Evidence for chorus-driven electron acceleration to relativistic energies from a survey of geomagnetically disturbed periods

Authors


Abstract

[1] We perform a survey of the plasma wave and particle data from the CRRES satellite during 26 geomagnetically disturbed periods to investigate the viability of a local stochastic electron acceleration mechanism to relativistic energies driven by Doppler-shifted cyclotron resonant interactions with whistler mode chorus. Relativistic electron flux enhancements associated with moderate or strong storms may be seen over the whole outer zone (3 < L < 7), typically peaking in the range 4 < L < 5, whereas those associated with weak storms and intervals of prolonged substorm activity lacking a magnetic storm signature (PSALMSS) are typically observed further out in the regions 4 < L < 7 and 4.5 < L < 7, respectively. The most significant relativistic electron flux enhancements are seen outside of the plasmapause and are associated with periods of prolonged substorm activity with AE greater than 100 nT for a total integrated time greater than 2 days or greater than 300 nT for a total integrated time greater than 0.7 days. These events are also associated with enhanced fluxes of seed electrons and enhanced lower-band chorus wave power with integrated lower-band chorus wave intensities of greater than 500 pT2 day. No significant flux enhancements are seen unless the level of substorm activity is sufficiently high. These results are consistent with a local, stochastic, chorus-driven electron acceleration mechanism involving the energization of a seed population of electrons with energies of a few hundred keV to relativistic energies operating on a timescale of the order of days.

1. Introduction

[2] The flux of relativistic electrons (E > 1 MeV) in the Earth's outer radiation belt (3 < L < 7) varies substantially during geomagnetically disturbed periods. Much of this variability is associated with nonadiabatic processes that cause enhanced acceleration and loss. For a typical storm the flux of relativistic electrons may fall by up to two or three orders of magnitude over a period of several hours during the initial and main phases. The flux then typically increases gradually over a period of a few days during the storm recovery phase to peak flux levels that exceed the prestorm values (e.g., Meredith et al. [2002a], case 1). However, although most storms result in a net increase in the flux of relativistic electrons, some storms result in a net decrease (e.g., Meredith et al. [2002a], case 2) and a recent study suggests that approximately 25% of all storms show such a response [Reeves et al., 2003]. Understanding the mechanisms that affect the relativistic electron dynamics is important since enhanced fluxes of relativistic electrons have been associated with a number of spacecraft anomalies and even failures [Baker et al., 1994; Baker, 1998]. Consequently, forecasting the behavior of MeV electrons is one of the outstanding challenges of magnetospheric physics today [Singer et al., 2001].

[3] Studies have shown that relativistic electron flux enhancements are caused by acceleration processes within the magnetosphere itself [Li et al., 1997a, 1997b], although the exact nature of these processes remains elusive (see, for example, recent reviews by Li and Temerin [2001], Horne [2002], and Friedel et al. [2002]). Radial diffusion is known to be an important radial transport and energization mechanism in the magnetosphere [Schulz and Lanzerotti, 1974] and is likely to be enhanced during storms and substorms. Furthermore, there is considerable evidence to suggest that ULF waves, which are one of the drivers for radial diffusion, may play a significant role in the energization process [Elkington et al., 1999; Liu et al., 1999; Hudson et al., 2000; Mathie and Mann, 2000; Green and Kivelson, 2001; O'Brien et al., 2001, 2003]. However, recent modeling of the 9 October 1990 geomagnetic storm has shown that radial diffusion alone leads to an underestimate of the flux enhancement by a factor of 5 at L = 4 [Brautigam and Albert, 2000]. Furthermore, for this storm the radial profile of the phase space density for electrons with M > 700 MeV/G peaks near L = 4, which is inconsistent with inward radial diffusion from a source in the outer magnetosphere and is indicative of an additional local acceleration source.

[4] Enhanced storm time convection electric fields provide a seed population of outer radiation belt electrons with energies up to a few hundred keV [Obara et al., 2000]. The injection of these lower-energy plasma sheet electrons into the outer zone leads to the excitation of intense whistler mode chorus emissions outside of the plasmasphere on the dawnside of the magnetosphere [e.g., Tsurutani and Smith, 1977; Meredith et al., 2001]. However, the wave particle interactions are not limited to these lower-energy electrons. Wave-particle interactions with higher-energy electrons provide a potential mechanism for accelerating this seed population of electrons to relativistic energies [Temerin et al., 1994; Horne and Thorne, 1998; Ma and Summers, 1998; Summers et al., 1998; Roth et al., 1999; Summers and Ma, 2000]. Recent model calculations by Summers and Ma [2000] have shown that substantial acceleration can be caused by enhanced whistler mode chorus lasting for 1 or 2 days.

