Metallic ion transport associated with midlatitude intermediate layer development

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A1, 1019, doi: /2002ja009411, 2003 Metallic ion transport associated with midlatitude intermediate layer development R. L. Bishop 1 and G. D. Earle 2 Received 29 March 2002; revised 25 September 2002; accepted 3 October 2002; published 15 January [1] Although intermediate layers are frequently observed by the Arecibo Incoherent Radar Observatory and by ionosondes around the world, many questions still remain regarding their formation, structure, and composition. In this paper, we explore the effect of metallic ions, specifically Fe +, on intermediate layer development and evolution. Several studies have demonstrated that layers can form from either molecular or metallic ions. This paper extends these earlier studies by quantifying the effect of metallic ions on intermediate layer morphology. We show that the efficiency of metallic ion transport depends significantly on the amplitude and wavelength of the imposed horizontal wind field. Specifically, larger amplitudes and longer wavelengths result in increased ion transport in the direction of the propagating neutral wind field. INDEX TERMS: 2443 Ionosphere: Midlatitude ionosphere; 2439 Ionosphere: Ionospheric irregularities; 2499 Ionosphere: General or miscellaneous; 7843 Space Plasma Physics: Numerical simulation studies; KEYWORDS: midlatitude ionosphere, E-region, intermediate layers, ionization layers Citation: Bishop, R. L., and G. D. Earle, Metallic ion transport associated with midlatitude intermediate layer development, J. Geophys. Res., 108(A1), 1019, doi: /2002ja009411, Introduction [2] For over 50 years, midlatitude intermediate or descending layers have been observed in the E region by ionosondes [McNicol and Gipps, 1951; Wakai, 1967]. These layers of plasma form on the bottom side of the F peak and descend over several hours to altitudes near 120 km. Ionosonde observations provide information on plasma layer occurrence, coarse descent rates, and maximum density [Wilkinson et al., 1992; Szuszczewicz et al., 1995]. Since intermediate layers often have densities less than cm 3, any presence of the larger density Sporadic E tend to mask the higher altitude layers. By utilizing the midlatitude Arecibo Observatory (AO), intermediate layers are observed regardless of the presence of Sporadic E. AO provides frequent observations, and yields additional information on the variations in intermediate layer structure and evolution [Shen et al., 1973; Earle et al., 2000a]. Even with the addition of rocket [Smith, 1970; Bishop et al., 2000] and satellite [Heelis, 1999] observations there are still many questions that remain regarding midlatitude intermediate layer formation, evolution, and composition. [3] Intermediate layers may be comprised of molecular ions such as NO + and O 2 +, metallic ions such as Fe + and Mg +, or combinations of metallic and molecular species. Only a few observations have been made of intermediate layer composition and all of those have occurred at altitudes 1 Department of Physics and Astronomy, Clemson University, Clemson, South Carolina, USA. 2 William B. Hanson Center for Space Science, University of Texas at Dallas, Richardson, Texas, USA. Copyright 2003 by the American Geophysical Union /03/2002JA above 140 km. The AE-C and AE-E satellites measured the ion composition of high altitude intermediate layers. Both satellite measurements showed that the observed layers were comprised entirely of NO + and O 2 + [Miller et al., 1993; Heelis, 1999]. [4] Although there has not been an observation of an intermediate layer primarily consisting of metal ions, there are numerous papers with observations of metal ion dominated low altitude layers such as Sporadic E [Narcisi, 1968; Earle et al., 2000b]. When intermediate layers reach their final altitudes, they typically resemble thin layers with a slightly greater peak density than at their formation. Because the lower altitude thin layers exist for several hours it is reasonable to assume that metal ions, with their relatively slow recombination rate, are the dominant layer constituent. Further, we know that Sporadic E, is comprised almost solely of metals and is observed at altitudes slightly lower than typical final intermediate layer positions. It may be the case that when intermediate layers form they are comprised entirely of molecular ions but as they descend the composition evolves with an increasing percentage of metallic ions present. [5] In lieu of composition observations, modeling studies provide the primary information about intermediate layer composition. In recent years, several modeling studies have been performed focussing on this problem. A study completed by [Osterman et al., 1994, 1995] investigated the formation of intermediate layers comprised of molecular ions resulting from idealized sinusoidal neutral winds. Their study employed the Bailey ionospheric model, which includes comprehensive chemistry and ion motion along magnetic flux tubes [Bailey and Sellek, 1990]. Osterman et al. [1994] showed that intermediate layers comprised entirely of molecular ions such as NO + SIA 3-1

