Relative Contribution of Electrons to the Stormtime Total Ring Current Energy Content S

GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L03110, doi:10.1029/2004GL021672, 2005

Relative contribution of electrons to the stormtime total ring current energy content S. Liu,1 M. W. Chen,2 J. L. Roeder,2 L. R. Lyons,1 and M. Schulz3 Received 30 September 2004; revised 10 December 2004; accepted 5 January 2005; published 10 February 2005.

[1] We evaluate the relative importance of stormtime ring total stormtime ring current energy content. In this paper we current electrons to protons by calculating the energy evaluate the relative energy contribution of ring current content ratio of electrons to protons for typical ring current electrons to the proton ring current energy from both energies inferred from observations and simulations. We observational data and simulation results. We thereby analyze Explorer 45 measurements taken around the address the longstanding question of how important elec- minimum Dst(=171 nT) of the 17 December 1971 trons are to the stormtime ring current. storm. We simulate the electron and proton ring current [3] Unfortunately, aside from the old Explorer 45 data, energy content during a hypothetical storm using drift-loss there is not a reliable data set available that spans both the simulations. From the data analysis, we find that electrons desired energy (1–200 keV) range and spatial range (L with energies of 1–50 keV and protons with energies of 2–5. For example, the polar orbiting S3-3 satellite collected 10–200 keV contribute the most to the corresponding electron flux data from energies of 12 keV to 1.6 MeV. particle energy content. From both observations and However, the S3-3 orbit (apogee = 8048 km and perigee = simulations, the ring current electrons contribute only 236 km) was too close to the Earth so that there were no 1% as much energy content as ring current protons measurements of stormtime fluxes around 90 pitch angle during quiet times. However, this ratio increases to 8– from L = 3–5. The CRRES satellite was in a highly 19% during storm main phase. Thus, the ring current elliptical geosynchronous transfer orbit. Unfortunately, electrons can contribute significantly to the ring current measurements of electrons with energies of 20–153 keV, energy content during storms. Citation: Liu, S., M. W. Chen, the bulk of the ring current energy, from the CRRES/EPAS J. L. Roeder, L. R. Lyons, and M. Schulz (2005), Relative instrument suffered contamination [Korth et al.,1992]. contribution of electrons to the stormtime total ring current energy Similarly, stormtime ring current electron data from the content, Geophys. Res. Lett., 32, L03110, doi:10.1029/ polar orbiting POLAR satellite is contaminated. Thus, in 2004GL021672. this study we analyze the Explorer 45 electron and proton data to estimate the relative contribution of ring current electrons to the total stormtime ring current energy content. 1. Introduction [4] To provide further insight into the problem, we [2] The Earth’s ring current consists of both ions and employ drift-loss simulations of the stormtime ring current electrons with energies of 10–200 keV that drift within electron to estimate the relative energy contribution of the inner magnetosphere. There has been extensive previ- electrons to the proton ring current energy content. We ous research on characterizing and understanding the ion use an electron ring current simulation model [Liu et al., ring current [e.g., Chen et al., 1997; Kozyra and Liemohn, 2003] that we recently developed and the proton ring 2003, and references therein]. However, only a few studies current simulation model of Chen et al. [1994, 2003]. The have focused specifically on the role of electrons in the ring current simulation model of Liu et al. [2003] success- formation of the stormtime ring current. Several decades fully reproduced stormtime electron fluxes at 12 keV that ago [Frank, 1967] reported that electrons contribute 25% were measured by the CRRES satellite at 3 L 6 during two of ions to the ring current energy content. He analyzed storm events. We will simulate the energy content of both OGO 3 electron and ion data with energies of 200 eV to electrons and protons for a model storm and use the results 50 keV at 1 < L < 8 for a small storm (min Dst = 50 nT). to estimate the relative contribution of stormtime ring These measurements did not cover the higher energy range current electrons to the total ring current energy content. of ring current particles from 50–200 keV. Lyons and Williams [1975a, 1975b, 1980] examined stormtime 2. Instrument and Data enhancements of ring current ion and electron fluxes measured by the Explorer 45 satellite that did cover the [5] Explorer 45 was launched on 15 November 1971. Its higher ring current energies (1–800 keV). However, they orbit was very close to the equatorial plane (inclination did not estimate the relative contribution of electrons to the 3.5). Its perigee was 220 km and apogee was 5.24RE. There were one electrostatic plasma analyzer instrument and 1Department of Atmospheric and Oceanic Sciences, University of three solid state detectors on board [Lyons and Williams, California, Los Angeles, California, USA. 1975b]. The instruments measured proton fluxes from 2Space Science Applications Laboratory, The Aerospace Corporation, 0.73–872 keV, and electron fluxes from 0.73–560 keV Los Angeles, California, USA. 3 [Lyons and Williams, 1975a]. The reported ‘‘proton’’ fluxes Lockheed Martin Advanced Technology Center, Redwood City, are actually total ion fluxes (D. J. Williams, private com- California, USA. munication, 2004). However, we still regard them as proton Copyright 2005 by the American Geophysical Union. fluxes in the energy content calculations. We will discuss 0094-8276/05/2004GL021672$05.00 how this assumption affects our results in Section 5.

