside cusp region is the site of small-scale, relatively large amplitude field-aligned currents (Kervalishvili & Lühr, 2013;Neubert & Christiansen, 2003;Rother et al., 2007;Watermann et al., 2009). As an alternative to calculating the correlation coefficient between ⟨J ||,up ⟩ and ΔB EW spectral power P EW , as we have done here, we could have correlated ⟨J ||,up ⟩ with estimates of field-aligned current amplitude. This latter type of correlation study between field-aligned current amplitude and various ionospheric and thermospheric parameters has in fact been carried out elsewhere (Kervalishvili & Lühr, 2013;Shen et al., 2016). We have opted not to perform this type of analysis, primarily because our study takes the work of S05 and B11 as starting points of reference. Neither of these studies dealt with field-aligned current estimates. Performing a correlation study with the data sets we have presented that is based on field-aligned currents could yield additional physical insight, but we deem such work outside the scope of the present study.
We believe that a critical aspect of this study is the stringent criteria on spacecraft MLT, Mlat, altitude, and direction of approach to the cusp region. We have discussed in section 2 that the purpose of these criteria is to reduce potential Doppler shifting of field measurements and to exclude ram ions as much as possible.
With these criteria there emerges from the analysis of each group of orbits some common characteristics of the relationship between ion outflows and east-west magnetic field fluctuations, which we now discuss.
(Text S1 and Figures S1-S4 in the supporting information provides versions of the analysis in Figures 3-6 with the restriction to altitudes of 3,800 km or greater relaxed).
The most salient feature in panel c for each of Figures 3-6 in section 3 is that the correlation between ion outflows and east-west magnetic field fluctuations ΔB EW is high for spacecraft frame frequencies sc ≲ 0.7 Hz in every case. Only orbits in Group 2 (section 3.2) involve pole-to-equator traversals of the cusp region, and as we discuss below in connection with Table 4, Doppler shifting of Group 2 spacecraft frame frequency bands is one possible explanation for the different frequency characteristics of Group 2 orbits relative to the three groups of orbits, for which FAST approaches the cusp region from the equator. For Groups 1 and 4 orbits the upper limit of frequencies corresponding to high correlations is even narrower, sc ≲ 0.4 Hz.
On the other hand, the frequency characteristic of Group 3 orbits in Figure 5c are distinct from the frequency characteristics of the other three groups: the overall distribution of r values for Group 3 orbits is overall significantly shifted to higher r values, and is spread over an overall smaller range. Table 2 summarizes the properties of the distribution of r values for each of the four groups of orbits. From Table 2 it is evident that both the median and mean r values for Group 3 orbits are much higher than the median and mean r values for any of the other three groups of orbits. In other words, for Group 3 orbits the correlation coefficient between ⟨J ||,up ⟩ and P EW is high almost regardless of frequency band.
Regardless of the direction of approach or the distribution of r values, panel c for each of Figures 3-6 shows that the correlation coefficient r varies primarily with the lower bound bot ( axis) of a given frequency band, while the dependence on the upper bound top (x axis) is relatively much weaker. The dominating role of bot in the variation of the correlation coefficient arises due to the general shape of the PSD estimates corresponding to each orbit (transparent black lines in panel b for each of Figures 3-6). Each PSD estimate exhibits a logarithmic, and approximately monotonic, decrease with increasing frequency up to sc ∼ 1 Hz. Thus, the spectral power P EW obtained from integration of any frequency band with a lower bound bot ≤ 1 Hz is primarily determined by bot and largely invariant with respect to the upper bound top .
To make the results shown in Figures 3-6 easily implementable for modelers, Table 3 provides best fit relationships of the form J ||,i = J 0,i P EW between upward ion flux mapped to 130-km altitude J ||,i , spectral power P EW , and power law index ≃ 0.7-1.2 for the spacecraft frame frequency band 0.18-1.46 Hz. We have chosen this frequency band because it yields the "maximum average correlation coefficient"r max obtained as follows.