2 SIA 3-2 BISHOP AND EARLE: SIMULATING METALLIC INTERMEDIATE LAYERS Figure 1. The figure illustrates the formation of an ionization layer in the Northern Hemisphere by a shear in the meridional neutral wind. and O 2 + are capable of not only forming but also having significant lifetimes. [6] A second modeling study to explore layer formation was performed by Carter and Forbes [1999]. The primary purpose of their study was to simulate global metallic ion transport. By imposing tidal-like winds, they produced thin descending ionization layers of Fe + ions. They showed that descending layers are readily produced over AO. However, the simulated layers had thicker vertical extents below 140 km and descent rates significantly slower than typical AO observations. [7] Although the composition of plasma layers in the lower E region is fairly well known, the composition of intermediate layers above 115 km remains elusive. By understanding the composition of these layers, we can begin to understand the mechanisms behind the intermediate layer formation as well as ion transport within the region from 115 to 190 km. This paper investigates metallic ion transport associated with the evolution of an intermediate layer. We employ a model developed specifically to investigate the characteristics of intermediate layers and the mechanisms behind their formation. Our results allow us to quantify the effects of variations in the local horizontal neutral wind field on metallic ion transport in the middle and upper E region. 2. Layer Evolution and Dynamics (LEAD) Simulation [8] According to the classical wind shear model, intermediate layer formation occurs through a coupling process between ions constrained by the geomagnetic field and the neutral wind. Figure 1 illustrates the mechanism through which a meridional wind may form an ionization layer. Collisional coupling between neutrals and ions result in a drag force exerting on the ions. At the same time, the ions are magnetized, constraining their motion according to the Earth s geomagnetic field. To produce an ion layer an appropriately directed neutral wind shear must exist in the meridional component as shown in Figure 1. A zonal neutral wind with an appropriately directed shear is also capable of producing an ionization layer as illustrated in Figure 2. The ions are moved in the direction of the zonal wind through collisions with neutrals. This motion is modified by a ~V ~B force where ~V is the ion velocity and ~B is the geomagnetic field. Ionization layers may also form through a combination of both neutral wind components. [9] An expression for the vertical ion velocity resulting from the neutral wind field and including diffusion and gravity effects is found using the momentum equation. The expression for the vertical ion velocity is: V z ¼ h U x þ b U y þ g U z þ þ q E x þ E y þ E z ; where U x,u y, and U z and E x,e y, and E z are the zonal, meridional, and vertical neutral wind and electric field components, respectively. The coefficients depend on the geometry of the geomagnetic field, ion cyclotron frequency, and collision frequency. The term includes diffusion and gravity effects. The coupling coefficients for the meridional and zonal wind components respectively are: ð1þ ½ð h ¼ n in=w c ÞY þ Z X Š ½ðn in =w c ÞŠ 2 ; ð2þ ½ b ¼ Y Z ð n in=w c ÞX Š h i ð3þ ðn in =w c Þ 2 þ1 where n in is the ion-neutral collision frequency, w c the ion cyclotron frequency, and X, Y, and Z are the directional cosines of the geomagnetic field. A complete derivation and detailed description of the expression for the vertical ion velocity used in this paper is given by Earle et al. [1998]. [10] By comparing the magnitude of the horizontal neutral wind coupling coefficients, it is observed that at altitudes below 120 km the zonal wind component is more efficient at effecting ion motion. Above 130 km, the meridional wind component becomes the most efficient driver of ion motion. This idea is related to the dependence of the ratio of collision frequency to gyro frequency on altitude. Figure 3 shows the dependence of the coupling coefficients on this ratio. At higher altitudes (above 140 km), the ratio is very small and the meridional component dominates. At altitudes below 120 km, the ratio increases quickly due to the increase in collisions. In this region, the zonal wind is the most efficient at producing vertical ion transport. [11] From the momentum and continuity equations, the probability of a layer forming in a region of convergent ion velocity depends significantly on the angle of the geomagnetic field relative to the wind, as well as the interaction of the shears in the neutral wind components [Whitehead, 1961, 1971, 1972; Axford, 1963]. The classical theory adequately explains the formation of stationary ionization layers. However, intermediate layers descend with time. The Figure 2. The figure illustrates the formation of an ionization layer by a shear in the zonal neutral wind.

