Relative contribution of electrons to the stormtime total ring current energy content

GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L311, doi:1.129/24gl21672, 25 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. Schulz 3 Received 3 September 24; revised 1 December 24; accepted 5 January 25; published 1 February 25. [1] We evaluate the relative importance of stormtime ring current electrons to protons by calculating the energy content ratio of electrons to protons for typical ring current energies inferred from observations and simulations. We analyze Explorer 45 measurements taken around the minimum Dst(= 171 nt) of the 17 December 1971 storm. We simulate the electron and proton ring current energy content during a hypothetical storm using drift-loss simulations. From the data analysis, we find that electrons with energies of 1 5 kev and protons with energies of 1 2 kev contribute the most to the corresponding particle energy content. From both observations and simulations, the ring current electrons contribute only 1% as much energy content as ring current protons during quiet times. However, this ratio increases to 8 19% during storm main phase. Thus, the ring current electrons can contribute significantly to the ring current energy content during storms. Citation: Liu, S., M. W. Chen, J. L. Roeder, L. R. Lyons, and M. Schulz (25), Relative contribution of electrons to the stormtime total ring current energy content, Geophys. Res. Lett., 32, L311, doi:1.129/ 24GL21672. 1. Introduction [2] The Earth s ring current consists of both ions and electrons with energies of 1 2 kev that drift within the inner magnetosphere. There has been extensive previous research on characterizing and understanding the ion ring current [e.g., Chen et al., 1997; Kozyra and Liemohn, 23, and references therein]. However, only a few studies have focused specifically on the role of electrons in the formation of the stormtime ring current. Several decades ago [Frank, 1967] reported that electrons contribute 25% of ions to the ring current energy content. He analyzed OGO 3 electron and ion data with energies of 2 ev to 5 kev at 1 < L < 8 for a small storm (min Dst = 5 nt). These measurements did not cover the higher energy range of ring current particles from 5 2 kev. Lyons and Williams [1975a, 1975b, 198] examined stormtime enhancements of ring current ion and electron fluxes measured by the Explorer 45 satellite that did cover the higher ring current energies (1 8 kev). However, they did not estimate the relative contribution of electrons to the 1 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California, USA. 2 Space Science Applications Laboratory, The Aerospace Corporation, Los Angeles, California, USA. 3 Lockheed Martin Advanced Technology Center, Redwood City, California, USA. Copyright 25 by the American Geophysical Union. 94-8276/5/24GL21672$5. total stormtime ring current energy content. In this paper we evaluate the relative energy contribution of ring current electrons to the proton ring current energy from both observational data and simulation results. We thereby address the longstanding question of how important electrons are to the stormtime ring current. [3] Unfortunately, aside from the old Explorer 45 data, there is not a reliable data set available that spans both the desired energy (1 2 kev) range and spatial range (L 2 5. For example, the polar orbiting S3-3 satellite collected electron flux data from energies of 12 kev to 1.6 MeV. However, the S3-3 orbit (apogee = 848 km and perigee = 236 km) was too close to the Earth so that there were no measurements of stormtime fluxes around 9 pitch angle from L = 3 5. The CRRES satellite was in a highly elliptical geosynchronous transfer orbit. Unfortunately, measurements of electrons with energies of 2 153 kev, the bulk of the ring current energy, from the CRRES/EPAS instrument suffered contamination [Korth et al., 1992]. Similarly, stormtime ring current electron data from the polar orbiting POLAR satellite is contaminated. Thus, in 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. [4] To provide further insight into the problem, we employ drift-loss simulations of the stormtime ring current electron to estimate the relative energy contribution of electrons to the proton ring current energy content. We use an electron ring current simulation model [Liu et al., 23] that we recently developed and the proton ring current simulation model of Chen et al. [1994, 23]. The ring current simulation model of Liu et al. [23] successfully reproduced stormtime electron fluxes at 12 kev that were measured by the CRRES satellite at 3 L 6 during two storm events. We will simulate the energy content of both electrons and protons for a model storm and use the results to estimate the relative contribution of stormtime ring current electrons to the total ring current energy content. 