Let r i ( bot , top ) be the correlation coefficient for the ith orbit group, where i ∈ (0, 1, 2, 3) indicates one of the four groups of orbits in Tables 1 and 3, and ( bot , top ) denotes any of the 19,900 frequency bands represented by the x and axes of panel c in Figures 3-6. Then the "maximum average correlation coefficient"r max = a J 0,i is the mapped upward ion flux (in cm −2 s −1 ) for nominal spectral power P EW = 1 nT 2 . P EW is the integral of the ΔB EW PSD (in nT 2 /Hz) over 0.18-1.46 Hz. b The angle brackets ⟨⟩ 27 denote a backward-looking average over a 27-day window.
max(r A )= max( 1 4 ∑ i r i ( bot , top )) = 0.868 is obtained for the frequency band ( bot = 0.18 Hz, top =1.46 Hz). This frequency band also yields the maximum if we instead calculate the maximum via the geometric mean or the harmonic mean. Figure 7a shows, for all 132 orbits used in this study, individually observed ion outflow fluxes (mapped to 130-km altitude) as a function of season. Groups 1 and 3 upward ion fluxes (red plus and blue x symbols), which respectively occurred near fall equinox and summer solstice, are overall greater than Groups 2 and 4 upward ion fluxes (purple circle and orange triangle symbols), which both occurred near winter solstice. This observation leads us to consider the dependence of upward ion fluxes on season.
Two causes of long-term variation in the properties of outflowing ions are season and solar cycle. On point of season, Yau et al. (1985) found that the occurrence of O + upflows over altitudes of 8,000 to 23,000 km is favored by summer solstice, while they found no significant variation of the occurrence of H + with season. On point of solar cycle, Yau et al. (1988) found that the outflowing O + /H + ratio increases by an order of magnitude from solar minimum to solar maximum.
Based on these differences in season and solar cycle for the four groups of orbits, we expect that Groups 1 and 3 outflows are richest in O + , with Group 4 outflows somewhat poorer and Group 2 outflows poorest in O + . To directly demonstrate the existence of these differences, Figure 7b shows the O + /H + density ratio derived from analysis of ion composition measurements made by the Time-of-Flight Energy, Angle, Mass Spectrograph (TEAMS) instrument (Klumpar et al., 2001) aboard FAST. As with upward ion fluxes in panel a, each data point represents an individual O + /H + density ratio estimate for TEAMS observations made during 114 of the 132 orbits shown in Figure 7a. (TEAMS measurements were unavailable for the other 18 passes.) The density moment is calculated for each species distribution function measured by TEAMS by integrating over all angles, and from 4 eV up to the IESA energy cutoff E top given by the outflow identification algorithm in section 2.1. (For example, E top is indicated by the pink line in Figure 1d.) Each TEAMS measurement is required to meet the same criteria from section 2 that we have applied to FAST IESA and magnetometer data, and we include only those TEAMS measurements that correspond to time periods when ion outflow is positively identified in IESA measurements.
As mentioned in section 3, moderate to high levels of geomagnetic activity were also observed during Groups 1, 3, and 4 orbits. To exclude the effects of geomagnetic activity, the boxplots composed of dashed lines in Figures 7a and 7b indicate outflow and O + /H + statistics for K p ≤ 2.5. (K p values were obtained from the publicly available OMNI database at https://omniweb.gsfc.nasa.gov/form/dx1.html.) Figure 7b indicate that the upflows observed near or during summer solstice are relatively much richer in O + than those during winter, as expected. On the other hand, comparison of the dashed-line boxplots reveals that the overall distributions of "geomagnetic quiescence" outflow fluxes are mostly similar and apparently somewhat independent of season. This fact highlights that geomagnetic activity and seasonal effects may be conflated in the analysis presented in Figures 3-6.