3 BISHOP AND EARLE: SIMULATING METALLIC INTERMEDIATE LAYERS SIA ] for the 1998 spring equinox. The selection of the 1998 equinox is not significant to this study. No electric fields are imposed in the following studies and the ion species modeled are NO +,O 2 +, and Fe +. The case studies result from 6 hours of simulated local time beginning after sunset at 2000 LT. Figure 3. The panel on the left shows the variation of the meridional and zonal coupling coefficients to the ratio (n in / w c ). The mass for Fe + and the geomagnetic field above AO is used to calculate the coefficients. The right panel shows the altitude dependence of (n in /w c ). nightly observations of intermediate layers as well as their average rates of descent indicate that tidal winds are most likely the primary driver of the phenomenon [Fujitaka and Tohmatsu, 1973; Harper, 1977; Mathews et al., 1993]. Observations made by the AO have shown that the structure, descent rate, number of layers observed in a given night, and the altitude of layer formation all vary significantly from night to night [Earle et al., 2000a]. Possible factors contributing to these variations include small-scale neutral wind field variations such as gravity waves, electric fields, and composition variations. [12] We have developed a numerical simulation to explore these and other factors contributing to intermediate layer morphology. The LEAD simulation allows investigation of intermediate layer development by varying imposed conditions. LEAD is comprised of three independent phases, the third of which is used for this work. LEAD is a 2-D code (altitude, time) that solves the ion electron continuity and momentum equations simultaneously over the altitude range km with a 100 m step size. Model assumptions include a horizontally stratified atmosphere, quasi-neutrality, and open boundaries to molecular ions. In LEAD the horizontal neutral winds evolve with time and are used along with imposed initial neutral and ion composition, temperature profiles, and chemical reactions to calculate the corresponding ion densities versus time. A detailed explanation of LEAD code is given by Bishop [2001]. [13] LEAD requires an initial electron density profile, up to three initial ion density profiles, and electron and ion temperature altitude profiles specified by the user. The user may specify an electric field or neutral wind field that varies with time. This allows focused case studies to highlight the effects of different forcing on layer development and motion. For the following case studies, unless otherwise stated, initial ion/electron density and temperature profiles are generated from the International Reference Ionosphere (IRI) model [Bilitza et al., 1993], and the initial neutral density and temperature profiles are generated by the Mass Spectrometer and Incoherent Scatter (MSIS) model [Hedin, 3. Simulated Metal Transport [14] The first step in any model analysis is to generate a baseline resulting from quiet conditions which may be used for comparison with other runs. For metal transport, we establish a baseline by initializing LEAD with a constant Fe + density profile of 100 cm 3 between 100 and 190 km. The density value chosen is an average value selected after reviewing a number of Fe + profiles from rocket and satellite observations [Kopp, 1997; Grebowsky et al., 1998]. The model simulates 10 hours of real time with the only forcing due to gravity and diffusion. The resulting downward ion motion also depends upon the geomagnetic field, collision frequency, and gyrofrequency through the coupling coefficient, h i ðn in =w c Þ 2 þ Z 2 ¼ h i: ð4þ n in ðn in =w c Þ 2 þ1 The Fe + ions are allowed to move out of the region but no ions are allowed to enter. Chemistry is included in the calculations with the molecular ions subject to the major loss reactions. Recombination reactions for Fe + are also included even thought the lifetime for the metal ions is much greater than that of the molecular ions. The presence of the Fe + ions enhances the local electron density and thus the subsequent recombination lifetimes of molecular ions. Detailed explanation of the chemistry imposed in LEAD is given by Bishop [2001]. [15] Figure 4 shows the initial Fe + profile and the Fe + profile after 6 hours as the solid and dashed lines, respectively. As expected, Fe + ions descend over time. It is interesting to note that the metal ions actually form a broad layer that is centered near 138 km. This corresponds to the collision frequency below 140 km quickly increasing with decreasing altitude. At the same time, the gyrofrequency is also increasing with decreasing altitude but at a much slower rate. These two trends result in a slowing of diffusive motion and a higher concentration of long-lived Fe + ions in this altitude range. [16] The boundary condition requiring only movement in one direction across the boundaries at 100 and 190 km may be partially responsible for the decrease in Fe + density above 160 km. If a continuous source of Fe + ions were available above 190 km they would likely diffuse into the region, lessening the depletion observed. There is some evidence to suggest that there are metal ions within the F region [Kumar and Hanson, 1980; Grebowsky and Reese, 1989; Grebowsky et al., 1998]. [17] After understanding the motion of Fe + ions in the absence of a horizontal neutral wind field, the next step is to impose an ideal sinusoidal neutral wind in only one of the horizontal components. An initial constant profile of 100 cm 3 for Fe + is again imposed with Fe + prohibited from

