Seasonal and Hemispheric Asymmetries of F Region Polar Cap Plasma Density: Swarm and CHAMP Observations

One of the primary mechanisms of loss of Earth's atmosphere is the persistent “cold” ( T≲ 20 eV) ion outflow that has been observed in the magnetospheric lobes over large volumes with dimensions of order several Earth radii. As the main source of this cold ion outflow, the polar cap F region ionosphere and conditions within it have a disproportionate influence on these magnetospheric regions. Using 15 years of measurements of plasma density Ne made by the Swarm spacecraft constellation and the Challenging Mini Satellite Payload (CHAMP) spacecraft within the F region of the polar cap above 80° Apex magnetic latitude, we report evidence of several types of seasonal asymmetries in polar cap Ne. Among these, the transition between “winter‐like” and “summer‐like” median polar cap Ne occurs 1 week prior to local spring equinox in the Northern Hemisphere (NH) and 1 week after local spring equinox in the Southern Hemisphere (SH). Thus, the median SH polar cap Ne lags the median NH polar cap Ne by approximately 2 weeks with respect to hemispherically local spring and fall equinox. From interhemispheric comparison of statistical distributions of polar cap plasma density around each equinox and solstice, we find that distributions in the SH are often flatter (i.e., less skewed and kurtotic) than those in the NH. Perhaps of most significance to cold ion outflow, we find no evidence of an F region plasma density counterpart to a previously reported hemispheric asymmetry whereby cold plasma density is higher in the NH magnetospheric lobe than in the SH lobe.


Introduction
A substantial fraction of the plasma in the Earth's magnetosphere is supplied by the ionosphere (e.g., Chappell et al., 1987Chappell et al., , 2000 through the outflow of ions from the high-latitude polar cap regions, where terrestrial magnetic field lines are open and connected to solar wind magnetic field lines. Ion outflow is the result of ionization of atmospheric gases and outward transport due to vertical forces and is considered to be a primary means of loss of the Earth's atmosphere (e.g., André, 2015). Recent results suggest that low-energy ions from the open polar cap area usually dominate the ion density and the outward flux in populating large volumes of the magnetosphere. Furthermore, ionization (i.e., availability of free charges) rather than transport is thought to be the limiting factor for ion outflow Haaland et al., 2012). Ionization is primarily driven by solar illumination, although other processes such as cosmic rays (e.g., Adams & Masley, 1965;Velinov, 1970) and particle precipitation also contribute (e.g., Rees, 1963Rees, , 1982. Solar radiation at ultraviolet (UV) and extreme ultraviolet (EUV) wavelengths is the most efficient source of ionization in terms of ionizing atmospheric atoms and molecules and producing ion-electron pairs (e.g., Appleton, 1956;Brekke, 1997;Ivanov-Kholodnyy, 1962;Rees, 1989;Schunk & Nagy, 2009). Since the ionosphere as a whole is quasi-neutral, both the electron number density and ion number density are often simply referred to as the plasma density.
The resulting plasma density in the atmosphere is a balance between production (ionization) processes on the one hand and losses by recombination and transport processes on the other hand (e.g., Khocholava, 1977;Quinn & Nisbet, 1965;Rees, 1989;Rishbeth, 1997). Since production and loss processes do not necessarily work on the same time scale, the plasma density at a given location can vary significantly over time. In the terrestrial atmosphere the peak plasma density is typically located in the ionospheric F layers, around 200to 400-km geodetic altitude (e.g., Feldstein et al., 1975;Rishbeth, 1962). Since ionization is strongly driven by solar illumination, plasma density exhibits solar cycle variations as well as strong seasonal and diurnal variations (e.g., Appleton, 1939). Typical plasma densities are of order 10 5 -10 6 cm −3 in the sunlit ionosphere but can be less by an order of magnitude or 2 in darkness.
In the polar regions the variation of plasma density with season is strongest, followed by diurnal variation and variation with solar cycle (e.g., Feldstein et al., 1975). The seasonal variation can largely be understood on the basis of solar illumination: Under summer conditions, the polar cap is fully illuminated. Conversely, under winter conditions major portions of the polar cap are in complete darkness. The Sun-Earth distance plays a lesser, though nonnegligible, role for variations in solar illumination (e.g., Dang et al., 2017). One would therefore expect solar illumination, ionization, and plasma production around equinox to be very similar in the Northern Hemisphere (NH) and Southern Hemisphere (SH).