[5] Relativistic electron enhancements are associated with the presence of high-speed solar wind streams [Paulikas and Blake, 1979] and southward IMF during the recovery phase of geomagnetic storms [Iles et al., 2002]. In such cases, the storm recovery phase will contain prolonged substorm activity and hence enhanced levels of whistler mode chorus activity outside of the plasmapause [Tsurutani and Smith, 1977; Meredith et al., 2000, 2001], supporting the suggestion that whistler mode wave activity may be important in the acceleration process. Meredith et al. [2002a] examined wave and particle data from the CRRES spacecraft during three geomagnetically disturbed periods in 1990 and demonstrated that the gradual acceleration of electrons to relativistic energies was indeed associated with prolonged substorm activity and enhanced levels of whistler mode chorus.

[6] Horne et al. [2003] examined the temporal evolution of the electron pitch angle distributions in the energy range 0.15 < E < 1.58 MeV during the 9 October 1990 geomagnetic storm and observed energy-dependent flat-top distributions during the recovery phase, characteristic of pitch angle scattering by Doppler-shifted cyclotron resonance with whistler mode waves. In addition, the spectral hardening observed during the recovery phase of this storm was found to take place over a range of energies appropriate to the resonant energies associated with Doppler-shifted cyclotron resonance, as supported by the construction of realistic resonance curves and resonant diffusion curves [Meredith et al., 2002b]. Furthermore, a model kinetic equation for the electron energy distribution was able to reproduce the observed spectral hardening when utilizing the observed wave and particle data from the CRRES spacecraft during the storm [Summers et al., 2002].

[7] In a separate study, Miyoshi et al. [2003] investigated the behavior of the particles and waves during the 3 November 1993 geomagnetic storm using data from NOAA and EXOS-D. They observed a peak in the phase space density of the relativistic electrons in the outer zone near L = 4 that increased gradually during the recovery phase. While this feature is inconsistent with inward radial diffusion from a source outside L = 6, their simulations showed that it could be explained by a local acceleration mechanism involving Doppler-shifted cyclotron resonance with whistler mode chorus waves.

[8] To date, combined wave and particle studies examining chorus-driven acceleration to relativistic energies have focused on four separate geomagnetically disturbed periods [Meredith et al., 2002a; Miyoshi et al., 2003]. Here we extend the analysis by examining a total of 26 geomagnetically disturbed periods during the CRRES mission to see if the results from this larger sample are consistent with an acceleration mechanism driven by whistler mode chorus. We deliberately exclude the very rapid acceleration associated with the great storm of 24 March 1991, which has been well-studied and attributed to a shock-induced electric field [Li et al., 1993].

2. Instrumentation and Data Analysis

[9] The Combined Release and Radiation Effects Satellite (CRRES) is particularly well-suited to studies of wave-particle interactions in the radiation belts both because of its orbit and sophisticated suite of wave and particle instruments. The spacecraft was launched on 25 July 1990 and operated in a highly elliptical geosynchronous transfer orbit with a perigee of 305 km, an apogee of 35,768 km and an inclination of 18°. The orbital period was approximately 10 hours, and the initial apogee was at a magnetic local time of 0800 MLT. The satellite swept through the heart of the radiation belts on average approximately 5 times per day, providing good coverage of this important region for almost 15 months.

2.1. Electron Flux

[10] The electron data used in this study were collected by the Medium Electrons A (MEA) experiment. This instrument, which used momentum analysis in a solenoidal field, had 17 energy channels ranging from 153 keV to 1.582 MeV [Vampola et al., 1992]. The perpendicular electron differential number flux, J, was determined as a function of energy, half-orbit (outbound or inbound), and L in steps of 0.1 L as described by Meredith et al. [2002a].

[11] The combination of the Earth's dipole tilt and the inclination of the CRRES orbit restricts the magnetic latitude coverage of the CRRES spacecraft to the range −30° < λm < 30°. The observed perpendicular flux will be a function of the magnetic latitude of the spacecraft when the particle distribution function is anisotropic. This can lead to a modulation of the flux with geomagnetic latitude, which is reduced in this study by using data from near-equatorial passes (−15° < λm < 15°) of the outer radiation belt.

2.2. Chorus Magnetic Field Intensities

[12] The wave data used in this study were provided by the University of Iowa plasma wave experiment. This experiment provided measurements of electric fields from 5.6 Hz to 400 kHz, using a 100 m tip-to-tip long wire antenna, with a dynamic range covering a factor of at least 105 in amplitude [Anderson et al., 1992]. Since energy diffusion rates scale as the magnetic field intensity [Summers and Ma, 2000], the chorus electric field spectral intensities, SE, were first converted to magnetic field spectral intensities, SB, using the expression:

equation image

derived from Maxwell's third equation and using the cold plasma dispersion relation for parallel-propagating whistler mode waves. Here c is the speed of light, ω is the wave frequency, Ωe is the electron gyrofrequency, and ωpe is the electron plasma frequency. The electron gyrofrequency was determined directly from the fluxgate magnetometer instrument on board the spacecraft [Singer et al., 1992] and the electron plasma frequency was estimated from the plasma wave spectra as described by [Meredith et al., 2002b]. Since relativistic electrons interact most readily with lower-band, 0.1 fce < f < 0.5 fce, chorus [Horne and Thorne, 1998], we integrate the derived wave spectral intensity (pT2 Hz−1) over this frequency range. The resulting lower-band chorus magnetic field intensities were then rebinned as a function of half orbit (outbound or inbound) and L in steps of 0.1 L.