2. Instrument and Data [5] Explorer 45 was launched on 15 November 1971. Its orbit was very close to the equatorial plane (inclination 3.5 ). Its perigee was 22 km and apogee was 5.24R E. There were one electrostatic plasma analyzer instrument and three solid state detectors on board [Lyons and Williams, 1975b]. The instruments measured proton fluxes from.73 872 kev, and electron fluxes from.73 56 kev [Lyons and Williams, 1975a]. The reported proton fluxes are actually total ion fluxes (D. J. Williams, private communication, 24). However, we still regard them as proton fluxes in the energy content calculations. We will discuss how this assumption affects our results in Section 5. L311 1of5

[6] Lyons and Williams [1975b, 1976, 198] reported on variations of equatorially mirroring proton and electron fluxes observed by Explorer 45 for two storms: 17 December 1971 and 18 June 1972. Data at L > 4 for the 18 June 1972 storm was not published in those papers. Thus, we selected the 17 December 1971 storm with a min Dst = 171 nt and a main phase of 6 hours for our event study. Orbit 97 inbound of Explorer 45 corresponded to the orbit prior to the 17 December 1971 storm onset, while orbit 11 inbound corresponded to a time around the peak of the Dst [Lyons and Williams, 198, Figure 2]. These two inbound orbits covered magnetic local times of 21 2 MLT. [7] We digitized Explorer 45 proton and electron spectra (differential flux versus energy) published by Lyons and Williams [198] and Lyons [1976]. Pre-storm proton and electron spectra for orbit 97 inbound at L = 3.5 and 4. are shown in Figure 5 of Lyons and Williams [198]. Main phase electron spectra (orbit 11 inbound) at L = 2.5, 3., 3.5, and 4. are shown in Figure 7 of Lyons and Williams [198]. In that plot, the energy range of the electron spectra is 1 366 kev. Main phase flux spectra at L = 4.5 and 5 for the same orbit can be obtained from Figure 5a of Lyons and Williams [1975b]. However, these spectra span energies of only 5 366 kev. We extrapolated the radial flux profiles of 1 5 kev electrons to obtain their fluxes at L = 4.5 and 5. The extrapolated fluxes agree well with CRRES/LEPA [Hardy et al., 1993] electron flux data at energies of 1 2 kev during a storm event. [8] We digitized the main phase proton flux spectra (orbit 11 inbound) at L = 2.5, 3., 3.5, 4., 4.5, and 5. shown in Figure 2 of Lyons [1976]. In this figure, the proton spectra were plotted as 2m p f(=j/e k ) versus E 97, where m p is the proton rest mass, f is the phase space density, j is the differential flux, E k is the measured kinetic energy. In order to keep the first adiabatic invariant m constant, E 97 is the energy corrected to the pre-storm orbit 97 and is defined as E 97 E k (B 97 /B), where B is the actual magnetic field intensity, and B 97 is the magnetic field at the pre-storm orbit 97 outbound. This corrected energy efficiently took account 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 E 97 = 1 kev to 1 MeV. However, the measured kinetic energy ranges of the proton data from this figure vary for different L values. For example, at L = 3.5 the uncorrected kinetic energy ranges from 1 6 kev, while at L =5.,the kinetic energy ranges from 1 24 kev. We compiled these digitized data in terms of differential flux j versus kinetic energy. Both proton and electron flux spectra cover the full typical energy range of the stormtime ring current. [9] In this study, we first convert flux versus energy spectra to phase space density f versus m. f is calculated by f = j/2me k, where m is proton or electron mass. m is computed with E k and in-situ magnetic field data obtained from Lyons and Williams [1976]. We utilize the f versus m spectra to calculate the electron and proton energy content and to estimate the relative contribution of electrons energy content to proton s. 3. Simulation Model Description [1] To complement the data analysis, we also calculate stormtime electron and proton energy content from our simulation results. We briefly describe our ring current electron [Liu et al., 23] and ring current ion [Chen et al., 1994, 23] simulation models. More complete description can be found in the above mentioned references. In our simulations we trace the guiding center ~E ~B, and gradientcurvature drifts of a large number of representative equatorially mirroring particles that conserve m in our magnetic field and electric field models. We consider protons and electrons with m values from 1 1 MeV/G over equatorial positions that range from 2 to 6.6R E spaced every.2r E and all local times spaced every 5. The magnetic field model is a geomagnetic dipole field plus a