JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, A11214, doi: /2007ja012314, 2007

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2007ja012314, 2007 Multisatellite determination of the relativistic electron phase space density at geosynchronous orbit: An integrated investigation during geomagnetic storm times Y. Chen, 1 R. H. W. Friedel, 1 G. D. Reeves, 1 T. E. Cayton, 1 and R. Christensen 1 Received 30 January 2007; revised 3 July 2007; accepted 8 August 2007; published 22 November [1] An integrated investigation method, which can study the relativistic electron phase space density distribution and check the reliability of employed magnetic field models simultaneously, is developed and applied to the geosynchronous orbit region for 53 geomagnetic storms during a 190-d period. First, to test how the magnetospheric magnetic field affects the study of phase space density, two approaches are taken on handling the magnetic field model: One is to use an existing empirical model through the whole storm period; the other is to select one from a list of existing magnetic field models for each time bin during the period by fitting to multipoint in situ measurements. The magnetic field models in both approaches are again tested by Liouville s theorem, which requires the conserved phase space density for fixed phase space coordinates given no local losses and sources. Then on the basis of the selected magnetic field model, the phase space density is calculated by transforming the flux data from three Los Alamos National Laboratory geosynchronous satellites. By following the procedure developed here and using the cross-satellite calibration achieved in previous work, we deduce the storm time electron phase space density distribution for the region near geosynchronous orbit, covering a range of L shells with L* centered 6. This work establishes the radial phase space density gradient at constant adiabatic invariants as a function of universal time during storm times, and three types of geomagnetic storms are defined according to the degree of energy-dependent enhancements of energetic electrons during recovery phases. Initial results from this study suggest a source outside geosynchronous orbit for low-energy electrons and a major source inside for high-energy electrons. Citation: 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,, doi: /2007ja Introduction [2] Bearing the intrinsic merit of allowing spacecraft to remain in fixed positions relative to the Earth, the geosynchronous (GEO) orbit hosts a number of satellites, which have accumulated long-term measurements of relativistic electrons (with kinetic energy comparable to or larger than the electron rest energy of MeV, also called energetic electrons). Previous studies have revealed that GEO relativistic electron flux varies and the variation is associated with many factors, including the periodic ones, such as the daily change, solar rotation [Williams, 1966], seasonal change, and solar cycle [Vassiliadis et al., 2003, and references therein], and nonperiodic and recurring ones, such as the geomagnetic storm and substorm. Among these factors, geomagnetic storms observe the most prominent and dramatic variation with a typical timescale of several days. For example, relativistic electron fluxes at GEO orbit 1 Los Alamos National Laboratory, Los Alamos, New Mexico, USA. Copyright 2007 by the American Geophysical Union /07/2007JA are often seen to drop out in the main phase of a storm, followed in the recovery phase by an enhancement to times the prestorm level [Reeves, 1998]. Indeed, similar fluctuations have been observed to be the characteristic behavior of relativistic electrons throughout the outer radiation belt during geomagnetic storms (with some exceptions, such as rapid enhancements of relativistic electrons have been observed in the slot region during the main phase of some storms [Nagai et al., 2006]). Therefore as a critical issue of the study on space weather, to understand what drives such large variations during storms is of great significance from both practical and theoretical perspectives. [3] During the past decades, many competing acceleration/loss theories and models have been developed. For the acceleration part, possible mechanisms basically fall into two categories: external, which relies on an external source initially located in the plasma sheet and then radially diffused earthward, and internal, which relies on localized wave-particle interactions (e.g., Horne and Thorne [1998] and Summers et al. [1998], as well as a review by Friedel et al. [2002]). Among the possible wave modes, interaction with whistler model chorus is currently considered the most 1of16