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[6] Lyons and Williams [1975b, 1976, 1980] reported on simulation results. We briefly describe our ring current variations of equatorially mirroring proton and electron electron [Liu et al., 2003] and ring current ion [Chen et fluxes observed by Explorer 45 for two storms: 17 Decem- al., 1994, 2003] simulation models. More complete descrip- ber 1971 and 18 June 1972. Data at L > 4 for the 18 June tion can be found in the above mentioned references. In our 1972 storm was not published in those papers. Thus, we simulations we trace the guiding center ~E ~B, and gradient- selected the 17 December 1971 storm with a min Dst = curvature drifts of a large number of representative equato- 171 nT and a main phase of 6 hours for our event study. rially mirroring particles that conserve m in our magnetic Orbit 97 inbound of Explorer 45 corresponded to the orbit field and electric field models. We consider protons and prior to the 17 December 1971 storm onset, while orbit 101 electrons with m values from 1–100 MeV/G over equatorial inbound corresponded to a time around the peak of the Dst positions that range from 2 to 6.6RE spaced every 0.2RE and [Lyons and Williams, 1980, Figure 2]. These two inbound all local times spaced every 5. The magnetic field model is orbits covered magnetic local times of 2100–0200 MLT. a geomagnetic dipole field plus a constant southward field [7] We digitized Explorer 45 proton and electron spectra [Dungey, 1961]. Over this modeled magnetosphere we (differential flux versus energy) published by Lyons and impose corotation, quiescent Stern-Volland, and storm- Williams [1980] and Lyons [1976]. Pre-storm proton and associated enhancements in the convection electric field. electron spectra for orbit 97 inbound at L = 3.5 and 4.0 are [11] Using the simulated particle trajectories, we map the shown in Figure 5 of Lyons and Williams [1980]. Main phase space density along representative particle trajectories phase electron spectra (orbit 101 inbound) at L = 2.5, 3.0, backward in time by applying Liouville’s theorem modified 3.5, and 4.0 are shown in Figure 7 of Lyons and Williams by particle loss. We consider the proton loss due to charge [1980]. In that plot, the energy range of the electron spectra exchange (see Chen et al. [1994] for details). For electrons, is 1–366 keV. Main phase flux spectra at L = 4.5 and 5 for we consider losses due to wave-particle interactions (see Liu the same orbit can be obtained from Figure 5a of Lyons and et al. [2003] for details). Williams [1975b]. However, these spectra span energies of [12] In order to perform the phase-space mapping, we only 50–366 keV. We extrapolated the radial flux profiles specify particle boundary and initial conditions. The bound- of 1–50 keV electrons to obtain their fluxes at L = 4.5 and 5. ary conditions for both protons and electrons are 12-year The extrapolated fluxes agree well with CRRES/LEPA averages of LANL/MPA data, which are binned in every [Hardy et al., 1993] electron flux data at energies of 1– half hour of MLT and parameterized by Kp. The LANL/ 20 keV during a storm event. MPA data were provided by H. Korth, and explained by [8] We digitized the main phase proton flux spectra (orbit Korth et al. [1999]. The electron [Albert, 1994] and proton 101 inbound) at L = 2.5, 3.0, 3.5, 4.0, 4.5, and 5.0 shown in [Chen et al., 1994] initial conditions are taken from theo- Figure 2 of Lyons [1976]. In this figure, the proton spectra retical solutions of steady state transport equations, and were plotted as 2mpf(=j/Ek) versus E97, where mp is the normalized with quiet time boundary conditions. We use proton rest mass, f is the phase space density, j is the averaged LANL/MPA data for Kp = 1 as the quiet time differential flux, Ek is the