3. Event Selection

[13] The geomagnetic indices for the entire CRRES mission are shown in Figures 1a and 1b. In each set of two panels the Kp index (color-coded) and AE index (black trace) are plotted in the upper panel, and the Dst index (color-coded) is plotted in the lower panel.

Figure 1a.

The geomagnetic indices for the first half of the CRRES mission. The Kp index (color-coded) and AE index (black trace) are plotted in the upper panel and the Dst index (color-coded) is plotted in the lower panel. The event number and duration are marked as described in the text.

Figure 1b.

The geomagnetic indices for the second half of the CRRES mission. The Kp index (color-coded) and AE index (black trace) are plotted in the upper panel and the Dst index (color-coded) is plotted in the lower panel. The event number and duration are marked as described in the text.

[14] The behavior of the Dst index during the CRRES mission is initially examined to select isolated geomagnetic storm periods for further study. The original notation of Sugiura and Chapman [1960], modified by Loewe and Prolss [1997], is adopted to describe the storms as strong when −200 nT < Dstmin < −100 nT, moderate when −100 nT < Dstmin < −50 nT and weak when −50 nT < Dstmin < −30 nT. In addition, for the purposes of this study, the Dst index is defined as being at quiet time values when −25 < Dst < 15 nT.

[15] Event 7 (E7, and henceforth each event will be referred to as E* where the asterisk represents the event number) represents a typical isolated storm signature. This storm begins on day 281 with a sudden increase in the Dst index which lasts for several hours and is known as the initial phase. The initial phase is followed by the main phase which is characterized by a rapid fall in the Dst index to its minimum value. The main phase is then followed by the recovery phase as the Dst index gradually returns to quiet time values. Some storms do not possess an initial phase and in these cases the storm simply begins with the main phase (see, for example, E1). Isolated storms are selected for analysis when there is a near-equatorial crossing of the CRRES spacecraft before the storm (when the Dst index is at quiet time values) and when there is a near-equatorial crossing of the CRRES spacecraft after the storm when the Dst index has returned to quiet time values. Good data coverage is required during these half-orbits and also either side of the Dst minimum. Four strong, eight moderate, and nine weak storms were found to satisfy these criteria. The selected storm intervals are depicted in Figures 1a and 1b. Here, for each storm the time from the first measurement before the storm to the time of the Dst minimum is colored black and the time from the Dst minimum to the time of the last measurement at the end of the storm is colored according to storm type with red, green, and cyan bars representing strong, moderate, and weak storms respectively.

[16] The behavior of the AE index and Dst index during the CRRES mission was then examined to identify intervals of prolonged substorm activity lacking a magnetic storm signature (PSALMSS). Here a PSALMSS event is defined as an interval of between 1 and 4 days during which the Dst index lies in the range −30 < Dst < 10 nT and the AE index is greater than 100 nT for an integrated time of greater than 1 day. E19 represents a typical PSALMSS event. The event begins at 1430 UT on DOY (here and henceforth day since start of 1990) 418 with a small, positive excursion of the Dst index. This is then followed by a period of 3.9 days during which −30 < Dst < 10 nT and AE > 100 nT for an integrated time of 1.8 days. The event ends at the next positive turning of the Dst index at 2330 UT on DOY 422. E20 is included as a PSALMSS event since the Dst index lies outside of the given range for just one measurement (Dst = −31 nT at 0400 on DOY 426) in the 4.4 day period of the event. These events are distinct from High Intensity Long Duration Continuous AE Activity (HILDCAA) events [e.g., Tsurutani and Gonzalez, 1987] which require enhanced AE values for a period of 2 or more days with a peak AE of greater than 1000 nT and AE falling below 200 nT for no more than 2 hours. In fact, not one of the PSALMSS events has a peak AE of greater than 1000 nT. Moreover, although HILDCAA events must occur outside of the main phase of a storm, they are primarily associated with the storm recovery phase.

[17] We select events which have a near equatorial crossing before and after the event when the Dst index is at quiet time values. Five PSALMSS events were selected for further analysis. The selected PSALMSS intervals are depicted in Figures 1a and 1b. Here, for each event the time from the first measurement before the event to the time of the end of the initial positive Dst excursion is colored black and the time from the end of the initial positive Dst excursion to the time of the last measurement at the end of the event is colored blue.