2 likely candidate during storms with prolonged substorm activity (or even a substorm without the presence of a storm) [Meredith et al., 2002; Summers et al., 2004]. As for the loss of electrons, the associated mechanisms include precipitation due to the pitch angle scattering with waves, such as the electromagnetic ion cyclotron (EMIC) [Summers et al., 1998; Green et al., 2004], adiabatic motion of electrons [Green et al., 2004], and magnetopause shadowing followed by outward diffusion [Li et al., 1997; Green et al., 2004; Shprits et al., 2006]. [4] Previous efforts have already been devoted to determine the behavior of relativistic electrons during the geomagnetic storm, which is generally defined by the Dst index. Early works [e.g., Nagai, 1988; Baker et al., 1990] have focused on establishing a relationship between the electron flux and magnetic indices, such as the Dst, Kp, and AE. Reeves [1998] examined the relationship between the relativistic electron flux enhancement events at geosynchronous orbit and magnetic storm occurrence. From the enhancement events during 1992 to 1995, he found that storms could occur with no appreciable enhancements, although every relativistic electron enhancement during the years was associated with a magnetic storm. He concluded that additional factors, besides those generating ring current responses, were involved to determine whether a storm can produce an enhancement or not. This conclusion was later confirmed by the work of Iles et al. [2002]. In that paper, Iles el al. examined the relativistic electron content from satellites STRV-1/2, covering L shells from 3.5 to 6.5, in 17 storms, and studied the relationship between solar wind conditions and the relativistic electron responses in recovery phases, and drew the conclusion that intense enhancements of electrons were closely associated with extended intervals (2 d or more) of fast solar wind and predominately southward z component of interplanetary magnetic field. Similar results were achieved by Li et al. [2005] in the study of the response of synchronous energetic electron fluxes to the upstream solar wind conditions, and they also found electrons respond in an energy-dependent way. [5] In order to obtain an accurate description of relativistic electrons during geomagnetic storms, an appropriate approach is to interpret observations in the frame of phase space coordinates so as to remove adiabatic effects, especially the Dst effects [Kim and Chan, 1997]. In addition, since the radial diffusion equation determines that electrons can only diffuse from L shells with large phase space density (PSD) toward those with small PSD [Schulz and Lanzerotti, 1974], tracing the temporally evolving electron PSD radial gradients can help to differentiate external acceleration processes from internal ones. Therefore in this paper we extend the study of PSD distribution at geosynchronous orbit from quiet times [Chen et al., 2005] to geomagnetic storm times. We anticipate that an accurate dynamics specification of the electron global PSD at constant adiabatic invariants during storm times should help to identify the nonadiabatic loss and source and further to shed some light on the underlying physical processes. Here we confine our study to storms and do not attempt to identify the possible accompanying substorms. [6] While having the advantage of removing adiabatic effects, the study of PSD suffers from its heavy reliance on the accuracy of magnetospheric magnetic field models, which determine the phase space coordinates (PSCs) (m, K, L*). These coordinates are closely associated with the three adiabatic invariants and their definitions and the derivation method can be found in the work of Chen et al. [2005]. The fact that the reliability of magnetic field models is still an unresolved issue (especially on large spatial scales and during strongly disturbed times) makes it difficult to evaluate the errors in the final results. To address this problem, here we use PSD matching by employing Liouville s theorem [Chen et al., 2005]. This is because, given the calibration obtained during quiet times [Chen et al., 2005] and the short drift times of energetic electrons between satellites, the condition of the absence of losses and sources on those timescales are almost always satisfied (apart from substorm injection events and the possible fast localized losses). Therefore given enough data samples, which is the case in the geosynchronous region, we expect to be able to determine where these losses and injections occur and still match PSD values in the remaining regions so long as the magnetic field model is good enough. To manifest PSD matching can be used to test the reliability of a magnetic field model is another goal of this paper. [7] A description of the instrumentation and data is presented in section 2. Section 3 focuses on the methodology of calculating PSD radial distributions and testing magnetic field models. Section 4 presents the results by applying of our method to a 190-d period followed by discussions, and the paper is concluded in section Instrumentation and Data [8] The directional electron flux data are provided by the Synchronous Orbit Particle Analysis (SOPA) [Belian et al., 1992] instruments aboard three Los Alamos National Laboratory Geosynchronous (LANL GEO) satellites: , , and LANL-97A. Since these satellites carry no magnetometers, pitch angles are derived from symmetries of the plasma distribution measured by another instrument on board. Detailed description of the derivation method can be found in the work of Chen et al. [2005]. Flux data used in this work extend 190 d and include two intervals: One in year 2001 from 15 October to 9 December and the other in year 2002 from 15 July to 31 December. [9] The magnetic field data are from four satellites: GOES-8, GOES-10, Polar, and CLUSTER 1. In the work of Chen et al. [2005] we have described the spinning twinfluxgate magnetometer on board GOES-8 and GOES-10, which provide two-point in situ magnetic field vector measurements. The GOES data used in this study have a 1-min time resolution. Polar was launched in 1996 into a highly elliptical polar orbit with an apogee/perigee of 9/1.8 R E and a period of 18 h. Polar s magnetic field vector data are from the Magnetic Field Experiment (MFE) [Russell et al., 1995], consisting of two triaxial fluxgate magnetometer sensors mounted on a 6-m boom, and have a time resolution of 103 s in this work. The CLUSTER spacecraft also have a polar orbit with an apogee/perigee of 19.6/4 R E and a period of 57 h. This orbit allows the satellites to go deeper into the tail region. Each CLUSTER satellite (totally 4 forming a tetrahedral configuration) uses the Fluxgate Magnetometer (FGM) [Balogh et al., 2001] instrument 2of16