In contrast to ionization and production of ionospheric plasma, which are primarily due to solar EUV radiation, transport of ionospheric plasma is driven mostly by electromagnetic forces and is organized with respect to the geomagnetic rather than the geographic poles. Horizontal transport is mainly driven by large-scale magnetospheric convection setup by reconnection at the dayside magnetopause (e.g., Dungey, 1963) and thermospheric neutral winds (e.g., Förster et al., 2008).
Vertical transport-upflow and outflow-is due to a combination of various forces. For example, according to the classical polar wind paradigm (e.g., Axford, 1968;Banks & Holzer, 1968;Dessler & Michel, 1966;Nishida, 1966) light ion species in the ionosphere gain upward mobility via plasma and neutral pressure gradients as well as ambipolar electric fields formed and sustained by requiring charge balance between electrons and ions in the ionosphere. Due to the mirror force, any additional transverse acceleration at the exobase (500-1,000 km) and above effectively acts as upward acceleration (e.g., Klumpar, 1979). At altitudes of a few Earth radii, centrifugal forces (Cladis, 1986;Horwitz et al., 1994;Liu et al., 1994;Nilsson et al., 2008Nilsson et al., , 2010 become dominant. Thus, the significant difference in magnetic topology of the NH and SH polar regions (e.g., Cnossen & Förster, 2016;Laundal et al., 2017) is a likely factor in reported hemispheric asymmetries in ionospheric outflow around equinox (e.g., Haaland et al., 2017;Li et al., 2020;Maes et al., 2016). This difference plays a role, for example, in the seasonal variation of thermospheric and ionospheric winds (Aruliah, Farmer, Fuller-Rowell, et al., 1996, Aruliah, Farmer, Rees, & Braändström, 1996Mikhailov & Schlegel, 2001). Precisely establishing the role of this topological difference in ion outflow is however complicated, since the size and shape of the source regions (primarily the open polar cap and also the cusp and auroral zone) vary greatly in response to solar wind driving (Li et al., 2012;Milan, 2009;Milan et al., 2008;Sotirelis et al., 1998).
In this study, we follow up on previous studies Haaland et al., 2012Haaland et al., , 2017 indicating or otherwise suggesting that available ionospheric plasma rather than transport is the limiting factor for cold ion outflow from the polar cap. Using a large database of ionospheric plasma density measurements made by the Swarm and Challenging Mini Satellite Payload (CHAMP) satellites in both hemispheres, we seek to determine under which seasons hemispheric asymmetries in cold plasma outflow might be expected on the basis of available ionospheric plasma.

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This study is organized as follows. In section 2 we describe the Swarm and CHAMP combined polar cap plasma density database. In section 3 we identify and describe a number of seasonal and hemispheric asymmetries in polar cap plasma density.
In section 4 we discuss results from the preceding section and describe some implications for cold ion outflow. In section 5 we summarize the results of this study and conclude.

Swarm and CHAMP Plasma Density Measurements
We use plasma density measurements made by two separate missions, the original three-satellite Swarm constellation (Friis-Christensen et al., 2008) and the CHAMP satellite (Reigber et al., 2006).
The original three Swarm satellites complete approximately 15 orbits per day in a near-polar orbit, over the 6-year period extending from launch on 22 November 2013 to the present. The two lower satellites, Swarm Alpha (Swarm A) and Swarm Charlie (Swarm C), cover the range of geodetic altitudes between 445 and 500 km (up to 527 km during commissioning phase); Swarm Bravo (Swarm B) covers the range of geodetic altitudes between 510 and 545 km (down to 500 km during commissioning phase). The Electric Field Instrument (EFI) (Knudsen et al., 2017) aboard the three original Swarm satellites includes two dedicated low-gain and high-gain Langmuir Probes (LPs). The two LPs measure plasma density and electron temperature at 2 Hz. The most complete in-flight calibrations and validations of the Swarm LP plasma density and electron temperature measurements, based on comparisons with plasma density measurements measured by other satellites and ground-based instruments, have been performed by Lomidze et al. (2018).
