Radial gradients of phase space density in the inner electron radiation

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2012ja018211, 2012 Radial gradients of phase space density in the inner electron radiation Kyung-Chan Kim 1 and Yuri Shprits 2,3 Received 15 August 2012; revised 8 October 2012; accepted 31 October 2012; published 8 December [1] While the outer radiation belt (3.5 < L < 8.0) is highly variable with respect to geomagnetic activity, the inner radiation belt (1.2 < L < 2.0) is relatively stable. Less attention has been paid to the inner electron belt in recent years. It has been generally accepted that the equilibrium structure of radiation belt electrons is explained by the slow inward radial diffusion from a source in the outer belt and losses by Coulomb collision and wave-particle interaction. In this study, we examine this well accepted theory using the radial profiles of the phase space density (PSD), inferred from in situ measurements made by three different satellites: S3 3, CRRES, and POLAR. Our results show that electron PSD in the inner electron belt has a clear prominent local peak and negative radial gradient in the outer portion of the inner zone, i.e., decreasing PSD with increasing L-value. A likely explanation for the peaks in PSD is acceleration due to energy diffusion produced by lightning-generated and anthropogenic whistlers. These results indicate that either additional local acceleration mechanism is responsible for the formation of the inner electron belt or inner electron belt is formed by sporadic injections of electrons into the inner zone. The currently well accepted model of slow diffusion and losses will be further examined by the upcoming Radiation Belt Storm Probes (RBSP) mission. Citation: Kim, K.-C., and Y. Shprits (2012), Radial gradients of phase space density in the inner electron radiation, J. Geophys. Res., 117,, doi: /2012ja Introduction [2] The Earth s energetic electron radiation belts exhibit a two-zone structure with the inner zone (1.2 < L < 2.0) being very stable and the outer belt (3.5 < L < 8.0) varying on the timescales of hours, weeks, and months. The two zones are separated by a slot region where relativistic electron radial flux profile exhibits a pronounced minimum. The commonly accepted theory of the origin of relativistic electrons in the radiation belts suggests that electrons are brought in from the outer region into the inner region and accelerated by means of very slow inward radial diffusion that conserves the first and second adiabatic invariants [Kellogg, 1959; Fälthammar, 1965]. [3] Lyons and Thorne [1973] modeled the equilibrium structure of the electron radiation belts by accounting for the slow inward radial diffusion from a source above L = 5.5 as sole source process and for losses by Coulomb collision and wave-particle interaction. The modeling successfully reproduced a two-zone structure and explained the presence of the 1 Korea Astronomy and Space Science Institute, Daejeon, South Korea. 2 Skolkovo Institute of Science and Technology, Moscow, Russia. 3 Department of Earth and Space Sciences, University of California, Los Angeles, California, USA. Corresponding author: K.-C. Kim, Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon , South Korea. (kckim@kasi.re.kr) American Geophysical Union. All Rights Reserved /12/2012JA slot region between the inner and the outer belts. It also successfully explained the formation of the inner belt as a result of very slow inward diffusion (on a timescale of a week and more) and loss, suggesting that monotonic profiles of phase space density (PSD), i.e., increasing PSD with increasing L-value, for the fixed first and second adiabatic invariants would be required to reach the equilibrium twozone structure. Beutier and Boscher [1995] and Kim et al. [2011] reconfirmed, through global modeling, that the twozone structure in fluxes at a fixed energy as measured by spacecraft can simply be understood as a balance between inward radial diffusion and precipitation losses by Coulomb scattering and wave-particle interactions. [4] In a recent decade, intensive studies have been conducted to investigate radial gradients of PSD in the outer zone to challenge the well-established theory that the inward radial diffusion is the only source of relativistic electrons [e.g., Brautigam and Albert, 2000; Selesnick and Blake, 2000, 2002; Green and Kivelson, 2004; Iles et al., 2006; Chen et al., 2005, 2006, 2007; Shi et al., 2009; Turner et al., 2010; Fennell and Roeder, 2008; Shprits et al., 2007, 2012]. Recent studies have shown that electrons in the outer belts can be accelerated locally by gyroresonant acceleration with whistler mode chorus waves [e.g., Summers et al., 1998; Baker et al., 2004; Miyoshi et al., 2003; Albert and Young, 2005; Horne et al., 2005; Shprits et al., 2006, 2007]. [5] While the outer belt can change by several orders of magnitude within a few hours, the inner belt remains relatively stable and has received less attention in recent years. Nevertheless, during the early years of radiation belt 1of6