3 Figure 1. Flow chart illustrates how the methodology is implemented to reduce errors in a multisatellite PSD analysis. Blocks in black are the general steps of PSD calculation. After the intersatellite calibration is accomplished during magnetic quiet times (blue), the magnetic field models are tested during disturbed times in two steps (red). For each satellite S n, the PSD f Sn is a function of the first adiabatic invariant m, the second adiabatic invariant K, the drift shell label L*, and time t. aboard to measure magnetic field. Data used in this work are from CLUSTER 1 and have a time resolution of 4 s. 3. Methodology and Test of Magnetic Field Models 3.1. Methodology [10] As discussed previously [Chen et al., 2005], errors come into the multisatellite PSD analysis from various sources, among which two major ones are the spacecraft/ instrument intercalibration and the magnetic field model. Hence to minimize the errors, we develop a methodology to derive PSD radial gradient from multipoint measurements, as illustrated in Figure 1. This method consists of a series of steps, with the core of PSD matching that is applicable during both quiet and storm periods. [11] In Figure 1, the black blocks are the general steps for transforming flux into PSD, while the blue block is specifically for the intercalibration during quiet times when magnetic field models work reasonably well, and this step has been implemented between the three LANL GEO satellites in the paper by Chen et al. [2005], to which the reader is referred for details and the intercalibration factors. During storms, extra caution is used to test the reliability of magnetic field models on both local and global scales, shown by the two red blocks in Figure 1. Locally, we compare models output with measured multipoint magnetic field vectors, as indicated by the red block 1, hereinafter referred to as Step 1. Furthermore, taking advantage of the energetic electron capability of fully accessing magnetic field topology on a global scale, we use an additional constraint to test the model at a different level, shown in the red block 2 and is hereinafter referred to as Step 2. In this step the PSD matching is again applied. A good magnetic field model requires the PSD matching condition, that is, the PSD values at fixed PSCs are preserved by the adiabatic transport in the inner magnetosphere given no loss and gain as stated by Liouville s theorem, to be satisfied. Below we explain these two steps in more detail and demonstrate the method by applying it to a short storm period Step 1: Testing Magnetic Models by Local Measurements [12] In this paper, we always use the International Geomagnetic Reference Field (IGRF) as the internal magnetic model. As for choosing the external magnetic field model, we follow two schemes. One is the conventional way in which one existing model is selected from the list shown in Table 1 and then the model is used through the whole storm period. The other scheme is that, during each given short time bin (e.g., 5 min here), we first test all the existing field models in Table 1 by fitting to multipoint measurements of magnetic vectors, and then the model with the best performance is selected from a given criterion and applied for the PSD calculation. Thus a dynamic magnetic model constructed in this way, named the best-fitting model, is actually composed of several existing models which jump from one to another for different times. [13] The fitting criterion is defined by " e j BFM ¼ min X i X i ; X i! j~b i ~B i;k¼1 j w i ; j~b i j! j~b i ~B i;k¼2 j w i ; ð1þ j~b i j!# j~b i ~B i;k¼n j w i j~b i j which means that in the time bin j, for the k th magnetic field model, the error percentage between the model output ~B i,k and in situ measurement ~B i by satellite i is calculated and then summed over all satellites; then from all models with k = 1 to n the one with the minimum error percentage 3of16

4 Table 1. Empirical External Magnetic Field Models Model Name Input Parameters Valid Range T89c: [Tsyganenko, 1989] y, Kp r GEO <70R e OP77: [Olson and Pfitzer, 1977] y r GEO <15R e OP88: [Pfitzer et al., 1988] dens, velo, Dst r GEO <60R e T96: [Tsyganenko and Stern, 1996] y, Dst, P, By, Bz r GEO <40R e OM97: [Ostapenko and Maltsev, 1997] y, Dst, P, Bz, Kp no limit T01: [Tsyganenko, 2002a, 2002b] y, Dst, P, By, Bz x GSM > 15 R e T01s: [Tsyganenko et al., 2003] y, Dst, P, By, Bz, Gs x GSM > 15 R e j e BFM is selected to be the best-fitting model (BFM) during the interval j. Here w i is the weight function for satellite i and in this paper we use the same definition for all satellites which is w ~B ( 1 : j~bj 60nT ¼ 3 j~bj=60j : otherwise where 60 nt is the threshold value of local magnetic field magnitude imposed to prevent the possible large error in weak field region, such as the tail through which CLUSTER 1 crosses, being overweighted in the criterion function. Since the fitting criterion can vary for different needs, here the best-fitting model obtained by applying equations (1) and (2) is called test model 1 or TST1. [14] After selecting a magnetic field model, we calculate PSD values for the three LANL GEO satellites. Results for 25 d in year 2001 are shown in Figure 2, which for clarity only shows results from three models, OP77 (static model), T01s (storm model), and TST1. From Figures 2a and 2b we see the TST1 (orange) generally gives the best fitting to GOES-8 data as expected. The envelops of error percentages for all models as defined in equation (1) are plotted in Figure 2c, which shows large absolute values and wide distributions during storms in general. TST1 always has the minimum error percentage by definition. Figure 2d shows the PSD values from T01s, with K =0.1G 1/2 R E and three m values, and large variances in PSD occur during storms. The three m values, 167, 462, and 2083 MeV/G, which approximately correspond to electron energies of 120 kev, 300 kev, and 1000 kev at GEO orbit are used to represent the low-, moderate-, and high-energy cases, respectively. PSD values calculated from the other two models vary within one order of magnitude comparing to those by T01s and are not plotted here. In Figure 2e, the L* values from the static model OP77 show only diurnal changes, while those from T01s and TST1 show significant features during storm main phases (MPs) and recovery phases (RPs). Though the L* points from T01s and TST1 are mostly the same, frequently the time series of L* from TST1 show a discontinuity, which arises owing to the fact that TST1 jumps from one model to another and there is no normalization between the models. This drawback eventually leads us not to use TST1 to trace PSD evolving with time. Figures 2f 2i present the 3-hourly averaged Dst, upstream IMF z component, solar wind speed, and flow pressure during the time period, respectively. ð2þ 3.3. Step 2: Testing Magnetic Field Models by PSD Matching [15] As mentioned in section 3.1, Step 2 uses PSD matching to further test magnetic field models during disturbed (storm) times. For the same time period as in Figure 2, PSD matching results for all the magnetic field models in Table 1 are shown in Figure 3. Here the value of m is selected to be MeV/G, corresponding to electron energy of 400 kev, so that the effects of electric field can be safely ignored, and so do substorm injections, which generally only affect energies above 300 kev at GEO [Baker et al., 1979]. The PSD matching ratio R, comparing the PSD values between a pair of satellites with the same PSCs, is defined as R ¼ f large =f small where f is PSD and the numerator is always the one with larger value in the pair to keep the ratio larger than unity. The values of R are plotted in Figures 3a 3h in time series for all magnetic field models. Figure 3i shows the normalized PSD radial gradient for TST1 (discussed below). The envelops of the magnetic field (B) error percentages for all models are again plotted in Figure 3j. The values of R generally increase during storm periods, following roughly the same pattern for each model, though sometimes PSD matching points can be found for some models but not for the others. For example, comparing the ratio R in Figure 3h (from TST1) and the B error percentage in Figure 3j, we see they change in an overall consistent way, while times with moderate B error percentage and large R do exist, for example, at the time when the minimum Dst in storm 7 is reached and also in the recovery phase of storm 6. To further clarify this point, the blue symbols in Figure 3k indicate the changing models for TST1, comparing to the red symbols that are the models selected from the criterion of minimum PSD ratio R instead of magnetic field fitting error. It is obvious that for most of time different models are selected depending on the criterion used. By counting the number of time bins for each model, we see that magnetic field fitting gives a distribution centered on T01s, while the PSD ratio criterion does not seem to favor a single model. We therefore conclude that although the PSD matching at GEO by itself is not a very sensitive criterion for choosing between models, it can be used as an additional means to test a model s performance on large scales and further estimate the errors caused by the model. Figure 3l again shows the Dst and Kp indices during the time period. ð3þ 4of16