3.1. Estimation of the Relativistic Electron Flux Enhancement Associated With Nonadiabatic Acceleration During the Storm Recovery Phase

[18] The overall change in the perpendicular flux of relativistic (1.09 MeV) electrons at given L, ΔJS,⟂(L)overall, associated with a given geomagnetic storm is determined as follows:

equation image

where JS,⟂(L, t1) is the flux at the start of the event when the Dst index is at or near quiet time levels and JS,⟂(L, t3) is the flux at the end of the event when the Dst index has returned to quiet time levels. Any adiabatic effects associated with the Dst effect [Kim and Chan, 1997] are naturally accounted for by this method since the observations are made at times of near-equal Dst. However, there may be significant nonadiabatic electron loss during the initial and main phase of the storm due to a number of factors including precipitation to the atmosphere during resonant interactions with enhanced plasma waves [e.g., Thorne and Kennel, 1971; Smith et al., 1974; Summers and Thorne, 2003; Meredith et al., 2003], and outward drift and loss via scattering at the magnetopause [Li et al., 1997a]. ΔJS,⟂(L)overall does not identify these potentially important losses separately and may thus significantly underestimate the non-adiabatic flux enhancement due to acceleration processes during the event. ΔJS,⟂(L)overall is therefore a lower limit to the nonadiabatic acceleration during the event. In some cases ΔJS,⟂(L)overall is less than zero, indicative of a net loss of particles.

[19] The change in the perpendicular electron flux during the recovery phase at given L, ΔJS,⟂(L)recovery, associated with a given geomagnetic storm is determined as follows:

equation image

where JS,⟂(L, t2) is the perpendicular flux associated with the Dst minimum and JS,⟂(L, t3) is the perpendicular flux at the end of the event when the Dst index has returned to quiet time levels. Since the Dst minimum does not coincide exactly with a given measurement the flux at a given L associated with a given Dst minimum is set to be equal to the minimum of the flux values measured either side of the Dst minimum at that L. The maximum temporal offset from the nearest Dst minimum using this method is of the order of 3 to 4 hours at L = 6 and L = 3, respectively. Although this method does not identify separately the adiabatic flux increase associated with the increase in Dst during the recovery phase, it does represent an upper bound to the nonadiabatic flux enhancement during this period.

[20] The nonadiabatic relativistic electron flux enhancement associated with acceleration processes during the recovery phase of a particular storm is likely to lie between ΔJS,⟂(L)overall and ΔJS,⟂(L)recovery. We therefore calculate ΔJS,⟂(L)overall and ΔJS,⟂(L)recovery for each storm, as limiting values of the flux enhancement we seek to explain.

3.2. Estimation of the Relativistic Electron Flux Enhancement Associated With Nonadiabatic Acceleration Processes During a PSALMSS Event

[21] The overall change in the perpendicular flux of relativistic (1.09 MeV) electrons at given L, ΔJP,⟂(L)overall, associated with a given PSALMSS event is determined as follows:

equation image

where JP,⟂(L, t1) is the perpendicular flux at the start of the event when the Dst index is at or near quiet time levels and JP,⟂(L, t3) is the perpendicular flux at the end of the event. PSALMSS events are preceded by a pressure pulse whereby the Dst index goes positive for a few hours. This can result in nonadiabatic electron loss and this method may significantly underestimate the flux enhancement that occurs during the remainder of the event. The change in the perpendicular electron flux during the remainder of the event at given L, ΔJP,⟂(L)remainder, associated with a given PSALMSS event is determined as follows:

equation image

where JP,⟂(L, t2) is the perpendicular flux measured during the first near-equatorial half-orbit after the pressure pulse when the Dst index has returned to near quiet time levels and JP,⟂(L, t3) is the perpendicular flux at the end of the event. The flux enhancement associated with nonadiabatic acceleration processes during a particular PSALMSS event is likely to lie between these two extreme values. We therefore calculate ΔJP,⟂(L)overall and ΔJP,⟂(L)remainder for each PSALMSS event, as limiting values to the flux enhancement we seek to explain.

3.3. Estimation of the Seed Population Associated With Each Event

[22] It is important to examine the behavior of the lower-energy seed electrons with energies of the order of a few hundred keV, since the proposed mechanism involves the energization of this population to relativistic energies. An estimation of the seed population associated with each event (J⟂,seed) was obtained by averaging the electron perpendicular differential number flux at 214 keV at each L, in steps of 0.1 L, over the event duration. Only near-equatorial (−15° < λm < 15°) fluxes were used to reduce the effect of changing magnetic latitude on the flux measurement. In addition, for the storm events, the half-orbit containing the Dst minimum and the next half orbit were excluded from the averaging process since the flux of seed electrons at 214 keV can fall considerably at the Dst minimum due to adiabatic effects associated with the change in Dst and other nonadiabatic loss processes.