The CHAMP satellite also completed approximately 15 orbits per day in a near-polar orbit over a ∼10-year period extending from 15 July 2000 to 19 September 2010. The nominal range of geodetic altitudes covered by CHAMP extended over ∼300-455 km. The Planar Langmuir Probe (PLP) instrument (Rother et al., 2005) aboard CHAMP made measurements of plasma density at a 15-s cadence. In-flight calibration of the PLP instrument has been performed by McNamara et al. (2007).
In this study we use all Swarm Level 1B LP plasma density measurements downsampled to 15-s cadence, from the period between 10 December 2013 and 5 February 2020 (https://swarm-diss.eo.esa.int/). Downsampling is achieved by selecting every 30th measurement. We also use all CHAMP Level 2 PLP plasma density measurements from the period between 19 February 2002 and 21 December 2009 (https://dataservices. gfz-potsdam.de/portal/?q=CHAMP*) made at ≥350-km geodetic altitude. We impose this altitude restriction on CHAMP density measurements to ensure that all plasma density measurements are made above the altitude at which the F2 layer plasma density peak hmF2 is located (e.g., Bjoland et al., 2016;Burns et al., 2012;Shim et al., 2011). To Swarm plasma density measurements, we apply the Lomidze et al. (2018) in-flight calibrations (see Appendix A).
Since ion outflow and ionosphere-magnetosphere coupling are organized by the geomagnetic field, we are here concerned with the geomagnetic polar cap, which we define (Table 1) as the region at and above 80 • magnetic latitude in the modified apex coordinate system at a reference geodetic altitude of 110 km (i.e., MA 110 coordinates) (Laundal & Richmond, 2016;Richmond, 1995). In the MA 110 coordinate system, which is based on the International Geomagnetic Reference Field (IGRF) model (Thébault et al., 2015), all points along a particular IGRF field line have the same magnetic latitude (MLat) and longitude (MLon). To find the MLat and MLon of a satellite at a particular time, the location of the satellite is traced earthward, along the relevant IGRF field line, to the 110-km reference altitude. We perform the conversion of geocentric coordinates to MA 110 coordinates via the apexpy Python package (Emmert et al., 2010;van der Meeren et al., 2018). Table 1 summarizes some properties of the polar caps in each coordinate system.
The total numbers of plasma density (N e ) measurements in the NH and SH geomagnetic polar caps are respectively 2,410,423 and 1,045,654. There are two primary reasons that the statistical coverage of the NH geomagnetic polar cap is greater. First, as a result of the greater displacement of the SH geomagnetic pole relative to the geographic pole than the displacement in the NH, the Swarm and CHAMP satellites pass less frequently through the SH geomagnetic polar cap. Second, the SH geomagnetic polar cap area is approximately 9% smaller than the NH geomagnetic polar cap area (Table 1 and Figure S1 in supporting information). The difference in geomagnetic polar cap area arises because the Earth's magnetic field is stronger in the vicinity of the SH magnetic pole than in the vicinity of the NH magnetic pole . The measurement coverage is approximately the same in both hemispheres (2.64 and 2.68 million measurements in the NH and SH geocentric polar caps, respectively) if one instead considers the polar caps defined in a geocentric coordinate system.
In the remainder of the manuscript all references to N e and statistics refer only to measurements made in the geomagnetic polar caps, unless specified otherwise.