5 Figure 2. Effects of magnetic field models and calculated PSD during a 25-d period in year Results from three models, OP77 (sky blue), T01s (yellow), and TST1 (orange), are presented. (a, b) Magnetic field magnitudes (measurements in black) and angles between model and measurement vectors are compared. In Figure 2b the time series of selected models (i.e., TST1) is plotted by the color stripe in the bottom. (c) The jbj error percentages, as defined by equation (1), for all models in Table 1 are shown. (d) PSD time series of calculated from T01s for three m with K =0.1G 1/2 R E are shown. (e) L* values from three models are shown. (f i) Three-hourly averaged Dst, upstream IMF z component, solar wind speed, and flow pressure, respectively, are shown. Negative Bz component in Figure 2g is highlighted in yellow. Horizontal dashed lines in Figures 2h and 2i indicate the average solar wind speed (375 km/s) and the average flow pressure (2 npa). In vertical, each gray block with a line inside marks a geomagnetic storm and the time point of minimum Dst. Storms are numbered on both top and bottom in different colors: Black color indicates no significant recovery in the energetic electrons PSD; green means a recovery close to the prestorm level; red color means overshoot. 5of16

6 Figure 3. Results of PSD matching during the same time period as in Figure 2, showing (a h) the PSD ratio Rs for all magnetic models and symbols with different gray colors for different pairs of satellites. For all PSD points shown here, m = MeV/G and K is within the range of [0, 0.2]G1/2RE. The red curve in Figure 3h is the jdl*j defined by equation (6). Also shown is (i) the normalized PSD radial gradient for TST1 and (j) the envelope lines of the B error percentages for all models, and the red curve is again the jdl*j curve. (k) Symbols are the models selected by magnetic field fitting (blue) or PSD matching (red). (l) Dst (black) and Kp (gray) time series are shown. [16] Given good spacecraft inter calibrations, one reason for the PSD ratio R straying from unity is errors in the calculation of K and L* caused by the magnetic field model, which leads us to compare two PSD values with PSCs not exactly the same. Defining the total deviation in the PSD value f for given (m, K, L*) as: df ðm; K; L*; fi df ; dm þ dk þ i ð4þ we see that df depends on dm, dk, and dl* and the corresponding spectra shapes. Given neither local loss nor source, f is independent of three phase coordinates fi so that the last term in above equation is ignorable. (However, this is not always true, as in cases of substorm injections from night sector.) Therefore with given PSD gradient and PSD matching ratio, we may roughly estimate the error in PSC caused by magnetic models. [17] Here shows an example of estimating the error in L* calculation in an ideal case. Figure 3i plots the curve of normalized PSD radial gradient defined as (@f/@l*)/ f, where f is the arithmetic average of PSD values in the L* range. This gradient curve shows strong relationship to the B error curve in Figure 3j (note that in Figure 3i the missing of normalized PSD gradient spikes in the main phases of storms 6 and 8 is caused by data gaps). With an assumption that the nonunity PSD matching points are caused by the error of L* only and PSD normalized gradient is independent of K, we have 6 of 16 flarge fsmall ð@f =@L*Þ= f ¼ : j dl*j f ð5þ