2 Figure 1. Dependence of (left) kinetic energy and (right) equatorial pitch angle on L-value for a fixed value of m = 35 MeV/G and three values of K = 0.1 (black), 0.5 (blue), and 0.9 (red) G 0.5 R E. research, the inner belt received a lot of attention following the observations of the remnant electrons from the Starfish nuclear test on July 9, 1962 [e.g., Paulikas et al., 1967; Vampla, 1967]. The early theories of the origin of the inner belt assumed that it was produced by Cosmic Ray Albedo- Neutron Decay (CRAND). The process is, however, too weak to produce a measureable amount of low-energy and high-energy (>1 MeV) electrons [Hess and Poirier, 1962]. [6] Therefore, if radial diffusion is the only source of relativistic electrons, the profile of the inner zone PSD should be monotonically increasing with increasing L-shell below L = 2.0 and electrons are transported inward from a source outside of inner zone. In contrast, if internal source mechanism inside of inner belt is operational or periodic injections bring in relativistic electrons, PSD will show localized peaks similar to the peaks observed in the outer zone. The goal of this paper is to examine the well-established theory that the slow inward radial diffusion is principally responsible for accelerating electrons in the inner zone by calculating PSD using observations of relativistic electrons made by S3 3, CRRES, and POLAR satellites, which operated at different time periods and measured relativistic electron fluxes below L = 2.0. The paper is organized as follows. In section 2, we briefly introduce the energetic electron detectors on board S3 3, CRRES, and POLAR satellites, and the calculation of PSD using in situ observations. Then, in section 3, we analyze the inferred PSD from the observations of the three satellites in the inner electron zone. The summary and conclusions are given in section Observations and Phase Space Density Calculations [7] The S3 3 satellite ( B) was launched during July, 1976 as a U.S. Air Force Space Test Program vehicle, which is a polar-orbiting satellite with an initial inclination of 97.5 degrees, an apogee of 8040 km, a perigee of 240 km, and an orbital period of approximately three hours. The spin vector was maintained nearly perpendicular to the orbit plane, so particle instruments viewed radially obtained nearly complete pitch angle distributions most of the time. The data used in this study are from the Magnetic Electron Spectrometer (MES) measuring electrons from to 1.6 MeV in twelve energy channels. The data for the whole mission is available on the VIRBO Web site. [8] The CRRES (Combined Release and Radiation Effects Satellite) was launched in July It maintained a Sunpointing spin axis with a spin rate of 2 rpm and operated in an inclining orbit of 10 degrees from the magnetic equator and a geosynchronous transfer orbit with a perigee of 305 km and an apogee of 35,768 km. In this study, we use energetic electron observations from both the Medium Electron Sensor A (MEA) and the High Energy Electron Fluxmeter (HEEF) onboard CRRES, and the data are available from the VIRBO Web site. The MEA observes electrons from 153 kev to MeV in 17 differential channels and the HEEF observes electrons with energies from 0.6 to 8 MeV in 10 differential channels. [9] The POLAR satellite, launched on February 24, 1996, is in a highly elliptical, 86 degree inclination orbit with a period of about 17.5 h, an apogee at 9 R E, and a perigee at 1.8 R E geocentric distances. The Imaging Electron Sensor (IES) and High Sensitivity Telescope (HIST) instruments on board POLAR provide 24-s resolution electron flux data at energies between 0.02 and 10 MeV in 24 energy channels, giving full pitch angle coverage with a 20 bin width. The POLAR/HIST data, covering an energy range from 0.35 to 10 MeV, are mostly used here. [10] The steps we used to obtain the PSD profiles from available spacecraft flux observations given as a function of kinetic energy and local pitch angle at each satellite location are outlined below. 