We seek to investigate seasonal and hemispheric asymmetries via statistical comparison of plasma density measurements in the geomagnetic polar cap made by different satellites. Such an investigation is complicated by a number of factors, including the following: 1. Differences in the altitudes of each satellite, which vary on time scales of days and years due to satellite drag and operational maneuvers and which are systematically different in the two hemispheres due to both the shape of each satellite's orbit and the oblateness of the Earth (Text S2 and Figures S2 and S3 of the supporting information). These differences correspond to sampling of different heights in the ionosphere. 2. Variations in solar and geomagnetic activity, which lead to differences in ionospheric conditions. We partially account for these factors via (i) application of an empirically derived scale height to N e measurements that "maps" N e to a common geodetic altitude of 500 km and (ii) application of an empirically derived correction factor that accounts for the variation of N e measurements with 10.7-cm wavelength solar radio flux (otherwise known as the F10.7 index). The latter correction scales N e to a nominal solar activity (normalized solar radio flux index) of ⟨F10.7⟩ 27 = 80, where ⟨F 10.7⟩ 27 is a rolling average of the preceding 27 days of the F10.7 index. Throughout this manuscript, we use the notation N * e to refer to these final adjusted densities. More details about the derivation of the relevant scaling factors are located in Appendix A and in the supporting information. This database of adjusted geomagnetic polar cap density measurements (N * e ) is publicly available (Hatch et al., 2020). Figure 1a shows N * e in the NH (blue) and SH (red) geomagnetic polar caps as a function of day of year. The solid blue and dashed red lines, respectively, indicate the median NH and SH N * e values within 10-day bins. One of the apparent differences between the median N * e values in the NH and SH geomagnetic polar caps is that N * e takes on more extreme values in the SH than in the NH. This difference may be related to the "ionospheric annual asymmetry," which has to do with NmF2, the ionospheric F2 layer peak plasma density, being about 30% greater globally around December solstice than around June solstice (Rishbeth & Müller-Wodarg, 2006). The ionospheric annual asymmetry and related phenomena are well documented (e.g., Chartier et al., 2019;Dang et al., 2017;Lei et al., 2016;Mendillo et al., 2005;Rishbeth & Müller-Wodarg, 2006;Sai Gowtam & Tulasi Ram, 2017;Torr et al., 1980;Xiong et al., 2018); the asymmetry is the result of a combination of effects related to solar irradiance, atmospheric chemistry, neutral winds, and the global geomagnetic field configuration. The precise role of the global geomagnetic field configuration, in particular, apparently remains to be determined (Dang et al., 2017). Here N * e denotes plasma density measurements that are scaled to a common geodetic altitude of 500 km and to a nominal solar activity of ⟨F10.7⟩ 27 = 80, as described in Appendix A. (a) N * e measurements and binned medians. The transparent "x" and "+" markers, respectively, indicate 50,000 randomly selected individual measurements made in the NH and SH geomagnetic polar cap for each hemisphere. (Most readers will need to view the plot at full resolution or zoom in to see the distinction between these symbols.) Median N * e values within each 10-day bin are, respectively, indicated by the solid blue (north) and dashed red (south) line. Error bars indicate the 95% confidence interval of the bin median, calculated as described in Text S3 of the supporting information. (b) MAD(N * e ) in the NH (solid blue line) and SH (dashed red line) geomagnetic polar caps, in 10-day bins. In both panels the dotted black lines at DOY ≈ 79.9 and DOY ≈ 266.3, respectively, indicate the average DOY on which March and September equinoxes occur during the years 2000-2020; the time and date of each equinox are calculated as described in section 3. MAD≡median absolute deviation.

Hemispheric and Seasonal N * e Variations
Central tendency and variation of a statistical quantity are often indicated by the mean and standard deviation, respectively. However, N * e distributions in each bin in Figure 1a are heavy-tailed, and the mean is not a robust indicator of central tendency. In Figure 1a we therefore show median N * e statistics in each bin. Likewise, in Figure 1b we show the median absolute deviation instead of standard deviation to indicate the variation of N * e in each 10-day bin. Figure 1b shows MAD(N * e ) in the NH and SH as solid blue and dashed red lines, respectively.
Two salient aspects of MAD(N * e ) curves in Figure 1b are (i) the SH MAD(N * e ) is typically greater than NH MAD(N * e ) and (ii) MAD(N * e ) in the NH geomagnetic polar cap evinces two distinct peaks, before March equinox and after September equinox, while MAD(N * e ) in the SH geomagnetic polar cap evinces one primary peak after March equinox, a MAD(N * e ) "plateau" that extends from September to the end of December and a global minimum near June solstice.