7 Figure 4. The PSD ratio as a function of K during one storm day (4 December 2001). Dst reached the lowest value at UT = 14 h (.6 d). The value of m is MeV/G. By combining equations (3) and (5), we can estimate the jdl*j since jdl* j ¼ R 1 =@L* R þ 1 ð Þ=2 f j ð6þ and the curve (red) for TST1 is plotted in Figures 3h and 3j. It can be seen that most of time jdl*j is less than 0.2 and the values can get larger either during storms (e.g., the storm 7) or when the normalized gradient gets very close to zero. In the latter case, the above assumption breaks down and other factors should be considered to cause a PSD matching ratio larger than one, such as the error in the calculation of K. One example is shown in Figure 4, where PSD matching ratios are plotted as a function of K during the day of 4 December 2001 when a moderate storm occurred (storm 7 in Figure 3). Before the Dst minimum at 14 h UT, the ratio R had a weak dependence on K, while afterward when the magnetic field was more stretched, the dependence on K was much stronger, although we know that the ratio R should not depend on the value of K at all with a good magnetic field model. Therefore the jdl*j curve plotted in Figure 3 should be only taken as the error in L* calculation in an ideal case. Additionally, the assumption of PSD normalized gradient being independent of K is based on our calculation of radial gradient at different Ks showing small difference (not included here). This assumption is also oversimplified, which is equivalent to ignoring the secondorder derivation 2 f/(@l*@k) and is valid only within a small range of K in the general sense (here we use the f at K =0.1G 1/2 R E and confine the K of PSD matching points between [0, 0.2]G 1/2 R E ). [18] One byproduct of the TST1 model is the obtaining of one magnetic field model with the best performance statistically of fitting to multipoint magnetic field measurements. Figure 5 shows the number of times each magnetic model was selected as a function of Dst. This shows that for quiescent times, with Dst within [ 30, 50] nt, several models (including T01s) compete to each other and have similar performance, all with reasonably low error percentages (see Figure 2c and Figure 3j), while for storm times with Dst within [ 180, 30] nt, T01s has best performance and the largest chance of providing the best fits to the magnetic field measurements. For more intensive storms, the results shown here are not trustworthy statistically owing to the low counts (Figure 5b). Though this study is not exhaustive since the selection criterion in equations (1) and (2) can be defined in different ways, the results strongly suggest that among all models in Table 1, the T01s should be the best candidate model for storm times. Additionally, Figure 5. The magnetic field models performance measured by the counts of time bins, showing (a) percentages of counts being normalized for each Dst bin and (b) the absolute counts. 7of16

8 Figure 6 8of16

9 since T01s does not suffer from the discontinuities in L* time series as TST1, all following results shown in this paper are from the model T01s only. 4. PSD Distributions at GEO During Storm Times 4.1. Overview of PSD Distributions at GEO [19] In this section we present the geosynchronous electron PSD distribution obtained by applying the method discussed in section 3 to 190 d of electron data from three LANL GEO satellites. Besides those shown in Figure 2, results for the days in year 2002 are also illustrated in Figures 6 and 7, in which PSD values and normalized radial gradients for moderate energy (m = MeV/G) and high energy (m = MeV/G) are presented as functions of time and L*. [20] Although the radial position of a GEO satellite is fixed in space, its L* value varies with time in phase space: The average value is 6.1 when using T01s and, apart from the diurnal change, the value of L* gets smaller in main phase when the Dst drops and recovers in the recovery phase. This is because during the main phase the enhanced ring current leads to an increment of the absolute value of net magnetic flux enclosed by a drift shell; therefore this drift shell has to move outward to conserve the flux values and consequently leaves the GEO satellite behind to find itself on a new drift shell with smaller L*; the same reason causes the change of L* during the recovery phase. The changing L* of GEO, as plotted in Figures 6a and 6c and Figures 7a and 7c, shows a strong relationship to the Dst index. It is quite reasonable since the varying current systems contribute simultaneously to the variations of L* and Dst. This relationship can be fit reasonably well by a linear function, which is L* ¼ 6:14 þ 0:016 * Dst ð7þ for the three LANL GEO satellites in average. Small variations (<2.5% in the constant and <1.5% in the linear coefficients) exist when fitting for each single satellite. Equation (7) can be used for calculating the change of L* caused by the Dst. It should also be noted that the diurnal variance in L* during quiet times can be as large as 0.5 [Chen et al., 2005]. [21] In storms shown in Figures 2, 6, and 7, values of PSD at GEO orbit generally decrease in the main phase and then recover, more or less, in the recovery phase. This changing PSD value, combined with varying L*, forms the overall picture of geosynchronous electrons during storm times. [22] We need to trace the temporally evolving PSD at constant adiabatic invariants to remove the adiabatic effects. One way to do it is to get known the average radiation belt PSD profile, to which instantaneous PSD values at given L* during storms can be compared. Figure 8 shows the result of averaging all GEO PSD data we have for a given m and K as a function of L*. For comparison, profiles from AE-8 model are also shown in dashed lines [Cayton, 2005]. It should be emphasized that the averaged GEO profiles shown in Figure 8 are biased and not representative of the real average radiation belt PSD profile as mentioned above. It is because that, since all measurements are made on GEO orbit only, data points with L* smaller than 5.5 come mainly from main phases and early recovery phases, when the PSD values tend to be small, and the points with L* larger than 6.5 are mainly from late recovery phases. The profiles in Figure 8 are actually average PSD versus L* traces of GEO during storms rather than the average radiation belt profiles. Therefore in this study we only use these profiles as a general reference, instead of a rigid standard. [23] Another way to distinguish adiabatic changes from actual losses and increases is to trace curves in a PSD-L* plot: In the case that the branch of the curve during the main phase almost overlaps with that during the recovery phase, the storm only causes adiabatic changes at GEO, otherwise nonadiabatic processes have to be acting. In many storms studied in this paper, the PSD values in two phases are quite different, which indicates nonadiabatic processes at GEO orbit during storms. We use both these ways in this and the next subsections. [24] Several general features exist in the GEO electrons storm time PSD distributions: [25] First, the loss of electrons in main phases shows no or weak dependence on the energy, as depicted by Figure 2d. From the curves for the three m s in Figure 2d, we see that PSD values start dropping almost simultaneously, often with similar decreasing rates. Such synchronized losses also occur in storm main phases plotted in Figures 6 and 7. However, the minimum PSD values for different energies are often reached at different times, such as the storm 1 in Figure 2, as may be a consequence of an energy-dependent recovery of electrons. Since here energies involved can be as low as 120 kev, such loss cannot be explained by the precipitation caused by EMIC waves alone [Summers and Thorne, 2003]. However, since precipitation can also be caused by other waves, such as whistler-model chorus and plasmaspheric hiss, considering the large value of radial diffusion coefficient at GEO region, we cannot differentiate the loss being caused by precipitation or outward diffusion in this work without observations at low altitude and further model simulation. Figure 6. Time series of GEO electron PSD distribution, Dst/Kp, and upstream solar wind parameters in year 2002 from 15 July to 7 October. Shown are (a, c) are the PSD time series from LANL-97A with m = MeV/G and m = MeV/G, respectively, and (b,d) normalized PSD radial gradient time series from three satellites, respectively. Also shown are (e h) the Dst(black)/Kp(blue), upstream IMF z component, solar wind speed, and flow pressure, respectively. Negative Bz component in Figure 6f is highlighted by yellow. Horizontal dashed lines in Figures 6g and 6h indicate average solar wind speed (375 km/s) and average flow pressure (2 npa). Each vertical gray block indicates a storm which is also numbered on both top and bottom of the figure. In each storm, the vertical gray straight line indicates the minimum Dst. Storm numbers have three colors indicating different types of storms: Type I (black), Type II (green), and Type III (red), as defined in section of16