Both sets of boxplots in
Removing outflowing ion fluxes observed during K p > 2.5 unfortunately removes more than 50% of all observations in Groups 1 and 3 orbits. We therefore have insufficient statistics to perform a separate analysis based only on observations during geomagnetic quiescence, and in this study we are not able to untangle the effects geomagnetic activity and seasonal variations.
TEAMS measurements are currently undergoing additional calibration and dead-time correction by a study coauthor (E. J. Lund). At present these measurements likely underestimate the actual densities of each species and are not suitable for the correlation analysis that we have performed in section 3. But the overall trends and order-of-magnitude differences are sufficient to underscore that the composition of ionospheric outflow likely play a role in seasonal variations of the relationship between ionospheric outflow and magnetic field perturbations that we have demonstrated. Thus Figure 7 demonstrates that ion composition should not be neglected in any comprehensive model of wave-driven energetic ion outflows. Although outside the scope of this study, we reserve extended treatment of ion composition as a possible focus of future work.
On the question of Doppler shifting raised in section 2 and at the beginning of this section, other studies based on FAST and Freja observations (Chaston et al., 2006; have explicitly demonstrated that low-frequency waves with short perpendicular wavelengths (of order ∼0.01-10 km) on the dayside are observed by these satellites as broadband waves in the spacecraft frame of reference via Doppler shift.
While we emphasize that our approach does not allow us to determine the properties of the field perturbations we have analyzed in this study, we show here that the two following assumptions 1. magnetic field perturbations observed by FAST over 0-4 Hz in the spacecraft frame of reference are either spatial structures or wave structures with frequencies near zero (i.e., (k) ≃ 0); 2. the variation of magnetic field perturbations is primarily perpendicular to the background magnetic field (i.e., k ⟂ ≫ k || ); With these assumptions the observed spacecraft frame frequencies arise via Doppler shifting according to where v F,⟂ is the perpendicular speed of FAST and V is the poleward plasma convection speed. Thus, the spacecraft frame frequency sc corresponds to a perpendicular spatial scale Typical convection speeds in the dayside cusp region at ionospheric altitudes (i.e., hundreds of kilometers) range from hundreds of m∕s up to 2-3 km∕s during active conditions (Moen et al., 1996;Skjaeveland et al., 2011Skjaeveland et al., , 2014, and typical speeds of FAST perpendicular to the background magnetic field near apogee are |v F,⟂ | =5.2-5.6 km∕s. We assume V =1 km∕s and v F,⟂ = ±5.5 km∕s, where the positive sign corresponds to poleward orbits (i.e., Groups 1, 3, and 4) and the negative sign corresponds to equatorward orbits (i.e., Group 2). We then apply equation 3 to the range of "start frequencies" bot , indicated on the axis of panel c for Figures 3-6, for which r ≥ r 90% . (The subscript "0.9" denotes the 0.9 quantile of all calculated r values for a particular orbit group. For example, 10% of all r values in Figure 3c are 0.91 or greater; thus r 90% = 0.91 in Table 4.) The rightmost column of Table 4 shows the resulting range of perpendicular spatial scales near FAST apogee for each group of orbits. If the above-stated assumptions are valid, east-west field perturbations with perpendicular spatial scales of order tens of kilometers are associated with ion outflow. Indeed, it has been shown (e.g.,  and section 2.2 as well as Figure 3 of  that much of the temporal variation observed in the FAST and Freja spacecraft frame of references at these altitudes is due to Doppler shifting of dispersive Alfvén wave structures. As a consistency check, applying equation (2) to the range of scale sizes L ⟂ = 10-42 km corresponding to Group 2 in Table 4 shows that if FAST had been moving poleward instead of equatorward in the presence of plasma convecting poleward at 1 km/s, these scale sizes would have been observed over the spacecraft frequency range bot = 0.11-0.44 Hz. Though not proof, range is more consistent with the bot ranges for Groups 1, 3, and 4 in Table 4, and suggests that the above assumptions are at least plausible.