4 SIA 3-4 BISHOP AND EARLE: SIMULATING METALLIC INTERMEDIATE LAYERS is greater for the meridional imposed wind. The second layer that forms near 180 km at 2200 LT has a much smaller peak density than the layer formed earlier. This shows that as the convergent null propagates downward the metals are transported downward, resulting in less Fe + ions available for each subsequent layer. [19] The resulting Fe + layer produced by the zonal wind has a broader altitude extent above 140 km then the layer produced by the meridional wind. Below 130 km, the layer becomes narrower and the depletions on either side of the layer are larger than seen in the meridional wind case. These differences result from the zonal wind being more efficient at ion transport below 130 km than a similar meridional wind. The reverse trend is true above 140 km. [20] By varying the amplitude and wavelength of the individual neutral wind components we can investigate the relative effectiveness of the winds on Fe + transport. Figures 6 and 7 illustrate the percent change in metallic ions as a function of time for a neutral wind of varying amplitudes and wavelengths, respectively. We define the following metric in order to quantify the Fe + transport produced. Instead of looking at each individual altitude point, the region of interest ( km) is broken into 15 km intervals. Within each interval, the ions are summed for the profile, which result from the imposed wind and the motions due to gravity and diffusion (Figure 3). The metric is the percentage change in Fe + using these two values. Mathematically it is expressed as: ½Fe þ Š ð% Þ ¼! ½Fe þ ðz; tþšdz Fe þ o ðz; tþ 1 100:0%; dz R zf z R o zf ð5þ Figure 4. The figure illustrates the motion of Fe + due to gravity and diffusion as calculated by the LEAD simulation. The solid and dashed lines represent the initial and final Fe + density profiles in the absence of winds, respectively. The profiles shown result after 6 hours of simulated time. crossing the boundaries into the simulation region. Figure 5 shows the Fe + and N e density profiles resulting from the meridional(left) and zonal(right) neutral wind profiles shown. We selected a sinusoidal meridional and zonal neutral wind with an amplitude of 20 m/s, wavelength of 40 km, and an initial convergent null, or the center of a shear region that produces a convergent ion drift, located at 160 km. Both wind components propagate downward at 1.5 m/s. These parameters are chosen to correspond to AO observations of intermediate layers and are the same conditions imposed by the Osterman et al. [1994] modeling study. [18] For the imposed meridional and zonal winds, as the convergent nulls move downward the layers follow in both the N e and Fe + profiles. The meridional wind forms a well defined layer near 160 km within the first hour of the simulation. On either side of this layer (initially at 160 km) in the Fe + profile, there is a significant depletion of metal ions. Because the meridional wind is more efficient at moving ions above 130 km, the depletion above the layer where Fe + (z, t) is the value of ions resulting from an imposed wind at an altitude z and time t, Fe o + (z, t) isthe value of ions resulting from no imposed wind at an altitude z and time t, and and z f are the upper and lower boundaries of the altitude interval, respectively. A value of 100% implies that all Fe + has been removed from the altitude interval. This calculation is repeated every 2.5 min. Thus, the curves shown in Figures 6 and 7 illustrate the net motion of the Fe + ions due solely to forcing by the neutral winds as a function of time. [21] Figure 6 illustrates the variation of Fe + transport for a meridional or zonal wind with a wavelength of 40 km. The panels on the left side result from a meridional wind with amplitudes varying from top to bottom of 10, 20, and 40 m/s. The panels on the right have similar amplitudes for an imposed zonal wind. [22] Figure 7 illustrates Fe + transport resulting from zonal and meridional neutral winds of varying wavelengths. The amplitude of the neutral wind components remain constant at 20m/s for all cases shown. Similar to Figure 5, the panels on the left (right) show transport resulting from a meridional (zonal) neutral wind. The wavelengths from top and bottom are 20, 40, and 80 km, respectively. 4. Discussion [23] Initially a convergent null of the wind for either component is centered at 160 km for the simulation runs shown in Figures 6 and 7. The downward propagating

5 BISHOP AND EARLE: SIMULATING METALLIC INTERMEDIATE LAYERS SIA 3-5 Figure 5. The figure shows LEAD results after applying a sinusoidal meridional wind with an amplitude of 20 m/s, a wavelength of 40 km, and a downward propagating velocity of 1.5 m/s. The panels on the left (right) show the meridional (zonal) results. The dashed and solid lines represent the Fe + and N e density profiles resulting form the imposed wind shown.