measured kinetic energy. In order boundary conditions to normalize our initial conditions, and to keep the first adiabatic invariant m constant, E97 is the for Kp = 3 as the stormtime boundary conditions. The LANL/ energy corrected to the pre-storm orbit 97 and is defined as MPA does not resolve mass. However, because Kp = 3 does E97 Ek(B97/B), where B is the actual magnetic field not represent a highly disturbed condition, we believe that intensity, and B97 is the magnetic field at the pre-storm orbit the boundary conditions we specify here are mostly from 97 outbound. This corrected energy efficiently took account protons. of variations in the magnetic field due to the stormtime ring current. The main phase proton phase space spectra in Figure 2 of Lyons [1976] span corrected energies of E97 = 4. Calculated Energy Contents From Both 1 keV to 1 MeV. However, the measured kinetic energy Observation and Simulation ranges of the proton data from this figure vary for different L [13] From both Explorer 45 data and the simulation values. For example, at L = 3.5 the ‘‘uncorrected’’ kinetic results, we obtain spectra (f versus m)ofequatorially energy ranges from 1–600 keV, while at L =5.0,the mirroring proton and electron at different radial distances. kinetic energy ranges from 1–240 keV. We compiled From the phase space spectra, the energy content in a certain these digitized data in terms of differential flux j versus L range (L –L ) can be calculated from kinetic energy. Both proton and electron flux spectra cover 1 2 the full typical energy range of the stormtime ring current. Z Z Z L2 1 1 [9] In this study, we first convert flux versus energy 2 3=2 1=2 2 U ¼ 4p ðÞ2m0 ðÞmE=a m =L fEk dmdKdL; spectra to phase space density f versus m. f is calculated L1 0 0 by f = j/2mEk, where m is proton or electron mass. m is ð1Þ computed with Ek and in-situ magnetic field data obtained from Lyons and Williams [1976]. We utilize the f versus m where U is the energy content, m0 is particle’s mass, mE = spectra to calculate the electron and proton energy content 4 3 3.05 10 nT RE is the geomagnetic dipole moment, f is and to estimate the relative contribution of electrons’ energy 2 2 content to proton’s. the MLT averaged phase space density, K J /8m0m, and J is the second adiabatic invariant. A derivation of (1) is explained in Appendix B of Chen et al. [1994]. 3. Simulation Model Description [14] If we assume that the particle pitch-angle distribu- [10] To complement the data analysis, we also calculate tions are sharply pancaked at equatorial pitch-angle of 90, stormtime electron and proton energy content from our the integral of dK can be approximated by a small but finite

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energy content is higher at larger L values. For example, (dU/dL)e/(dU/dL)p =17%atL =5.0.Ifwehaddata available at larger L (L > 5) values, we might find that the relative electron to proton energy content ratio to be larger than our estimate. [18] The two asterisks and the two diamonds at L =3.5 and 4.0 in Figure 1 are prestorm dU/dL values for protons and electrons, respectively. From these data points we find that electrons only have 1% as much energy content as protons during quiet times, which is much less than the electrons’ contribution during storm times. This is because ring current electrons are typically lost much more rapidly than protons, and they have a lower temperature source in Figure 1. dU/dL profiles of both electrons and protons the plasma sheet. calculated from 101 inbound data of Explorer 45 during the [19] The Explorer 45 data mentioned above were main phase of December 17, 1971 storm. The two stars and observed on the night side (2100–0200 MLT). In the inner two open diamonds are dU/dL values for ions and electrons magnetosphere, electrons