1. Pick any desired value for the first (m) and second (K) invariants. In this analysis, a value of 35 MeV/G was chosen for the first adiabatic invariant, and various values from 0.0 to 1.0 G 0.5 R E were chosen for the second adiabatic invariant. These values correspond to relativistic electron energies (>0.5 MeV) for L < 3.0, assuming a dipole magnetic field (see Figure 1). 2. Find energy E and local pitch angle a that correspond to the chosen m and K. In this step, we calculate K values for local pitch angles from 5 to 90 at 5 intervals at each satellite location using the Tsyganenko T96 field model [Tsyganenko and Stern, 1996] and interpolate between the 18 values of K to find the pitch angle corresponding to the chosen K. The corresponding energy is also determined for a given rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m and local pitch 2Bm angle from the equation E ¼ E 0 þ 1 1 E 0 sin 2 ðaþ where E 0 = is the electron rest energy in MeV and B is the measured local magnetic field strength in Gauss. 3. Calculate L* at each satellite location that corresponds to determined E and a using the T96 field model. The L* is defined as follows [Roederer, 1970]: L*=2pk 0 /(R E F), where k 0 is the Earth s dipole magnetic moment, R E is the Earth s radius, and F is the third invariant. 4. To obtain the electron flux at a satellite s location for E and a, interpolate two neighboring energy channels using the satellite flux j(e, a, r). 5. Obtain electron flux j for E and a that correspond to the chosen m and K. 6. Obtain a radial profile of PSD from the equation f ðm; K; L* Þ ¼ 10 3 je; ð a; rþ ce ð 2 þ 2E 0 E 2 Þ where PSD f is given in units of (MeV/c cm) 3 [see Chen et al., 2005; Shprits et al., 2007], j in units of cm 2 s 1 sr 1 kev 1, E and E 0 (= 0.511) in MeV. The method used in this study is similar to that of Green and Kivelson [2004]. 2of6

3 Figure 2. (a) PSD radial distributions obtained from the measurements made by S3 3, (b) CRRES, and (c) POLAR satellites for a fixed m = 35 MeV/G and three values of K = 0.1 (first column), 0.5 (second column), and 0.9 (third column) G 0.5 R E. The calculation of PSD requires a magnetic field model to compute the three adiabatic invariants (m, K, and L*). Thereby the results are inevitably dependent on the choice of the magnetic field model, which often leads to contradictory estimates of PSD radial gradients [Green and Kivelson, 2004]. However, in this analysis we concentrate on the inner electron zone below L = 2.0, where the Earth s magnetic field is close to the magnetic dipole field and the PSD analysis is insensitive to the magnetic field model. 3. Profiles of PSD Radial Distribution in the Inner Electron Zone [11] Electron PSD profiles versus L* for a fixed value of m = 35 MeV/G and three values of K = 0.1 (first column), 0.5 (second column), and 0.9 (third column) G 0.5 R E obtained from the measurements made by the S3 3 satellite in 1977 (first row), the CRRES satellite in 1990 (second row), and the POLAR satellite in 2001 (third row) are shown in Figure 2 with each trace color coded by month. Each of the figures corresponds to the analysis of 200 days. Note that, for the CRRES data used to infer PSD, we chose a time interval from July 1990 through February 1991 to avoid proton contamination in the electron data, initiated by the March 24, 1991 prompt injection through the outer zone [Blake et al., 1992; Li et al., 1993]. [12] At lower values of K (= 0.1 G 0.5 R E ) a prominent local peak in PSD at L* 1.6 is clearly seen in CRRES observations. A choice of higher K, corresponding to lower equatorial pitch angles, allows us to infer PSD for a relatively large range of L-shells. At an intermediate value of K (= 0.5 G 0.5 R E ), the PSD has a steep negative radial gradient, i.e., decreasing PSD with increasing L*, for L* < 2.0, thus forming a local minimum in PSD profiles between L*= 2.0 and 2.5. This feature is observed in observations of all three spacecraft. For electrons with relatively high values of K (= 0.9 G 0.5 R E ), the same feature is clearly confirmed only for the POLAR observations due to lack of data points for the other two satellites inside L* = 2.0. In contrast to the inner zone trends, above L* 2.0, PSD tends to increase monotonically with a local minimum in the slot region, which can be seen in observations of all three spacecraft for all values of m and K for which sufficient data is available. Note that the steepness of the PSD radial gradient for L* > 2.5 dynamically changes in response to internal (magnetospheric) or external (solar wind-driven) variations, but still keeping a positive gradient. Whereas, for L* < 2.0, the variations in the radial gradient is relatively slow, which implies 3of6