10 Figure 7. Time series of GEO electron PSD distribution, Dst/Kp and upstream solar wind parameters in year 2002 from 8 October to 31 December. 10 of 16

11 Figure 8. Average GEO electron PSD-L* traces (red solid curves) for different ms and Ks. Gray pixels in the background show the normalized occurrence distribution in each L* bin for electrons with m = MeV/G (whose traces are the red thick curves). Distributions from the AE-8 model are also plotted in red dashed lines for comparison. Left panel has K =0.1G 1/2 R E and right K =0.4G 1/2 R E. [26] Second, usually during recovery phases PSD values of electrons recover in an energy-dependent way, which has two characteristics: One is that high-energy electrons frequently lag behind from the beginning of the recovery; the other is that electrons with lower energy often recover at a fast pace and then stay almost constant during the rest of the recovery phase, while high-energy electrons recover more slowly. Examples can be seen from the tangents of PSD curves for three ms in Figure 2d. For example, there is a distinct time lag in storm 1, and the differential recovery paces are also distinguishable in storms 2, 5, and 8. Comparing the curves in Figures 6a and 6c and Figures 7a and 7c, we see that low m electrons have more chances to recover and often can reach values close to the prestorm level before the satellite moves back to the prestorm L shell. This energy-dependent recovery will be discussed further in the next subsection. [27] Another feature in the PSD distributions is the energy-dependent radial gradient. Three GEO satellites covering a narrow range of L* provide the opportunity of obtaining the PSD radial gradient. From the normalized gradient plotted in Figures 6 and 7, we see the gradients for low m electrons are close to zero (Figures 6b and 7b), while those for high m are dominantly negative (Figures 6d and 7d). Such energy-dependent gradients can also been seen from the average profile in Figure 8. This is also consistent with the results for quiet times [Chen et al., 2005]. Since the PSD radial distributions actually reflect the net outcome of competing loss and acceleration/diffusion processes and we know loss processes are primarily energy-independent, energy-dependent gradients can only be caused by energydependent acceleration/diffusion processes. [28] The above three features have been observed during two storms in our previous work [Chen et al., 2006], and here from this study over 53 storms, we show these features being persistent and common. Therefore the discussions on the source of energetic electrons during storms in the work of Chen et al. [2006] still apply and, to save the length, readers are referred to Chen et al. [2006] for more discussions Three Types of Storms Observed at GEO [29] On the basis of the behavior of energetic electrons observed at GEO orbit during recovery phases, we can categorize geomagnetic storms into three types: Types I, II, and III. Below are their definitions, and one example for each type is also presented. [30] Figure 9 shows a Type I storm that is characterized by the lack of a noticeable recovery in the PSD of energetic electrons, as shown in Figure 9e, along with a possible recovery in lower-energy electrons, as in Figure 9c. Traces in the PSD-L* plot (Figure 9b) also demonstrate that after the lasting loss during the main phase and early recovery phase ending at UT0000 on the day 1 November, though the PSD for electrons with low m almost recovers significantly in the middle of recovery phase, the PSD for the high m hardly shows any recovery signature during the more than 50 h long recovery phase. The starting time point for the recovery of the low m is marked by red arrows in Figures 9c 9f, when a substorm occurred, according to the AE index (not shown here), so that the injection should account for the observed recovery in low-energy electrons. The same reason can explain the slightly positive PSD gradient at that time point in Figure 9d, while no such feature in the PSD gradient for high-energy electrons in Figure 9f. This storm in Figure 9 is the storm 6 in Figure 2. Storms in Figures 2, 6, and 7 with numbers in black color all belong to Type I. [31] One Type II storm is shown in Figure 10. In this type of storm, comparing to the prestorm levels, the PSD of high 11 of 16