3.4. Estimation of the Integrated Lower-Band Chorus Intensity During Events

[23] Relativistic electrons interact most readily with lower-band, 0.1 fce < f < 0.5 fce, chorus [Horne and Thorne, 1998] and the energy diffusion rates scale as the wave magnetic field intensity, IB = Bw2, where Bw is the wave magnetic field amplitude [e.g., Summers and Ma, 2000]. The effectiveness of stochastic acceleration at relativistic energies during each event will thus be related to IB,int = 〈IB(lb)〉 ΔTevent, where 〈IB(lb)〉 is the average lower-band chorus magnetic field intensity during the event and ΔTevent is the event duration. For storm periods this is taken to be the recovery phase and for PSALMSS events the time from the end of the initial pressure pulse to the end of the event. Lower-band chorus activity is substorm dependent, being enhanced during moderate (100 < AE < 300 nT) and active conditions (AE > 300 nT) in the region 4 < L < 7, −15° < λm < 15° from 23:00 MLT through dawn to 1300 MLT [Meredith et al., 2001]. Therefore average lower-band chorus intensities as a function of L for a given event are calculated by using measurements solely from this latitude and MLT range. To achieve reasonable sampling, IB,int is only calculated at a given L if there are five or more measurements in this region at that L. When this criterion is applied IB,int cannot be determined at any L for six of the events (E11, E22, E23, E24, E25, and E26) and is only determined for a very limited range of L for a further three events (E2, E4 and E21).

3.5. Estimation of the Substorm Activity During Events

[24] Although IB,int is our best direct measure of the lower-band chorus activity during the event, it is an approximate parameter owing to the limited number of observations in the region of enhanced waves at any given L during any given event. However, since the chorus activity is substorm dependent, the AE index may be used as an alternate measure of the likely chorus activity. The AE index has the advantage of being available throughout each event at a high time resolution. In our statistical survey of the chorus amplitudes [Meredith et al., 2001], the substorm conditions are classified as being quiet (AE < 100 nT), moderate (100 < AE < 300 nT), or active (AE > 300 nT) depending on the value of the AE index at the time of the observation. Here we follow a similar scheme and choose two measures of the substorm activity. First, we quantify the amount of time during the event duration for which the substorm conditions are moderate or greater by determining the time during the event duration for which AE is greater than 100 nT (tAE>100). Second, we quantify the amount of time during the event duration for which the substorm conditions are active by determining the time during the event duration for which AE is greater than 300 nT (tAE>300).

4. Results

[25] The results are plotted as a function of L for each of the event types in Figures 25 respectively. For storms (Figures 24) the first panel shows the 1.09 MeV electron perpendicular differential number flux as a function of L before the storm (black trace), associated with the Dst minimum (blue trace), and after the storm (red trace). For PSALMSS events (Figure 5) the first panel shows the 1.09 MeV electron perpendicular differential number flux as a function of L before the event (black trace), from the first available near-equatorial half-orbit after the initial increase in Dst (blue trace), and at the end of the event (red trace). For each event the second panel shows IB,int as a function of L (black trace) and the average value of the perpendicular flux of seed electrons at 214 keV (dashed green trace). The dashed vertical line in both panels represents the average position of the postmidnight plasmapause during the event duration, 〈Lp〉, calculated using the expression Lp = 5.6 − 0.46Kp* where Kp* is the maximum value of Kp in the previous 24 hours [Carpenter and Anderson, 1992]. The bar to the right of the two panels shows the event duration (upper limit of black bar), tAE>100 (upper limit of green bar), and tAE>300 (upper limit of red bar). The event number, day of year since the start of 1990 (DOY) of the first measurement at the start of the event, the Dst minimum (for storms), and the MLT range for L > 3 are tabulated on the far right.

Figure 2.

Wave/particle data and event parameters for the strong storms. For each event the first panel shows the 1.09 MeV electron perpendicular differential number flux in units of cm−2s−1sr−1keV−1 as a function of L before the storm (black trace), associated with the Dst minimum (blue trace), and after the storm (red trace). The second panel shows IB,int (black trace) and the average flux of seed electrons in units of cm−2s−1sr−1keV−1 (dashed green trace) as a function of L. The dashed vertical lines in panels 1 and 2 represent the average position of the empirical postmidnight plasmapause. The third panel shows the duration of the recovery phase (upper limit of black bar), tAE>100 (upper limit of green bar), and tAE>300 (upper limit of red bar). The event number, DOY of the first measurement at the start of the event, storm type, and Dst minimum are tabulated on the far right.

Figure 3.

Wave/particle data and event parameters for the moderate storms in the same format as Figure 2.

Figure 4.

Wave/particle data and event parameters for the weak storms in the same format as Figure 2.

Figure 5.

Wave/particle data and event parameters for the PSALMSS events. For each event the first panel shows the 1.09 MeV electron perpendicular differential number flux in units of cm−2s−1sr−1keV−1 as a function of L before the event (black trace), from the first available near-equatorial half-orbit after the initial increase in Dst (blue trace), and at the end of the event (red trace). The second panel shows IB,int (black trace) and the average flux of seed electrons in cm−2s−1sr−1keV−1 (dashed green trace) as a function of L. The dashed vertical lines in panels 1 and 2 represent the average position of the empirical postmidnight plasmapause. The third panel shows the duration of the recovery phase (upper limit of black bar), tAE>100 (upper limit of green bar), and tAE>300 (upper limit of red bar). The event number and DOY of the first measurement at the start of the event are tabulated on the far right.