4 Figure 3. PSD radial distributions in time inferred from (a) S3 3, (b) CRRES, and (c) POLAR satellite observations. The PSD versus L* distribution for a fixed value m = 35 MeV/G, and K = 0.2, K = 0.1, and K = 0.5 G 0.5 R E for S3 3, CRRES and POLAR satellites, respectively (Figure 3a). PSD line profiles at two different L* values of 1.5 (blue) and 1.8 (red) (Figure 3b). Time variation of Dst geomagnetic index (Figure 3c). that longer time scales will have to be considered to interpret the local peak in the inner zone. [13] To understand the temporal evolution of the PSD in the inner electron zone in more detail, we present the inferred PSD radial distribution versus time. Figure 3 shows the PSD radial distributions obtained from S3 3 (Figure 3a), CRRES (Figure 3b), and POLAR (Figure 3c) observations for the same time period as shown in Figure 2. In each figure, the first panel shows the daily averaged color-coded PSD radial distribution as a function of time for a fixed value of m = 35 MeV/G and K = 0.2 G 0.5 R E for S3 3, K = 0.1 G 0.5 R E for CRRES, and K = 0.5 G 0.5 R E for POLAR. The different values of K are chosen to provide the best coverage in L-shells. The second panel shows the PSD evolution for the same values of m and K at two different L* values of 1.5 (blue) and 1.8 (red). The third panel gives the time variation of the Dst geomagnetic index. The PSD is consistently higher around L* = 1.5 than it is at higher L-shells, indicating a prominent negative gradient between L* = 1.5 and 2.0. Also, the PSD at L* = 1.8 tends to fluctuate more 4of6

5 than it does at L* = 1.5. This feature is seen for all three spacecraft observations (though it is difficult for the S3 3 observations to capture some features of the variation in PSD due to sparse data). A careful examination of the PSD evolution shows that during storm times a slow inward radial diffusion from the region above L* 2.0 with time scales from weeks to years [Lyons and Thorne, 1973] cannot explain these observations. The CRRES observations show a slowly but steadily increase at L* = 1.5 after 215 day in the storm recovery without particle injection above L* 2.0 while the PSD at L* = 1.8 decreases. The behavior at L* = 1.5 might be due to local sources. We discuss potential source mechanisms in the next section. Due to no available data before day 210, it is difficult to know what happened in the inner belt. Similar behavior can be seen in POLAR observations. For 80 to 140 days during the POLAR mission that includes number of storms with the strongest reaching a minimum Dst of 400 nt, the PSD at L* = 1.5 decreases slightly and recovers within a few weeks without particle injection from the outer regions above L* 2.0 and the PSD at L* = 1.8 also changes in response to the PSD variation at L* = 1.5. In other words, the difference in PSD between L* = 1.5 and 1.8 becomes smaller (larger), weakening (strengthening) steepness of radial gradient. 4. Summary and Discussion [14] In this study, we present the inferred PSD radial distribution using in situ measurements made by three different satellites, S3 3, CRRES, and POLAR, in order to investigate the spatial and temporal profile of the PSD radial gradient in the inner electron zone, i.e., below L* = 2.0. If the slow radial diffusion is the only acceleration mechanism, radial profiles of inner zone PSD should be monotonic. However, our results show that the inferred PSD profiles versus L* have a clear prominent local peak and negative radial gradient, i.e., decreasing PSD with increasing L* for L* < 2.0. [15] Two different scenarios can potentially explain the negative gradients above L = 1.5: 1) Particles may be injected during very strong geomagnetic storms and stay trapped in the inner belt for several years. Losses to the atmosphere, which can vary with radial distance, can potentially produce negative gradients in PSD as well as peaks in PSD. However, we confirmed