12 Figure 9. A Type I storm (with a weak recovery in the energetic-electron PSD). (a) The Dst index is shown, in which the vertical solid gray lines indicate the beginning, the minimum of Dst, and the end of the storm. Dashed gray lines in between indicate the times when Dst changes by ±10% of the magnitude. (b) Also shown are the PSD-L* traces of , connecting points measured at the times indicated by the vertical dashed gray lines in Figure 9a, with m = MeV/G (upper) and MeV/G (lower). The diamonds indicate the beginning of storm and the arrows show the evolving direction of the storm. Gray curves in the background of Figure 9b are from the averaged profiles in Figure 8. (c, e) Also shown are PSD values as functions of time and L* for two m s, respectively, and (d, f) the corresponding normalized PSD radial gradients. Red arrows indicate the starting of the recovery of electrons with low m. Here K has the value of 0.1G 1/2 R E. m electron can be partially or almost fully recovered and that of low m is generally fully recovered. In Figure 10, the recovery of electrons contains two steps. Red arrows in Figures 10c and 10e indicate the start of the first recovery, when a quick full recovery is seen for low m electrons while a weak recovery of high m. At the same time positive PSD gradients are seen for low m electrons in Figure 10d and high m electrons have gradients slightly larger than zero in Figure 10f as well. This enhancement of electrons might be explained by the continous disturbances in AE index (not shown here), which probably indicate injections. After experiencing a minor loss, however, electrons with high m have the the second and a prominent enhancement, with the starting time point indicated by the blue arrow in Figure 10e, companying with negative PSD radial gradients in Figure 10f. This enhancement moves the PSD of high m electrons to a level close to the prestorm one. Similar loss and enhancement in PSD can be seen for low m electrons in Figure 10c as well as the negative gradients in Figure 10d. Such an energy-dependent recovery phenomenon can be clearly seen from the two traces in Figure 10b: Electrons with high m has a slower recovery pace than electrons with low m. This storm in Figure 10 is the storm 41 in Figure 7. Storms in Figures 2, 6, and 7 with numbers in green color all belong to Type II. [32] A Type III storm has a strong recovery in energetic electrons which can reach values larger than not only prestorm levels but also averaged values. Storms of this type indicate an intense response at GEO orbit. One example is shown in Figure 11. Electrons with low energy in this storm experience a quick recovery (Figure 11c), starting even before the end of main phase at UT18 h on 16 October (indicated by red arrows), with slightly negative gradients at that moment in Figure 11d. Large PSD values are achieved in only several hours, a long time before GEO satellites go back to normal L* positions, and those values stay almost unchanged in the rest days of the recovery phase. However, in Figure 11e, electrons with high m 12 of 16

13 Figure 10. A Type II storm (with a moderate recovery in the energetic-electron PSD). recover quite differently. At the moment indicated by red arrow, a weak recovery (Figure 11e) is accompanied by slightly negative gradients (Figure 11f), while more prominent recoveries occurring at times indicated by the two blue arrows show a clear dominance of negative gradients, which strongly suggests an internal source for the enhancement of high-energy electrons. This storm in Figure 11 is the storm 28 in Figure 7. Storms in Figures 2, 6, and 7 with numbers in red color all belong to Type III. [33] Of the total 53 storms in Figures 2, 6, and 7, there are 12 storms belonging to Type I (22.6%), 27 storms belonging to Type II (50.9%), and 14 storms belonging to Type III (26.4%), as shown in Figure 12. We include in Figure 12 the possible relationship between our three types of storms and three storm intensity categories introduced by Gonzalez et al. [1994]. However, this relationship, if any, appears weak and nonlinear if we read the percentages in red color: Although storms with small intensity have the largest chance of being Type I storms (27.6%), intensive storms do not have the largest chance to have strong enhancements of energetic electrons (only 22.2% belonging to Type III). Considering the antirelationship between occurrence and storm intensity, as shown by the percentages in aquamarine in the rightmost column, strong enhancements of energetic electrons occur mainly during small and moderate storms, for example, a total of 60.7% of Type III storms occur during small and moderate storms and only 22.2% are from intensive storms. Therefore it is indicated that the factors causing the change of the Dst are not (or at least not the only) factors controlling energetic electrons dynamics at GEO. This conclusion is consistent with those from Reeves [1998]. With only moderate and intense storms being counted, the percentage of Type I storm here is 17%, which is consistent with the percentage 19% of storms which decrease electron fluxes derived by Reeves et al. [2003]. [34] Upstream solar wind conditions have been suggested [e.g., Iles et al., 2002; Li, 2004; Li et al., 2005] to be able to explain why the replenish of low-energy electrons appears much easier than that of high-energy electrons in storms. For example, for Type III storms in Figures 6 and 7, even for minor storms such as 0 and 43, a group of high-speed solar wind and sustaining southward B z in recovery phases can possibly account for the large and relatively rapid increment of energetic electrons at GEO, while the strong storm 16 sees no recovery of energetic electrons at all, probably owing to the sustaining northward IMF in the short recovery phase. In fact, most type III storms shown here are accompanied by sustaining sourthward B z in the recovery phase, but not all southward B z in recovery phases must see a strong recovery in energetic electrons, such as the storm 23. While a through study of the connection between upstream solar wind conditions and electron enhancements at GEO orbit is well beyond the scope this paper, we still want to point out that even such an connection can be established, it does not necessarily mean the enhancement of energetic electrons at GEO orbit are direct- 13 of 16