Asymmetries in Seasonal Variation
We now compare variations in N * e as a function of season. We wish to (i) avoid the systematic bias that would be introduced by performing a comparison based on day of year in the Gregorian calendar, which is inherently asymmetric from year to year with respect to the day of year on which equinoxes and solstices occur, and (ii) consistently account for variation in the length of the seasons themselves, which differ on the order of days. To accomplish this, we scale the precise time period between each equinox and solstice for each year such that the period between each equinox and solstice has a duration of 1, and the total duration of all four seasons (i.e., 1 year) is 4. We thus define the "global season parameter" s ∈ [0, 4), with March and September equinoxes, respectively, corresponding to s = 0 and s = 2. June and December solstices, respectively, correspond to s = 1 and s = 3. The time stamps of all N * e measurements are then scaled to values between 0 and 4. The dates and times of occurrence of each equinox and solstice for all relevant years between 2002 and 2020 are calculated to second precision via the skyfield Python package    e measurements within ±15 days around the relevant equinox or solstice and indicate multiple aspects of polar cap N * e that are not represented by either median or MAD statistics. We discuss these differences in terms of the two other common measures of central tendency, the mean and mode, and in terms of standard deviation. Estimation of the mode of N * e , which is a continuous variable, is nontrivial. We estimate the mode via the procedure described by Note. Statistics in columns 2-5 are given in 10 4 cm −3 . Statistics in columns 6-7 are unitless. Bickel and Frühwirth (2006); this methodology yields mode estimates that are very similar (typically differing by less than 0.1%) to mode estimates obtained by identifying the peak of the N * e distributions that are shown in Figure 2c. Table 2 shows that the SH N * e distribution mode is greater than the NH N * e distribution mode only during December solstice, which is local summer in the SH. On the other hand the SH N * e mean is greater than the NH N * e mean for all seasons except June solstice, and the SH N * e standard deviation is always greater than the NH N * e standard deviation. The NH and SH N * e distributions otherwise appear most similar during March and September equinox (respectively, s = 0 and s = 2) and most disparate during June and December solstice (respectively, s = 1 and s = 3), as expected. We further discuss the relevance of these differences to cold ion outflow in section 4. values in the SH is overall larger than the range of median NH N * e values, which is also visible in Figure 1a, and (ii) variation in median SH N * e lags behind median NH N * e around local spring and fall equinoxes by several days. We quantify this lag in the following subsection. These statistics also suggest that the annual maximum in median NH N * e occurs before local summer solstice, while the annual maximum in median SH N * e occurs at or perhaps slightly before local summer solstice. A secondary peak in median N * e between local summer solstice and local fall equinox is also apparent in both hemispheres.   Table 2 indicates that the SH N * e distribution mode is always less than the NH N * e distribution mode, and the SH N * e standard deviation is always greater than the NH N * e standard deviation. On the other hand the SH N * e mean is less than the NH N * e mean only during local spring solstice. The NH and SH N * e distributions otherwise appear most similar during local winter solstice ( l = 3).

Equinoctial Asymmetries
We now consider the evolution of the median N * e in each hemisphere around equinox. Figure 3a shows median NH N * e values relative to March equinox (thin blue line) and September equinox (thick blue line) in 15-day bins. Crossover occurs at −7.2 days relative to equinox. Figure 3b shows median SH N * e values relative to March equinox (thin red dotted line) and September equinox (thick dotted red line). Crossover occurs at +9.1 days relative to equinox. Figure 3c shows NH and SH median N * e values relative to March and September equinox, respectively, and Figure 3d shows NH and SH median N * e values relative to September and March equinox, respectively. That is, Figures 3c and 3d show median N * e values in each hemisphere relative to local spring and fall, respectively. Figure 3c shows that the local spring crossover between median NH N * e (solid blue line) and median SH N * e (dotted red line) occurs at +18 days relative to equinox. Figure 3d shows that the local fall crossover between median NH N * e (solid blue line) and median SH N * e (dotted red line) occurs at +58 days relative to equinox. However, it should be noted that these two lines also nearly cross at approximately +30 days. To calculate a CHAMP, Swarm A, Swarm B, and Swarm C. b Evidence for this asymmetry is weak, as Δt is small and exhibits spread around zero. c As indicated in section 3.2, median N * e in the NH and SH are within a few percent of each other over days 30 to 60 after equinox.

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10.1029/2020JA028084 the crossover point in each panel, we interpolate between each 15-day median with a resolution of 0.1 days and determine the relative day of year for which the two lines shown in each panel are nearest each other.