drift eastward while ions west- calculated from quiet time (orbit 97 inbound) data. ward because of the magnetic gradient and curvature drift. Liu et al. [2003] show that major stormtime enhancements of electron fluxes can occur on the dawn side. In addition, D K. The contribution to U per unit L can then be approx- ions with Ek > 30 keV have no access to dawn during imated by the storm main phase [Korth et al., 2000]. Thus, electrons might have an even larger contribution at the dawn side. Z dU m 1 [20] In order to evaluate electrons’ relative contribution to 4p2ðÞ2m 3=2DK E m1=2fKðÞ¼ 0 E dm: ð2Þ dL 0 aL2 k the total energy content in a global view, we use our 0 simulation results of the phase space density spectra of equatorially-mirroring protons and electrons for a 6-hr In this study the width of DK for protons is estimated from a hypothetical storm. We use (2) to calculate dU/dL from simulated stormtime pitch angle distribution of 48 keV the simulated phase space density spectra over m values of protons at L =3[Chen et al., 2000] that agree well with 1 to 100 MeV/G. CRRES observations. For electrons it is estimated from [21] Figure 2 shows the dU/dL profiles of protons and pitch angle distribution of 35–70 keV electrons at L =3 electrons at the end of main phase (dashed and solid curves, observed by Explorer 45 (orbit 102 outbound) [Lyons and respectively), and at the pre-storm or quiet conditions Williams, 1975b]. The full width of the equatorial pitch (dotted and dash-dotted curves, respectively) from the sim- angle at half maximum is estimated from the pitch-angle ulation results. We calculate the energy content over L = distributions. This is used to obtain DK (see Chen et al. 31 2.5–5.0 of protons during stormtime Ups (=1.3 10 keV) [2000] for details]. 30 and during quiescent time Upq (=4.7 10 keV), and of [15] We use (2) to compute the contribution of U per unit 30 electrons during stormtime Ues (=2.4 10 keV) and L from the f measured by Explorer 45, assuming MLT- 28 during quiescent time Ueq (=5.6 10 keV). The simulated independence of f and integrating from the lowest to the electrons contribute only 1.2% as much as the proton to the highest m values available in our data set. Figure 1 shows energy content during quiet times, which is consistent with the calculated dU/dL profiles of protons (dashed curve) and the result obtained from the analysis of the Explorer 45 data. electrons (solid curve) from L = 2.5 to 5.0 obtained from However, the electrons contribute as much as 19% during Explorer 45 data during the main phase (orbit 101 inbound) storm time in the simulation. This ratio is larger than what of 17 December 1971. By integrating the dU/dL curves shown in Figure 1 over L, we obtain the total energy 31 content for protons Up (=4.1 10 keV) and electrons 30 Ue (=3.1 10 keV) over L = 2.5–5.0. Taking the ratio of Ue /Up, we find that stormtime ring current electrons contribute 7.5% as much to the energy content as protons over L = 2.5–5.0. [16] As we mentioned earlier the observed ‘‘proton’’ fluxes are actually total ion fluxes. The total ion fluxes include fluxes of heavy ions such as O+ that are reported to contribute as much energy content as protons during storm main phase [Greenspan and Hamilton, 2002] of some storms. The O+ contribution is not accounted for in the data, so it is possible that the electrons contribute more to the protons than 7.5%. Thus, the 7.5% represents an underestimate. Figure 2. dU/dL profiles of electrons and protons [17] From Figure 1, we find that the electron dU/dL radial calculated from the simulation results at the beginning profile increases more rapidly with L than the proton profile. (quiet time) and the end (storm time) of the 6-hr Thus, we could expect that the ratio of electron to proton hypothetical storm.