that even during a superstorm for the POLAR mission particles are not injected into the inner belt from the outer source region above L 2.0. It is possible however that particles were injected during a previous storm; 2) Particles may be accelerated locally around L = 1.5. The observations suggest that this scenario seems more likely. Currently, the physics of such acceleration is unknown. One potential mechanism could be acceleration due to the energy diffusion by VLF/ ELF waves, including lightning-generated whistlers and VLF transmitters. Even though plasma density is high in the inner zone, a very strong magnetic field lowers the plasma to gyro frequency ratio and makes the resonant interactions with VLF/ELF waves very efficient. The presence of peaks at L = 1.5 may be a result of contamination by ultra-relativistic ions that populate the inner portion of the inner belt. However, the ion contamination should be insignificant in the outer region of the inner belt where we observe negative gradients. Unfortunately, a detailed analysis of the effect of contamination has not been done for these satellites. Also, if electron data shown in this study is an effect of contamination by protons, the time variation of PSD should be slow on time scales of the order of years for high energy protons [Miyoshi et al., 2000; Li et al., 2001]. The observations show that PSD variation at L* = 1.8 is relatively dynamic. It may imply that the observations are based on the variation of electron and not contamination. The definitive measurements of the inner zone electron PSD will not be available until the launch of the Radiation Belt Storm Probes (RBSP) mission. The search for a new mechanism in the formation of the inner electron belt should be a subject of future studies. A number of upcoming international missions, including NASA s RBSP mission, will shed light on the origin of the relativistic electrons in the inner belt. [16] Acknowledgments. Authors would like to thanks Joe Fennell and Paul O Brian for useful discussions. We are grateful to Reiner Friedel who provided the POLAR/CEPPAD data. This research was supported by NASA under grants NNX09AF51G and NNX10AK996 and by the Lab Fees Research Program. K.-C. Kim was supported by the Study of Near-Earth Effects by CME/HSS Project and basic research funding from KASI. We would also like to thank Bob Weigel and Bob Johnston for providing data. [17] Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper. References Albert, J. M., and S. L. Young (2005), Multidimensional quasi-linear diffusion of radiation belt electrons, Geophys. Res. Lett., 32, L14110, doi: /2005gl Baker, D. N., S. G. Kanekal, X. Li, S. P. Monk, J. Goldstein, and J. L. Burch (2004), An extreme distortion of the Van Allen belt arising from the Hallowe en solar storm in 2003, Nature, 432, , doi: /nature Beutier, T., and D. Boscher (1995), A three-dimensional analysis of the electron radiation belt by the Salammbô code, J. Geophys. Res., 100(A8), 14,853 14,861, doi: /94ja Blake, J. B., W. A. Kolasinski, R. W. Fillius, and E. G. Mullen (1992), Injection of electrons and protons with energies of tens of MeV into L < 3 on 24 March 1991, Geophys. Res. Lett., 19(8), , doi: / 92GL Brautigam, D. H., and J. M. Albert (2000), Radial diffusion analysis of outer radiation belt electrons during the October 9, 1990, magnetic storm, J. Geophys. Res., 105, , doi: /1999ja Chen, Y., R. H. W. Friedel, G. D. Reeves, T. G. Onsager, and M. F. Thomsen (2005), Multisatellite determination of the relativistic electron phase space density at geosynchronous orbit: Methodology and results during geomagnetically quiet times, J. Geophys. Res., 110, A10210, doi: / 2004JA Chen, Y., R. H. W. Friedel, and G. D. Reeves (2006), Phase space density distributions of energetic electrons in the outer radiation belt during two Geospace Environment Modeling Inner Magnetosphere/Storms selected storms, J. Geophys. Res., 111, A11S04, doi: /2006ja Chen, Y., R. H. W. Friedel, G. D. Reeves, T. E. Cayton, and R. Christensen (2007), Multisatellite determination of the relativistic electron phase space density at geosynchronous orbit: An integrated investigation during geomagnetic storm times, J. Geophys. Res., 112, A11214, doi: / 2007JA Fälthammar, C.-G. (1965), Effects of time-dependent electric fields on geomagnetically trapped radiation, J. Geophys. Res., 70(11), , doi: /jz070i011p Fennell, J. F., and J. L. Roeder (2008), Storm time phase space density radial profiles of energetic electrons for small and large K values: SCATHA results, J. Atmos. Sol. Terr. Phys., 70(14), , doi: /j.jastp Green, J. C., and M. G. Kivelson (2004), Relativistic electron in the outer radiation belt: Differentiating between acceleration mechanisms, J. Geophys. Res., 109, A03213, doi: /2003ja Hess, W. N., and J. A. Poirier (1962), Energy spectrum of electrons in the outer radiation belt, J. Geophys. Res., 67(5), , doi: / JZ067i005p of6