6 SIA 3-6 BISHOP AND EARLE: SIMULATING METALLIC INTERMEDIATE LAYERS 7 regardless of amplitude, wavelength, or applied neutral wind component. [24] Figure 6 shows several interesting relationships between amplitude and Fe + transport. First, the value of the percent change in the maxima for the intervals , , and km increases with increasing amplitude. Because the initial phase of all the imposed wind profiles places a convergent null at 160 km and the simulation is limited to 6 hours, the intervals and km contain a null for the longest amount of time. At these altitudes, the meridional wind is the more efficient of the two components at effecting ion transport. As the amplitude of the meridional wind increases, the removal of ions by the wind in the upper altitude intervals increases. The same effect is seen when the zonal wind amplitude is Figure 6. The figure shows the transport of Fe + as a function of local time. Each panel contains 6 profiles that correspond to 15 km intervals between 100 and 190 km. The net change in density at a particular time (t) is defined as (( R z f [Fe + (z, t)]dz)/( R z f [Fe + o (z, t)]dz) 1) 100.0%. The panels on the left (right) side illustrate the net flux of metallic ions as the amplitude of a sinusoidal meridional (zonal)wind profile varies. From top to bottom, the amplitude is 10, 20, and 40 m/s. The numbers 1, 2, and 3 show the increase in Fe + from the convergent null that started at 160 km. convergent nulls of the applied neutral wind in Figures 6 and 7 produces Fe + transport that is uniformly downward. An increase in the percentage change in the altitude interval containing the null is expected, followed by a decrease after the null moves into the next lower altitude interval. Thus, successively lower altitude intervals will contain local maxima as a function of time. This effect is illustrated with the numbers (1, 2, and 3) that label the lines showing the sequence of increases as the convergent null passes through the intervals. Ideally, each successive maxima in the percent change should increase as all the Fe + is swept downward. This is limited by the Fe + available in the region. An example of this behavior is observed in the middle left hand panel of Figure 6. The intervals (3), (2), and (1) km clearly display this trend. These three intervals display this behavior in Figures 6 and Figure 7. The figure shows the transport of Fe + as a function of local time. Each panel contains 6 profiles that correspond to 15 km intervals between 100 and 190 km. The net change in density at a particular time (t) is defined as (( R z f [Fe + (z, t)]dz)/( R z f [Fe + o (z, t)]dz) 1) 100.0%. The panels on the left (right) side illustrate the net flux of metallic ions as the wavelength of a sinusoidal meridional (zonal) wind profile varies. From top to bottom, the wavelength is 20, 40, and 80 km. The numbers 1, 2, and 3 show the increase in Fe + from the convergent null that started at 160 km.