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Table 1. Summary of the Relative Electron to Proton Contribution tion of ring current electrons to protons as 19%. This ratio to the Total Ring Current Energy Content From the Study by Frank represents an overestimate of relative electron to proton [1967], Our Analysis of Explorer 45 Data, and Our Simulation contribution to the stormtime ring current energy content Results because our simulation model tends to underestimate elec- Min Dst, nT MLT Coverage Energy Range tron losses. Furthermore, the quiet time energy contribution of electrons is 1% as much as protons from the simulation Frank [1967] 50 night side 200 eV–50 keV Explorer 45 171 2100–0200 1– 400 keV results, which agrees well with what we find in the analysis Simulation hFpci = 150 kV full 1–100 MeV/G of Explorer 45 data. [25] From this study we can conclude that the stormtime L Range U , U ,1030 keV U /U Est. Dst,nTa e p e p ring current electrons play an important role, especially, on Frank [1967] 1–8 3.31, 13.1 25% 13, 52 the dawn side and large L region, though their contribution Explorer 45 5.0–2.5 3.1, 41 7.5% 12, 163 Simulation 2.5–5.0 2.4, 13 19% 9.6, 52 during quiet times is negligible (1% relative to proton E keV energy content). The relative electron to proton contribution aEstimated with DPS relationship: Dst = rc nT 2:51 1029 (Ue/Up) to the total stormtime ring current energy content is 8–19%. Thus, we really should not neglect stormtime ring current electrons in future observational and theoretical we estimated from the analysis of Explorer 45 data. By studies. comparing Figures 1 and 2 we can see that the simulated and measured stormtime proton dU/dL profiles (dashed [26] Acknowledgments. We are grateful to Dr. D. J. Williams for his curves) are both relatively flat from L = 3 to 5. However, valuable discussions on the Explorer 45 data. The work of S. Liu, M. W. the simulated stormtime electron profile (solid curve Chen, and L. R. Lyons was supported by the NSF grant NSF-ATM-0202108 in Figure 2) has a peak at L 3.5, while the Explorer 45 and NSF-ATM-0207160. The work of M. W. Chen was also supported by The Aerospace Corporation’s Independent Research and Development dU/dL profile (solid curve in Figure 1) monotonically Program and a subcontract of the NASA grant NAG 5-12106 through increases with L from L = 2.5 to 5.0. This may be due to UCLA subaward 2090 GCC340. Computing resources were provided by an underestimating of the loss of electrons with Ek 50 keV UCLA Academic Technology Services. in our simulation model as discussed by Liu et al. [2003]. Thus, the 19% might be an overestimate of the actual References electron contribution relative to proton in terms of energy Albert, J. M. (1994), Quasi-linear pitch angle diffusion coefficients: content. Retaining high harmonics, J. Geophys. Res., 99, 23,741–23,745. Chen, M. W., L. R. Lyons, and M. Schulz (1994), Simulations of phase space distributions of storm time proton ring current, J. Geophys. Res., 5. Summary and Conclusion 99, 5745–5759. Chen, M. W., M. Schulz, and L. R. Lyons (1997), Modeling of ring current [22] Table 1 summarizes the relative electron to proton formation and decay: A review, in Magnetic Storms, Geophys. Monogr. Ser., vol. 98, edited by B. T. Tsurutani et al., pp. 173–186, AGU, contribution to the total ring current energy content (Ue/Up) Washington, D. C. from the study by Frank [1967], our analysis of Explorer Chen, M. W., L. R. Lyons, and M. Schulz (2000), Stormtime ring-current 45 data, and our simulation results. In our analysis of formation: A comparison between single- and double-dip model storms with similar transport characteristics, J. Geophys. Res., 105, 27,755– Explorer 45 data and our simulation results, we found that 27,766. electrons with energies of 1–50 keV contribute the most Chen, M. W., M. Schulz, G. Lu, and L. R. Lyons (2003), Quasi-steady drift to the stormtime electron energy content (e.g., at L =4,1– paths in a model magnetosphere with AMIE electric field: Implications 50 keV electrons contribute 93% of the electron dU/dL for ring current formation, J. Geophys. Res., 108(A5), 1180, doi:10.1029/ 2002JA009584. from energy range of 1–400 keV), while protons