4.1. Strong Storms

[26] The results for the four strong storms are summarized in Figure 2. Strong storms may result in electron acceleration over the whole of the outer zone as evidenced, in particular, by E7. This is the well-studied strong storm of 9 October 1990 [Brautigam and Albert, 2000; Meredith et al., 2002a, 2002b; Summers et al., 2002; Horne et al., 2003]. ΔJS,⟂(L)recovery is greater than 500 cm−2s−1sr−1keV−1 over the range 3.5 < L < 5.5, with a peak value of the order of 2000 cm−2s−1sr−1keV−1 at L = 4.2. This event contains prolonged substorm activity during the recovery phase with tAE>100 = 6.3 days. IB,int is greater than 1000 pT2 day over the range 3.5 < L < 6.5, with a peak value of more than 104 pT2 day around L = 5.

[27] However, strong storms may also result in a net loss in the flux of relativistic electrons as may be seen by comparing the red and the black traces for E1 and E26. Here, event E1 is the strong storm of 26 August 1990 (Meredith et al. [2002a], case 2). The recovery phases of these storms contain much less substorm activity with tAE>100 = 0.74 days and 0.37 days, respectively. IB,int is rather weak (of the order of 100 pT2 day) over the entire outer zone for E1. IB,int is not available for E26 but, based on the statistical study of Meredith et al. [2001], the low duration of enhanced AE activity associated with this event suggests that the wave activity should also be weak for this storm.

[28] The seed electrons are enhanced for all four storms, particularly in the region 3 < L < 4.5 where J⟂,seed > 104 cm−2s−1sr−1keV−1. The net loss in the flux of relativistic electrons in this region during E1 and E26 cannot be due to an insufficient seed population. Instead, the net loss seems to be related to the reduced substorm activity and reduced lower-band chorus intensities in the storm recovery phase.

4.2. Moderate Storms

[29] The results for the eight moderate storms are shown in Figure 3. The electron acceleration associated with moderate storms may also occur over the whole of the outer zone as evidenced, in particular, by E24. During this event ΔJS,⟂(L)recovery is greater than 500 cm−2s−1sr−1keV−1 over the range 3.3 < L < 5.5. The recovery phase of this event contains prolonged substorm activity (tAE>100 = 5.8 days) and enhanced fluxes of seed electrons (J⟂,seed > 104cm−2s−1sr−1keV−1 for 3 < L < 5.9). E11 and E21 are also associated with electron acceleration over a large portion of the outer zone. Here ΔJS,⟂(L)recovery is greater than 200 cm−2s−1sr−1keV−1 over the range 4.0 < L < 5.6 and 4.0 < L < 5.2, respectively. The recovery phases of these events also contain prolonged substorm activity and enhanced fluxes of seed electrons. In contrast, very small increases of the order of 10 cm−2s−1sr−1keV−1 are associated with E17. This event has relatively little substorm activity during the recovery phase (tAE>100 = 0.41 days) and reduced fluxes of seed electrons. IB,int is less than 300 pT2 day in the region 3.0 < L < 4.9 but is more variable, ranging from 30 to 2000 pT2 day in the region 4.9 < L < 6.5.

4.3. Weak Storms

[30] The results for the nine weak storms are shown in Figure 4. The acceleration signatures associated with weak storms tend to occur largely outside L = 4 as evidenced by E6, E9, E13, E14, E16, and E18. The largest flux increases are associated with E5, E6 and E9. Here Δ JS,⟂(L)recovery is greater than 100 cm−2s−1sr−1keV−1 over the range 4.0 < L < 6.0, 4.4 < L < 6.0, and 4.2 < L < 6.0, respectively. The recovery phases of these three events contain prolonged substorm activity with tAE>100 = 4.5, 4.0, and 2.0 days, respectively, and IB,int is typically greater than 1000 pT2 day in the spatial regions where large flux increases are observed. In contrast, E3 is an example of a weak storm with very little substorm activity during the recovery phase (tAE>100 = 0.08 days) and IB,int is less than 100 pT2 day in the region 3 < L < 5.8. Here net relativistic electron loss is seen over the majority of the outer radiation zone. The seed electrons often show evidence for a slot region around L = 3.5 as evidenced in particular by E13, E14, and E18. However, the seed electrons are typically larger further out, over the range 4 < L < 6 with fluxes of the order of 5000–10000 cm−2s−1sr−1keV−1.