14 Figure 11. A Type III storm (with a strong recovery in the energetic-electron PSD). Figure 12. Numbers and percentages of storms for each type (column) and storm intensity category (row). Definitions of storm intensity follow Gonzalez et al. [1994]. Three types of storms are defined by the degree of enhancement of energetic electrons during the recovery phase, where (I) is weak, (II) is moderate, and (III) is strong. Blue percentages in each column are partitions of all storm categories for one specified type; red percentages in each row are partitions of all types for one specified intensity category. In the last row, percentages in black are partitions of all types, and percentages in aquamarine in the last column are partitions for all storm categories. 14 of 16

15 ly sourced in solar wind or tail region. The relationship between the upstream solar wind conditions and wave activities (such as chorus waves) in the radiation belts must be also considered. 5. Conclusions [35] We present a methodology developed to determine the storm time relativistic electron phase space density distribution in the vicinity of geostationary orbit by combining the electron data from three LANL geosynchronous SOPA instruments with magnetic field measurements by two GOES, Polar, and CLUSTER 1 satellites. Employing the method and using the intercalibration obtained previously during quiet times, we have determined the electron PSD radial distributions at geosynchronous orbit for the 53 storms during a 190-d period. [36] In this paper, the approach of testing magnetic field models includes first fitting to multipoint magnetic field data and then checking the PSD matching ratio between points with the same combination of (m, K, L*). Among the list of models used in this study, T01s model statistically has the best performance in fitting to magnetic field data. Though the PSD matching at GEO by itself may not be a very sensitive criterion for selecting between models, it can be used as an additional means to determine when a model works well or not. [37] Results in the 53 storms show that though GEO satellites do experience adiabatic movements of drift shells during storms, nonadiabatic processes should account for the majority of electron flux variations during storm times. It is also confirmed that, while nonadiabatic loss occurs in almost every storm, the recovery of relativistic electrons varies storm by storm. On the basis of the behavior of relativistic electrons during recovery phases, three types of geomagnetic storms can be identified, and around 23% of storms (Type I) experience no significant recoveries. Since no obvious relationship between the storm intensity and recovery energetic electron is discovered, we confirm that the change of Dst and the recovery of relativistic electrons are governed by different physical processes, such as the chorus waves associated with the prolonged substorms. [38] During recovery phases at GEO orbit, the replenish of electrons, if any, shows energy-dependent behavior: Electrons with low energy are more often fully recovered to prestorm levels than those with high energy, the recovery of low-energy electrons starts earlier and at a faster pace than high-energy electrons, and low-energy electrons recover with positive radial gradients while high-energy electrons with negative gradients. All these differences indicate that electrons experience different acceleration processes: Lowenergy electrons are more likely to be replenished by a source outside GEO, while the dominant source for highenergy electrons is from in situ acceleration, although the external source may contribute, too. [39] In a parallel ongoing work, we are extending this study to more storms with a broader L* range. Future work will include investigations of the effects of prolonged substorm activity. Additionally, since it is evident that relativistic electrons are mainly energized locally, model simulation is needed to evaluate the relative roles of each proposed internal acceleration processes, which is an unreachable target for this data analysis work along. Another direction of efforts is to assimilate PSD data with existing diffusion model [Koller et al., 2007]. Indeed, the technique developed in this paper and Chen et al. [2005] is expected to contribute to a global data assimilation based radiation belts model which simultaneously describes the field and particle distributions. [40] Acknowledgments. We are grateful for the use of ONERA- DESP codes provided by D. Boscher and S. Bourdarie. This work was supported by the National Science Foundation s Geospace Environment Modeling Program. [41] Zuyin Pu thanks Dimitris Vassiliadis and another reviewer for their assistance in evaluating this paper. References Baker, D., J. Blake, L. Callis, R. Belian, and T. Cayton (1979), High-energy magnetospheric protons and their dependence on geomagnetic and interplanetary conditions, J. Geophys. Res., 84, Baker, D., R. McPherron, T. Cayton, and R. Klebesadel (1990), Linear prediction filter analysis of relativistic electron properties at 6.6 R E, J. Geophys. Res., 95, 15,133. Balogh, A., et al. (2001), The cluster magnetic field instrument: overview of in-flight performance and initial results, Ann. 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