These perpendicular scales are in between large scales (of order hundreds or thousands of kilometers, corresponding to quasi-static field-aligned currents and the electrojets) and kinetic scales (of order 1 m to a few km, corresponding to local ion gyroradii and the electron inertial length) within and in the vicinity of the dayside cusp. Thus, instead of corresponding to direct driving of energetic ion outflow, these scales may be related to a number of processes that are associated with ion outflow.
Both simulations (Chaston et al., 2004;Génot et al., 2004;Rankin et al., 2005) and satellite observations (Chaston et al., 2006) have shown that the interaction of shear Alfvén waves with a preexisting ionospheric density irregularity produces field-aligned broadband electron precipitation, transverse ion acceleration, ion heating, and plasma depletion (Chaston et al., 2006, Figure 6). This interaction also leads to phase 10.1029/2019JA027454 mixing and the production of field fluctuations over perpendicular scales ranging from the scale size of the density irregularity down to and below the electron inertial length, typically of order km in the magnetosphere-ionosphere transition region.
As observed by Lotko and Zhang (2018), evidence that these perpendicular spatial scales are associated with Alfvén waves has been reported by Ishii et al. (1992). Using DE-2 measurements at 300-km altitude they showed that field perturbations over DE-2 spacecraft frame frequencies of ≳0.25 Hz were more consistent with an Alfvénic rather than a quasi-static interpretation; treating this frequency range as resulting from Doppler-shifted structures, they reported perpendicular spatial scales of ≲30 km at 300-km altitude (≲60 km near FAST apogee).
As an additional plausibility check, we have determined from the Hatch et al. (2017) inertial Alfvén wave database that inertial Alfvén waves are observed during 83% (109 out of 132 total) of the cusp region passes. This percentage is presented only for the purpose of indicating that Alfvén waves are in fact often present during observed upflows, with a median of 26 Alfvénic current filaments identified per orbit for all 132 orbits.
Here we have favored interpretation of observed dayside field perturbations at FAST altitudes as Doppler-shifted Alfvénic structures. We should emphasize that this interpretation, while plausible, is not the only possibility. At mHz-to Hz-range frequencies, there exist alternative interpretations based on ion-cyclotron waves, ion-acoustic waves, and field gradients or energy density inhomogeneities (André et al., 1990Bouhram et al., 2002;Chernyshov et al., 2017;Chugunin et al., 2018;Kintner et al., 2000;Seyler & Wahlund, 1996;Wahlund et al., 1998). Our methodology does not allow for positive identification or exclusion of any of these alternative processes.
In conclusion, in this study we have validated and applied a new methodology for examining the relationship between ion outflows and field fluctuations in the dayside cusp region in both hemispheres and as a function of season. We have presented an algorithm that achieves automated identification of ionospheric-origin ion outflows, and a spectral method for analysis of the relationship between these outflows and east-west magnetic field perturbations over nearly arbitrary frequency bands. Using four groups of orbits, two from each hemisphere, we have found that field perturbations over spacecraft frame frequencies of less than 0.7 Hz show the highest correlation with cusp region ion outflows. Best fit relationships between these field perturbations and ion outflows yield power law indices between 0.7 and 1.2, where the lowest power law values are associated with winter/late fall and the highest values associated with fall equinox/summer.
Previous studies indicate that magnetic field perturbations over these frequency ranges are associated with a variety of wave modes. We have not attempted to positively determine or exclude which wave modes are in operation during the reported observations, although we have outlined the plausibility of an interpretation based on Alfvén waves. Regardless of wave mode we have shown that if the observed perturbations are related to purely Doppler-shifted structures, they correspond to perpendicular scale sizes of several to tens of kilometers.
We have also demonstrated that ion composition likely plays a significant role in the relationship between ionospheric-origin energetic outflows and field fluctuations. This study underscores the need for much larger ion outflow data sets made up of observations for which the effects of ram ions and Doppler shifting due to spacecraft motion are consistently accounted for or otherwise mitigated.