Discussion
Results in the preceding section indicate the existence of several seasonal and hemispheric asymmetries in the plasma density of the geomagnetic polar caps. Table 3 summarizes the equinoctial asymmetries identified from Figures 1-3 on the basis of the combined database of Swarm and CHAMP measurements.
A central purpose of this study is to determine whether the hemispheric asymmetry in magnetospheric lobe cold plasma density reported by Haaland et al. (2017) could be explained on the basis of plasma densities in the ionospheric polar caps. In specific, they found that cold plasma densities in the NH lobe were overall greater than the cold plasma densities in the SH lobe around September equinox and speculated whether this asymmetry was due to differences in outflow and plasma densities between NH and SH. No such corresponding asymmetry in median geomagnetic polar cap N * e at September equinox is apparent in Figures 1a  and 2a. And while there are clear differences between the distributions of N * e in each hemisphere at September equinox ( s = 2 in Figure 2c), as we discuss in section 3.1, we find no evidence suggesting that NH N * e is systematically greater than SH N * e around September equinox. In summary, on the basis of the Swarm and CHAMP N * e distributions that we have presented, the hemispheric asymmetry in Cluster-observed cold plasma densities in the magnetospheric lobes  has no clear correspondence with plasma densities in the geomagnetic polar caps. We believe that this is the most significant result of this study.
Among the possible causes of the hemispheric asymmetry in lobe cold plasma density are hemispherically asymmetric vertical transport, flux tube volume, or conductivities in the geomagnetic polar caps. Li et al. (2020) have shown, for instance, that the strength of the Earth's magnetic field is anticorrelated with ionospheric outflow. The cause of this apparent discrepancy between Swarm, CHAMP, and Cluster observations will be the subject of future work.
Another significant result of analysis in section 3.2 is displayed in Figure 3. In Figure 3a the crossover point of the two NH (solid blue) lines occurs approximately 7 days before equinox, whereas in Figure 3b the crossover point of the two SH (dotted red) lines occurs approximately 9.1 days after equinox. Thus, the days on which the local hemisphere geomagnetic polar cap density N * e crossover near local equinox occurs are hemispherically asymmetric. This asymmetry is also present when the polar caps are defined in geocentric coordinates (not shown) and so is not the result of a particular choice of coordinate system.
Comparison of median N * e curves from each geomagnetic polar cap around local spring ( Figure 3c) and around local fall (Figure 3d) shows that the crossover points in both hemispheres occur more than 2 weeks after equinox. This suggests the existence of a seasonal "phase offset" between the two hemispheres in median N * e around local spring and fall equinoxes, whereby median N * e in the SH geomagnetic polar cap lags median N * e in the NH geomagnetic polar cap by at least 2 weeks. The lag around local spring equinox is even more pronounced, 6 weeks or more, when the polar caps are defined in geocentric coordinates (not shown).
Thus, the relative lag between SH and NH polar cap N * e around local spring equinox is not the result of choosing a particular definition of the polar caps (i.e., geomagnetic versus geocentric; see Table 3). On the other hand there is apparently no lag between SH and NH geocentric polar cap median N * e around local fall equinox, which suggests that the relative lag exhibited by median N * e in the geomagnetic polar caps is related to the choice of coordinate system (i.e., geomagnetic instead of geocentric polar caps).
The different lags imply that there are at least two contributing factors to the delay, which likely operate somewhat differently in the two sets of polar caps during local spring and local fall. Here it is worth noting that the existence of a relative lag in geomagnetic polar cap N * e around local fall equinox may be related to reported hemispheric asymmetry in ion outflow processes and ionosphere-magnetosphere coupling that is organized by the geomagnetic field Haaland et al., 2012Haaland et al., , 2017.
To test the robustness of the asymmetries identified in Figures 1-3 and Table 1, we have also performed the analysis separately for each of the four satellites used in this study (not shown). The values obtained from each of these separate analyses are shown in the rightmost column of Table 3. All of the asymmetries we have just discussed also appear in the analyses based on measurements from individual satellites. More specifically with the exception of the weak evidence for a NH/SH crossover delay at September equinox, the other delays are consistent between all four spacecraft albeit with slight differences in the estimated Δt values.