6 Horne, R. B., R. M. Thorne, S. A. Glauert, J. M. Albert, N. P. Meredith, and R. R. Anderson (2005), Timescale for radiation belt electron acceleration by whistler mode chorus waves, J. Geophys. Res., 110, A03225, doi: /2004ja Iles, R. H. A., N. P. Meredith, A. N. Fazakerley, and R. B. Horne (2006), Phase space density analysis of the outer radiation belt energetic electron dynamics, J. Geophys. Res., 111, A03204, doi: /2005ja Kellogg, P. J. (1959), Van Allen radiation of solar origin, Nature, 183, , doi: / a0. Kim, K.-C., Y. Shprits, D. Subbotin, and B. Ni (2011), Understanding the dynamic evolution of the relativistic electron slot region including radial and pitch angle diffusion, J. Geophys. Res., 116, A10214, doi: / 2011JA Li, X., I. Roth, M. Temerin, J. R. Wygant, M. K. Hudson, and J. B. Blake (1993), Simulation of the prompt energization and transport of radiation belt particles during the March 24, 1991 SSC, Geophys. Res. Lett., 20(22), , doi: /93gl Li, X., D. N. Baker, S. G. Kanekal, M. Looper, and M. Temerin (2001), Long term measurements of radiation belts by SAMPEX and their variations, Geophys. Res. Lett., 28(20), , doi: / 2001GL Lyons, L. R., and R. M. Thorne (1973), Equilibrium structure of radiation belt electrons, J. Geophys. Res., 78, , doi: / JA078i013p Miyoshi, Y., A. Morioka, and H. Misawa (2000), Long term modulation of low altitude proton radiation belt by the Earth s atmosphere, Geophys. Res. Lett., 27(14), , doi: /1999gl Miyoshi, Y., A. Morioka, H. Misawa, T. Obara, T. Nagai, and Y. Kasahara (2003), Rebuilding process of the outer radiation belt during the 3 November 1993 magnetic storm: NOAA and Exos-D observations, J. Geophys. Res., 108(A1), 1004, doi: /2001ja Paulikas, G. A., J. B. Blake, and S. C. Freden (1967), Inner-zone electrons in 1964 and 1965, J. Geophys. Res., 72(7), , doi: / JZ072i007p Roederer, J. G. (1970), Dynamics of Geomagnetically Trapped Radiation, Springer, New York, doi: / Selesnick, R. S., and J. B. Blake (2000), On the source location of radiation belt relativistic electrons, J. Geophys. Res., 105, , doi: / 1999JA Selesnick, R. S., and J. B. Blake (2002), Relativistic electron drift shell splitting, J. Geophys. Res., 107(A9), 1265, doi: /2001ja Shi, Y., E. Zesta, and L. R. Lyons (2009), Features of energetic particle radial profiles inferred from geosynchronous responses to solar wind dynamic pressure enhancements, Ann. Geophys., 27, , doi: /angeo Shprits, Y., D. Kondrashov, Y. Chen, R. Thorne, M. Ghil, R. Friedel, and G. Reeves (2007), Reanalysis of relativistic radiation belt electron fluxes using CRRES satellite data, a radial diffusion model, and a Kalman filter, J. Geophys. Res., 112, A12216, doi: /2007ja Shprits, Y., M. Daae, and B. Ni (2012), Statistical analysis of phase space density buildups and dropouts, J. Geophys. Res., 117, A01219, doi: /2011ja Shprits, Y. Y., R. M. Thorne, R. B. Horne, S. A. Glauert, M. Cartwright, C. T. Russell, D. N. Baker, and S. G. Kanekal (2006), Acceleration mechanism responsible for the formation of the new radiation belt during the 2003 Halloween solar storm, Geophys. Res. Lett., 33, L05104, doi: /2005gl Summers, D., R. M. Thorne, and F. Xiao (1998), Relativistic theory of wave-particle resonant diffusion with application to electron acceleration in the magnetosphere, J. Geophys. Res., 103(A9), 20,487 20,500, doi: /98ja Tsyganenko, N. A., and D. P. Stern (1996), Modeling the global magnetic field of the large-scale Birkeland current systems, J. Geophys. Res., 101(A12), 27,187 27,198, doi: /96ja Turner, D. L., X. Li, G. D. Reeves, and H. J. Singer (2010), On phase space density radial gradients of Earth s outer-belt electrons prior to sudden solar wind pressure enhancements: Results from distinctive events and a superposed epoch analysis, J. Geophys. Res., 115, A01205, doi: /2009ja Vampla, A. L. (1967), Recent measurements of inner zone electron lifetimes, paper presented at COSPAR Plenary Meeting, Comm. On Space Res., London. 6of6