constant southward field [Dungey, 1961]. Over this modeled magnetosphere we impose corotation, quiescent Stern-Volland, and stormassociated enhancements in the convection electric field. [11] Using the simulated particle trajectories, we map the phase space density along representative particle trajectories backward in time by applying Liouville s theorem modified by particle loss. We consider the proton loss due to charge exchange (see Chen et al. [1994] for details). For electrons, we consider losses due to wave-particle interactions (see Liu et al. [23] for details). [12] In order to perform the phase-space mapping, we specify particle boundary and initial conditions. The boundary conditions for both protons and electrons are 12-year averages of LANL/MPA data, which are binned in every half hour of MLT and parameterized by Kp. The LANL/ MPA data were provided by H. Korth, and explained by Korth et al. [1999]. The electron [Albert, 1994] and proton [Chen et al., 1994] initial conditions are taken from theoretical solutions of steady state transport equations, and normalized with quiet time boundary conditions. We use averaged LANL/MPA data for Kp = 1 as the quiet time boundary conditions to normalize our initial conditions, and for Kp = 3 as the stormtime boundary conditions. The LANL/ MPA does not resolve mass. However, because Kp = 3 does not represent a highly disturbed condition, we believe that the boundary conditions we specify here are mostly from protons. 4. Calculated Energy Contents From Both Observation and Simulation [13] From both Explorer 45 data and the simulation results, we obtain spectra (f versus m) of equatorially mirroring proton and electron at different radial distances. From the phase space spectra, the energy content in a certain L range (L 1 L 2 ) can be calculated from U ¼ 4p 2 ð2m Þ 3=2 ðm E =aþ Z L2 Z 1 Z 1 L 1 m 1=2 =L 2 fek dmdkdl; where U is the energy content, m is particle s mass, m E = 3.5 1 4 nt R E 3 is the geomagnetic dipole moment, f is the MLT averaged phase space density, K 2 J 2 /8m m, and J is the second adiabatic invariant. A derivation of (1) is explained in Appendix B of Chen et al. [1994]. [14] If we assume that the particle pitch-angle distributions are sharply pancaked at equatorial pitch-angle of 9, the integral of dk can be approximated by a small but finite ð1þ 2of5

Figure 1. du/dl profiles of both electrons and protons calculated from 11 inbound data of Explorer 45 during the main phase of December 17, 1971 storm. The two stars and two open diamonds are du/dl values for ions and electrons calculated from quiet time (orbit 97 inbound) data. DK. The contribution to U per unit L can then be approximated by du dl 4p2 ð2m Þ 3=2 DK m E al 2 Z 1 m 1=2 fðk ¼ ÞEk dm: ð2þ In this study the width of DK for protons is estimated from a simulated stormtime pitch angle distribution of 48 kev protons at L =3[Chen et al., 2] that agree well with CRRES observations. For electrons it is estimated from pitch angle distribution of 35 7 kev electrons at L =3 observed by Explorer 45 (orbit 12 outbound) [Lyons and Williams, 1975b]. The full width of the equatorial pitch angle at half maximum is estimated from the pitch-angle distributions. This is used to obtain DK (see Chen et al. [2] for details]. [15] We use (2) to compute the contribution of U per unit L from the f measured by Explorer 45, assuming MLTindependence of f and integrating from the lowest to the highest m values available in our data set. Figure 1 shows the calculated du/dl profiles of protons (dashed curve) and electrons (solid curve) from L = 2.5 to 5. obtained from Explorer 45 data during the main phase (orbit 11 inbound) of 17 December 1971. By integrating the du/dl curves shown in Figure 1 over L, we obtain the total energy content for protons U p (=4.1 1 31 kev) and electrons U e (=3.1 1 3 kev) over L = 2.5 5.. Taking the ratio of U e /U p, we find that stormtime ring current electrons contribute 7.5% as much to the energy content as protons over L = 2.5 5.. [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, 22] 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. [17] From Figure 1, we find that the electron du/dl radial profile increases more rapidly with L than the proton profile. Thus, we could expect that the ratio of electron to proton energy content is higher at larger L values. For example, (du/dl) e /(du/dl) p = 17% at L = 5.. If we had data 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. 