We believe that these separate analyses are important indicators of the robustness of each asymmetry, since the Swarm and CHAMP satellites monitor polar cap plasma density at effectively three different altitude ranges over two different portions of a solar cycle, with two different and independent types of LP instruments and three different orbits.

Summary
Using 15 years of plasma density measurements made by the original three Swarm satellites and the CHAMP satellite, we have identified equinoctial asymmetries in F region ionospheric plasma density in the geomagnetic polar caps. In particular: 1. Haaland et al. (2017) have reported overall lower cold plasma densities in the SH magnetospheric lobe relative to the NH magnetospheric lobe around September equinox; they conjecture that the difference may be related to available ionospheric plasma in the polar cap. We find no evidence supporting this conjecture. 2. We present evidence that SH polar cap plasma density lags behind NH polar cap plasma density by at least 2 weeks around March and September equinox. 3. For every season the SH distribution of F region polar cap plasma density is spread over a wider range of values than the NH distribution. The mode of the SH distribution is also generally lower than the mode of the NH distribution.

Appendix A: Correction and Adjustment of Ne
Here we provide some additional details on the procedure for obtaining the final height-and solar flux-adjusted density measurements that are denoted N * e throughout the manuscript. A detailed description of this procedure and relevant figures is located in Text S2 and Figures S2 and S3 of the supporting information.
After applying the Lomidze et al. (2018) in-flight calibrations to Swarm plasma density measurements, we additionally account for differences in altitude and solar activity via (i) application of an empirically derived scale height to N e measurements that "maps" N e to a common geodetic altitude of 500 km and (ii) application of an empirically derived correction factor that accounts for the variation of N e measurements with 10.7-cm solar radio flux (otherwise known as the F10.7 index).
As pointed out in section 2 the CHAMP satellite and the three Swarm satellites cover different altitude ranges and thus different portions of the F region. The altitude range covered by the CHAMP satellite (315-455 km) is the lowest of all four satellites, while the altitude range covered by Swarm B (500-545 km) is mostly above those of the other satellites.
From 380 conjunctions between Swarm B and either Swarm A or Swarm C for which Swarm LP data are currently available (December 2013 through February 2020), we derive the Vertical Scale Height VSH ≡ dh∕(d ln N e ) (e.g., Hu et al., 2019). We use "robust regression" (e.g., Holland & Welsch, 1977;Huber, 1973) to estimate VSH from the ratio of plasma density measurements during the 380 identified conjunctions ( Figure S2c in supporting information). From this regression we obtain VSH values of 205 km on the dayside (6 ≤ MLT < 18) and 167 km on the nightside (MLT < 6 and MLT ≥ 18). These scale heights are within the range of typical estimates at geodetic altitudes of 350-500 km (e.g., Figure 2 in Hu et al., 2019 andFigure 1b in Stankov &Jakowski, 2006).
To each N e measurement, we then apply a scaling factor where h is the altitude at which the measurement is made. We arbitrarily select a reference geodetic altitude h 0 = 500 km. This scaling decreases the value of N e for measurements made below h 0 and increases the value of N e for measurements made above h 0 .

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In addition to variation with altitude polar cap N e also varies approximately linearly with ⟨F 10.7⟩ 27 , an average of the F10.7 index during the preceding 27 days. We use ⟨F 10.7⟩ 27 , as a proxy for solar EUV intensity. Another common choice for averaging the F10.7 index is a centered 81-day window (e.g., Liu & Chen, 2009;Schunk & Nagy, 2009). We have elected to use ⟨F 10.7⟩ 27 instead, since we find that the RMS error between this quantity and N e,h 0 is slightly (∼5%) lower than the RMS error between an 81-day centered average of the F10.7 index and N e,h 0 .
We use robust regression to fit N e,h 0 and ⟨F 10.7⟩ 27 values with a model of the form The resulting best fit model parameters are a = 0.02564 and N = 46,780 cm −3 . We apply the portion of the model in Equation A2 that is dependent on ⟨F 10.7⟩ 27 , namely, the parameter a, to each N e,h 0 value to finally obtain the height-and solar flux-adjusted density The numerator in Equation A3 scales the final adjusted density N e to a nominal solar flux level of ⟨F10.7⟩ 27 = 80. (Final adjusted densities are shown in Figure S3b of the supporting information.)