with Dessler, A. J., and E. N. Parker (1959), Hydromagnetic theory of geomag- energies of 10–200 keV all contribute to the proton energy netic storms, J. Geophys. Res., 64, 2239–2252. content. Since Frank [1967] included only the energy range Dungey, J. W. (1961), Interplanetary magnetic field and the auroral zones, Phys. Rev. Lett., 6, 47–48. of 200 eV–50 keV, the estimate that electrons contribute Frank, L. (1967), On the extraterrestrial ring current during geomagnetic 25% might be an overestimate of the relative electron to storms, J. Geophys. Res., 72, 3753–3767. proton contribution to the ring energy content because of Greenspan, M. E., and D. C. Hamilton (2002), Relative contributions of H+ and O+ to the ring current energy near magnetic storm maximum, the lack of contribution from protons with energies of 50– J. Geophys. Res., 107(A4), 1043, doi:10.1029/2001JA000155. 200 keV. Hardy, D. A., D. M. Walton, A. D. Johnstone, M. F. Smith, M. P. Gough, [23] The Explorer 45 data during 17 December 1971 A. Huber, J. Pantazis, and R. Burkhardt (1993), Low energy plasma storm have the full coverage of the ring current energy analyzer, IEEE Trans. Nucl. Sci., 40, 246–251. Korth, A., G. Kremser, B. Wilken, W. Guettler, S. L. Ullaland, and R. Koga range from L = 2.5 to 5.0. We estimate Dst from the (1992), Electron and Proton Wide-Angle Spectrometer (EPAS) on the calculated electron and proton energy content with the CRRES spacecraft, J. Spacecr. Rockets, 29, 609–614. Dessler-Parker-Sckopke (DPS) relation [Dessler and Korth, A., R. H. W. Friedel, C. G. Mouikis, J. F. Fennell, J. R. Wygant, and H. Korth (2000), Comprehensive particle and field observations of mag- Parker, 1959; Sckopke, 1966] and the sum of the estimated netic storms at different local times from the CRRES spacecraft, J. Geo- Dst is reasonable comparing with the observed Dst. Ring phys. Res., 105, 18,729–18,740. current electrons in this study may contribute 7.5% as much Korth, H., M. F. Thomsen, J. E. Borovsky, and D. J. McComas (1999), Plasma sheet access to geosynchronous orbit, J. Geophys. Res., 104, energy content as ring current protons over the L range. We 25,047–25,062. regard the 7.5% as an underestimate of the relative electron Kozyra, J. U., and M. W. Liemohn (2003), Ring current energy input and to proton contribution to the stormtime ring current energy decay, Space Sci. Rev., 109, 105–131. content. Liu, S., M. W. Chen, L. R. Lyons, H. Korth, J. M. Albert, J. L. Roeder, P. C. Anderson, and M. F. Thomsen (2003), Contribution of convective trans- [24] Calculation from our simulation results with full port to stormtime ring current electron injection, J. Geophys. Res., MLT coverage yields the relative energy content contribu- 108(A10), 1372, doi:10.1029/2003JA010004.

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Lyons, L. R. (1976), Explorer 45 observations of the proton ring current, Sckopke, N. (1966), A general relation between the energy of trapped in Magnetospheric Particles and Fields, edited by B. M. McCormac, particles and the disturbance field near the Earth, J. Geophys. Res., 71, pp. 137–148, Springer, New York. 3125–3130. Lyons, L. R., and D. J. Williams (1975a), The quiet time structure of energetic (35–560 keV) radiation belt electrons, J. Geophys. Res., 80, 943–950. Lyons, L. R., and D. J. Williams (1975b), The storm and poststorm evolu- tion of energetic (35–560 keV) radiation belt electron distributions, M. W. Chen and J. L. Roeder, Space Science Applications Laboratory, J. Geophys. Res., 80, 3985–3994. The Aerospace Corporation, Los Angeles, CA 90009-2957, USA. Lyons, L. R., and D. J. Williams (1976), Storm-associated variations of S. Liu and L. R. Lyons, Department of Atmospheric and Oceanic equatorially mirroring ring current protons, 1–800 keV, at constant first Sciences, UCLA, 405 Hilgard Ave., Los Angeles, CA 90095, USA. adiabatic invariant, J. Geophys. Res., 81, 216–220. ([email protected]) Lyons, L. R., and D. J. Williams (1980), A source for the geomagnetic M. Schulz, Lockheed Martin Advanced Technology Center, 1037 Twin storm main phase ring current, J. Geophys. Res., 85, 523–530. Oak Ct., Redwood City, CA 94061-1818, USA.

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