[31] Regions inside L = 4 tend to be associated with electron loss. These regions tend to be located inside the plasmapause (dashed lines) and are most likely associated with pitch angle scattering to the atmosphere via enhanced plasmaspheric hiss [e.g., Smith et al., 1974] and/or EMIC waves [e.g., Summers and Thorne, 2003].

4.4. PSALMSS Events

[32] The results for the five PSALMSS events are shown in Figure 5. The acceleration signatures associated with PSALMSS events tend to be restricted to the region outside L = 4.5 as evidenced by E4, E10, E15, and E19. The largest flux increases are associated with E10 and E20. Here ΔJP,⟂(L)remainder is greater than 100 cm−2s−1sr−1keV−1 over the range 4.8 < L < 5.8 and 4.5 < L < 6.9, respectively. Both events contain prolonged substorm activity with tAE>100 = 2.8 and 3.2 days, respectively. During E10, IB,int is greater than 1000 pT2 day outside of the plasmapause over the range 4.4 < L < 6.2. However, during E20, IB,int is much lower, of the order of 100 pT2 day or less over the outer zone, which is puzzling since the level of substorm activity during this event is greater than that associated with E10. However, this may be due to the limited sampling since only five measurements are used to determine IB,int for E20. The remaining three PSALMSS events are associated with weaker flux increases which are typically less than 100 cm−2s−1sr−1keV−1. There is relatively less prolonged substorm activity associated with these events with tAE>100 in the range 1.3–1.9 days. For each event the seed electrons exhibit a slot region around L = 3.7 and tend to peak at values of the order of 5000–10000 cm−2s−1sr−1keV−1 in the range 5 < L < 6, where the largest acceleration signatures associated with these events are observed. Regions inside L = 4.5 tend to be associated with relativistic electron loss. These regions lie inside the plasmaspause and are most likely associated with pitch angle scattering via enhanced plasma waves.

5. Statistical Survey

[33] The results presented above suggest that prolonged substorm activity, enhanced fluxes of seed electrons, and enhanced chorus power are associated with the events that exhibit evidence for electron acceleration to relativistic energies. In this section the flux change is related to the amount of substorm activity, the event-averaged seed flux and the integrated lower-band chorus wave intensity as a function of L value. Figure 6 presents the flux changes as a function of substorm activity, J⟂,seed, and IB,int over the spatial range 3 ≤ L ≤ 6 in steps of 0.5 L. For storms we plot ΔJS,⟂(L)overall and ΔJS,⟂(L)recovery linked by a vertical bar and for PSALMSS we plot ΔJP,⟂(L)overall and ΔJP,⟂(L)remainder linked by a vertical bar. The data point symbols are coded according to storm-type and color-coded according to the length of the event.

Figure 6.

The flux change for each event plotted as a function of (a) tAE>100, (b) tAE>100, (c) J⟂,seed, and (d) IB,int at a variety of L values going from L = 3.0 (bottom panels) to L = 6.0 (top panels) in steps of 0.5 L. The data point symbols are coded according to storm type and color coded according to the duration of the event.

[34] There is little or no change in the flux of relativistic electrons at L = 3 for the studied intervals, whatever the level of substorm activity as monitored by the AE index. Also IB,int for these events is small and less than 200 pT2 day. This is due to the fact that L = 3 tends to lie inside the plasmapause and hence inside the region of substorm-enhanced whistler mode chorus activity. The seed electrons can certainly be enhanced in this region, with fluxes greater than 2.0 × 104 cm−2s−1sr−1keV−1 inside the plasmapause for each of the strong storms, but the lack of chorus activity prevents significant acceleration. Indeed, the flux of relativistic electrons at L = 3 during the studied intervals tends to be very small, and this region is often in the slot region. There is one event (E1) where the change in flux is greater than 400 cm−2s−1sr−1keV−1. In this instance the inner edge of the outer zone moves inside L = 3 during the event. The flux increase in this case is more likely to be associated with this inward movement of the inner edge of the outer zone as opposed to a local internal acceleration mechanism operating at L = 3. This highlights the importance of making measurements over the whole of the outer zone since a flux signature at one location (in this case L = 3) may not be representative of the flux signatures at other locations in the outer zone.

[35] There is also little or no change in the flux of relativistic electrons at L = 3.5 and L = 4.0 for most of the events studies. However, there are two notable exceptions with large flux increases greater than 500 cm−2s−1sr−1keV−1. These large flux enhancements are associated with a strong (E7) and a moderate (E24) storm, both of which contain prolonged substorm activity during the recovery phase (tAE>100 = 6.3 and 5.8 days, respectively) and enhanced fluxes of seed electrons (J⟂,seed > 2.0 × 104 cm−2s−1sr−1keV−1). IB,int, which is available for E7, is about 1000 pT2 day and 5000 pT2 day at L = 3.5 and 4.0, respectively. There are two other storms with ΔJS,⟂(L)recovery of the order of 300 cm−2s−1sr−1keV−1 at L = 3.5 (E1 and E12). The error bar associated with the former is very large making it difficult to estimate the nonadiabatic flux increase during the recovery phase in this case, whereas the latter may be attributed to the inward movement of the inner edge of the outer belt.