7 BISHOP AND EARLE: SIMULATING METALLIC INTERMEDIATE LAYERS SIA 3-7 increased but to a lesser extent. The zonal wind is most efficient below 120 km. In Figure 6, a significant amount of Fe + is transported into the km as expected. [25] In Figure 6, the convergent region for the null would be 20 km for a neutral wind with a 40 km wavelength. The maximum percent change should occur when the convergent null is near the center of the interval. For the km range ideally the percent change would reach a maximum near 21.4 LT coincident with the convergent null at the center of the altitude interval. After 21.4 LT the percent change decreases in the km interval but begins to increase in the km interval. Within the km interval, the maximum percent change should ideally be near 24.2 LT. In all cases shown in Figure 6, the maximum percent change occurs later than 24.2 LT. The exact time of the maximum percent change varies between the cases shown. Further investigation is necessary to ascertain the significance of this feature. [26] The final feature to note in Figure 6 is the percent increase in the km interval. It occurs in all the results in Figure 6 except for the meridional wind of amplitude 40 m/s. The percent increase reaches a local maxima near 2300 LT. At this point a convergent null has entered the region and is at approximately 180 km. The net increase observed is a second convergent ion layer forming and following the convergent null downward as observed in Figure 5. The forming of the second layer means that not all of the Fe + ions were swept down by the first convergent null. In the bottom left panel of Figure 6 the amplitude is large enough (40 m/s) that the first null effectively removes all Fe + ions from the higher altitude intervals leaving no Fe + ions available to be gathered near the second null. Experimentally we have observed the opposite effect, with the second or third layer on a given night having higher peak density [Earle et al., 2000a]. Assuming that these layers are comprised of a significant amount of metallic ions, this increase in subsequent observed layer density may be indicative of flux tube aligned motion of metallic ions at midlatitudes throughout the night [Mathews, 1998]. [27] Several interesting relationships are also observed in Figure 7 between Fe + transport and the wavelength of the applied neutral wind. As the wavelength for either wind component increases the transport of Fe + downward increases. This increase in efficiency can easily be understood by looking at the depletion regions or the regions containing a divergent null. For the 20 and 80 km wavelength cases the interval is km. The equivalent depletion area is km for the 40 km wavelength case. As the wavelength increases the percent change in these intervals gets closer to 100%, or no Fe + present. This increase in transport efficiency is due to a larger altitude range affected by the convergent region of the neutral wind as the wavelength increases. [28] In Figure 7, there is an apparent lag in the Fe + transport by the zonal wind as compared to the meridional. This is most evident in the km interval for a wavelength of 80 km. The percent change in the interval reaches a maximum at approximately 24.4 LT for the meridional wind while the zonal wind maximum occurs at nearly 25 LT. The lag is the effect of the relative efficiencies of the wind components to transport ions, as previously discussed. [29] Varying the wavelength or amplitude of the imposed horizontal wind component also affects the thickness, peak density, and shape of the overall layer in the electron density profile. We found that the full width at half maximum (FWHM) of the Fe + layer is approximately equal to the overall FWHM of the layer for an imposed meridional wind. The FWHM of the Fe + and Ne layer decreases over time for the imposed zonal wind. This follows the fact that the convergent null enters lower altitudes later in time where the zonal wind becomes more efficient. The increase in efficiency collects the ions into a narrower layer, decreasing the FWHM. 5. Summary and Conclusions [30] This paper has focused on the transport of metallic ions, specifically Fe +, associated with intermediate layer development. Using a first principles numerical simulation, we have applied various sinusoidal meridional and zonal wind fields to investigate metallic ion transport. The wind fields imposed illustrate the relative dependence of metallic transport on the wavelength and amplitude of a shear region. The amplitudes and wavelengths of the wind fields imposed in our study are in rough agreement with typical midlatitude E region winds as measured by years of sounding rocket experiments [Rosenberg, 1968]. [31] Fe + ions are effectively transported downward coincident with the downward motion of the imposed neutral wind. The efficiency with which the bulk of the metallic ions are transported, as well as the characteristics of the Fe + layer formed, are a function of the wavelength, amplitude, and the specific horizontal neutral wind component applied. Metallic ion transport increases with increasing wavelength and amplitude, regardless of the horizontal wind component imposed. Even though this relationship is expected when examining the momentum and continuity equations, the rate at which transport efficiency changes with increasing wavelength of the wind field is surprising. [32] The next step in understanding intermediate layer composition and its affects on layer developments must include in situ observations. Sounding rockets will most likely provide the most useful measurements in this altitude range, although a dipper satellite with a low perigee could also provide valuable data. Experiments involving simultaneous composition and neutral wind measurements of an intermediate layer below 140 km will prove most valuable. [33] Acknowledgments. This work was partially supported by NASA grants NAGS-5257 and NAG and NSF grant ATM The authors would like to thank Rod Heelis and Miguel Larsen for their helpful insights and discussions. References Axford, W. I., The formation and vertical movement of dense ionized layers in the ionosphere due to neutral wind shears, J. Geophys. Res., 68, , Bailey, G. J., and R. Sellek, A mathematical model of the Earth s plasmasphere and its application in a study of He + at L = 3, Ann. Geophys., 8, , Bilitza, D., K. Rawer, L. 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