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 the plasma sheet. [19] The Explorer 45 data mentioned above were observed on the night side (21 2 MLT). In the inner magnetosphere, electrons drift eastward while ions westward because of the magnetic gradient and curvature drift. Liu et al. [23] show that major stormtime enhancements of electron fluxes can occur on the dawn side. In addition, ions with E k > 3 kev have no access to dawn during the storm main phase [Korth et al., 2]. Thus, electrons might have an even larger contribution at the dawn side. [2] In order to evaluate electrons relative contribution to the total energy content in a global view, we use our simulation results of the phase space density spectra of equatorially-mirroring protons and electrons for a 6-hr hypothetical storm. We use (2) to calculate du/dl from the simulated phase space density spectra over m values of 1 to 1 MeV/G. [21] Figure 2 shows the du/dl profiles of protons and electrons at the end of main phase (dashed and solid curves, respectively), and at the pre-storm or quiet conditions (dotted and dash-dotted curves, respectively) from the simulation results. We calculate the energy content over L = 2.5 5. of protons during stormtime U ps (=1.3 1 31 kev) and during quiescent time U pq (=4.7 1 3 kev), and of electrons during stormtime U es (=2.4 1 3 kev) and during quiescent time U eq (=5.6 1 28 kev). The simulated electrons contribute only 1.2% as much as the proton to the energy content during quiet times, which is consistent with the result obtained from the analysis of the Explorer 45 data. However, the electrons contribute as much as 19% during storm time in the simulation. This ratio is larger than what Figure 2. du/dl profiles of electrons and protons calculated from the simulation results at the beginning (quiet time) and the end (storm time) of the 6-hr hypothetical storm. 3of5

Table 1. Summary of the Relative Electron to Proton Contribution to the Total Ring Current Energy Content From the Study by Frank [1967], Our Analysis of Explorer 45 Data, and Our Simulation Results Min Dst, nt MLT Coverage Energy Range Frank [1967] 5 night side 2 ev 5 kev Explorer 45 171 21 2 1 4 kev Simulation hf pc i = 15 kv full 1 1 MeV/G L Range U e, U p,1 3 kev U e /U p Est. Dst, nt a Frank [1967] 1 8 3.31, 13.1 25% 13, 52 Explorer 45 5. 2.5 3.1, 41 7.5% 12, 163 Simulation 2.5 5. 2.4, 13 19% 9.6, 52 a Estimated with DPS relationship: Dst = E rc kev nt 2:51 129 we estimated from the analysis of Explorer 45 data. By comparing Figures 1 and 2 we can see that the simulated and measured stormtime proton du/dl profiles (dashed curves) are both relatively flat from L = 3 to 5. However, the simulated stormtime electron profile (solid curve in Figure 2) has a peak at L 3.5, while the Explorer 45 du/dl profile (solid curve in Figure 1) monotonically increases with L from L = 2.5 to 5.. This may be due to an underestimating of the loss of electrons with E k 5 kev in our simulation model as discussed by Liu et al. [23]. Thus, the 19% might be an overestimate of the actual electron contribution relative to proton in terms of energy content. 5. Summary and Conclusion [22] Table 1 summarizes the relative electron to proton contribution to the total ring current energy content (U e /U p ) from the study by Frank [1967], our analysis of Explorer 45 data, and our simulation results. In our analysis of Explorer 45 data and our simulation results, we found that electrons with energies of 1 5 kev contribute the most to the stormtime electron energy content (e.g., at L =4,1 5 kev electrons contribute 93% of the electron du/dl from energy range of 1 4 kev), while protons with energies of 1 2 kev all contribute to the proton energy content. Since Frank [1967] included only the energy range of 2 ev 5 kev, the estimate that electrons contribute 25% might be an overestimate of the relative electron to proton contribution to the ring energy content because of the lack of contribution from protons with energies of 5 2 kev. [23] The Explorer 45 data during 17 December 1971 storm have the full coverage of the ring current energy range from L = 2.5 to 5.. We estimate Dst from the calculated electron and proton energy content with the Dessler-Parker-Sckopke (DPS) relation [Dessler and Parker, 1959; Sckopke, 1966] and the sum of the estimated Dst is reasonable comparing with the observed Dst. Ring current electrons in this study may contribute 7.5% as much energy content as ring current protons over the L range. We regard the 7.5% as an underestimate of the relative electron to proton contribution to the stormtime ring current energy content. [24] Calculation from our simulation results with full MLT coverage yields the relative energy content contribution of ring current electrons to protons as 19%. This ratio represents an overestimate of relative electron to proton contribution to the stormtime ring current energy content because our simulation model tends to underestimate electron losses. Furthermore, the quiet time energy contribution of electrons is 1% as much as protons from the simulation results, which agrees well with what we find in the analysis of Explorer 45 data. [25] From this study we can conclude that the stormtime ring current electrons play an important role, especially, on the dawn side and large L region, though their contribution during quiet times is negligible (1% relative to proton energy content). The relative electron to proton contribution (U e /U p ) 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 studies. [26] Acknowledgments. We are grateful to Dr. D. J. Williams for his valuable discussions on the Explorer 45 data. The work of S. Liu, M. W. Chen, and L. R. Lyons was supported by the NSF grant NSF-ATM-2218 and NSF-ATM-2716. The work of M. W. Chen was also supported by The Aerospace Corporation s Independent Research and Development Program and a subcontract of the NASA grant NAG 5-1216 through UCLA subaward 29 GCC34. Computing resources were provided by UCLA Academic Technology Services. References Albert, J. M. (1994), Quasi-linear pitch angle diffusion coefficients: 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., 99, 5745 5759. Chen, M. W., M. Schulz, and L. R. Lyons (1997), Modeling of ring current formation and decay: A review, in Magnetic Storms, Geophys. Monogr. Ser., vol. 98, edited by B. T. Tsurutani et al., pp. 173 186, AGU, Washington, D. C. Chen, M. W., L. R. Lyons, and M. Schulz (2), Stormtime ring-current formation: A comparison between single- and double-dip model storms with similar transport characteristics, J. Geophys. Res., 15, 27,755 27,766. Chen, M. W., M. Schulz, G. Lu, and L. R. Lyons (23), Quasi-steady drift paths in a model magnetosphere with AMIE electric field: Implications for ring current formation, J. Geophys. Res., 18(A5), 118, doi:1.129/ 22JA9584. Dessler, A. J., and E. N. Parker (1959), Hydromagnetic theory of geomagnetic storms, J. Geophys. Res., 64, 2239 2252. Dungey, J. W. (1961), Interplanetary magnetic field and the auroral zones, Phys. Rev. Lett., 6, 47 48. Frank, L. (1967), On the extraterrestrial ring current during geomagnetic storms, J. Geophys. Res., 72, 3753 3767. Greenspan, M. E., and D. C. Hamilton (22), Relative contributions of H + and O + to the ring current energy near magnetic storm maximum, J. Geophys. Res., 17(A4), 143, doi:1.129/21ja155. Hardy, D. A., D. M. Walton, A. D. Johnstone, M. F. Smith, M. P. Gough, A. Huber, J. Pantazis, and R. Burkhardt (1993), Low energy plasma analyzer, IEEE Trans. Nucl. Sci., 4, 246 251. Korth, A., G. Kremser, B. Wilken, W. Guettler, S. L. Ullaland, and R. Koga (1992), Electron and Proton Wide-Angle Spectrometer (EPAS) on the CRRES spacecraft, J. Spacecr. Rockets, 29, 69 614. Korth, A., R. H. W. Friedel, C. G. Mouikis, J. F. Fennell, J. R. Wygant, and H. Korth (2), Comprehensive particle and field observations of magnetic storms at different local times from the CRRES spacecraft, J. Geophys. Res., 15, 18,729 18,74. Korth, H., M. F. Thomsen, J. E. Borovsky, and D. J. McComas (1999), Plasma sheet access to geosynchronous orbit, J. Geophys. Res., 14, 25,47 25,62. Kozyra, J. U., and M. W. Liemohn (23), Ring current energy input and decay, Space Sci. Rev., 19, 15 131. Liu, S., M. W. Chen, L. R. Lyons, H. Korth, J. M. Albert, J. L. Roeder, P. C. Anderson, and M. F. Thomsen (23), Contribution of convective transport to stormtime ring current electron injection, J. Geophys. Res., 18(A1), 1372, doi:1.129/23ja14. 4of5

Lyons, L. R. (1976), Explorer 45 observations of the proton ring current, in Magnetospheric Particles and Fields, edited by B. M. McCormac, pp. 137 148, Springer, New York. Lyons, L. R., and D. J. Williams (1975a), The quiet time structure of energetic (35 56 kev) radiation belt electrons, J. Geophys. Res., 8, 943 95. Lyons, L. R., and D. J. Williams (1975b), The storm and poststorm evolution of energetic (35 56 kev) radiation belt electron distributions, J. Geophys. Res., 8, 3985 3994. Lyons, L. R., and D. J. Williams (1976), Storm-associated variations of equatorially mirroring ring current protons, 1 8 kev, at constant first adiabatic invariant, J. Geophys. Res., 81, 216 22. Lyons, L. R., and D. J. Williams (198), A source for the geomagnetic storm main phase ring current, J. Geophys. Res., 85, 523 53. Sckopke, N. (1966), A general relation between the energy of trapped particles and the disturbance field near the Earth, J. Geophys. Res., 71, 3125 313. M. W. Chen and J. L. Roeder, Space Science Applications Laboratory, The Aerospace Corporation, Los Angeles, CA 99-2957, USA. S. Liu and L. R. Lyons, Department of Atmospheric and Oceanic Sciences, UCLA, 45 Hilgard Ave., Los Angeles, CA 995, USA. (hanzo@atmos.ucla.edu) M. Schulz, Lockheed Martin Advanced Technology Center, 137 Twin Oak Ct., Redwood City, CA 9461-1818, USA. 5of5