[36] There are six events at L = 4.5 with flux changes greater than 400 cm−2s−1sr−1keV−1. These strong enhancements are associated with one strong (E7), three moderate (E8, E11, and E24), and two weak (E5 and E9) storms. These events are all associated with prolonged substorm activity with tAE>100 > 2 days and enhanced fluxes of seed electrons (J⟂,seed > 1.5 × 104 cm−2s−1sr−1keV−1). When IB,int can be measured it is also enhanced with values greater than 500 pT2day.

[37] In the region 5 < L < 6 flux enhancements tend to be associated with prolonged substorm activity with tAE>100 for more than 1 day and enhanced fluxes of seed electrons (J⟂,seed > 1.2 × 104 cm−2s−1sr−1keV−1 at L = 5; J⟂,seed > 8000 cm−2s−1sr−1keV−1 at L = 6). IB,int, where available, is again enhanced with values greater than 500 pT2 day. The magnitude of the flux enhancements for a given event tend to be largest at L = 5 and fall off towards L = 6, mirroring the tendency for the fall-off in the flux of relativistic electrons in this region. At a given L in this region there is a general trend for larger flux enhancements to be associated with longer durations of prolonged substorm activity, larger fluxes of seed electrons and larger values of IB,int, consistent with an acceleration mechanism driven by whistler mode chorus.

[38] The fluxes of relativistic electrons in the outer radiation belt are highly variable but typically peak in the range 3.5 < L < 5 and then fall off rapidly towards the slot region and more gradually further out. The magnitude of the largest relativistic electron flux enhancements at a given L are also L-shell dependent with, for example, the most significant relativistic flux enhancements being in the range 400–1500 cm−2s−1sr−1keV−1 at L = 4.5, falling to values in the range 100–200 cm−2s−1sr−1keV−1 at L = 6. The ranges of the most significant flux enhancements at each L shell in the range 3.5 < L < 6.0 are tabulated in Table 1 in steps of 0.5 L, together with the associated threshold values of tAE>100, tAE>300, J⟂,seed, and IB,int.

Table 1. Significant Relativistic Electron Flux Enhancement Ranges and Parameter Thresholds as a Function of L Shell
LΔJ⟂,sig (cm2ssrkeV)−1tAE>100 daystAE>300 daysIB,int pT2 dayJ⟂,seed (cm2ssrkeV)−1
3.5500 < ΔJ < 1400>5.8>3.35.0 × 103>2.0 × 104
4.01200 < ΔJ < 2000>5.8>3.3103>2.0 × 104
4.5400 < ΔJ < 1500>2.0>0.7>500>1.5 × 104
5.0400 < ΔJ < 1000>2.0>0.7>500>1.2 × 104
5.5200 < ΔJ < 500>2.0>0.7>103>104
6.0100 < ΔJ < 250>2.0>0.7>103>8000

[39] No significant relativistic electron flux enhancements are seen in the heart of the outer radiation belt for any event, regardless of storm strength and seed level, during low levels of lower-band chorus activity (IB,int < 100 pT2 day) and low levels of substorm activity (tAE>100 < 1 day; tAE>300 < 0.4 days).

[40] Our survey of 26 geomagnetically disturbed periods from the CRRES mission suggest that significant relativistic electron flux enhancements are likely to occur in association with periods of prolonged substorm activity lasting over a period of days (tAE>100 > 2 days), enhanced fluxes of seed electrons (e.g., J⟂,seed > 1.5 × 104 cm−2s−1sr−1keV−1 at L = 4.5), and enhanced levels of whistler mode chorus activity (IB,int > 500 pT2 day). These results provide further strong circumstantial evidence for the local stochastic acceleration of a seed population of electrons with energies of the order of a few hundred keV to relativistic energies driven by wave particle interactions involving whistler mode chorus.

[41] Bühler and Desorgher [2002] recently conducted a series of correlation studies and concluded that the mechanism producing relativistic electron acceleration in the outer belt is related to substorm activity. In particular, they found that it is not large substorms that were important but rather enhanced substorm activity over an extended period of time. The results presented here support this conclusion and go further to show that relativistic flux enhancements are associated with an enhanced seed population of electrons with energies of a few hundred KeV and enhanced chorus wave power. However, they do not rule out other acceleration mechanisms in all cases. For example, the rate of radial diffusion is known to be closely correlated with Kp [e.g., Brautigam and Albert, 2000 and references therein] and is likely to be enhanced during storms and substorms. Enhanced radial diffusion could thus also contribute to the acceleration signatures in the events presented here. However, enhanced radial diffusion cannot produce peaks in phase space density observed near L = 4 [e.g., Brautigam and Albert, 2000; Miyoshi et al., 2003] and cannot produce the flat top pitch angle distributions that have been observed at MeV energies during an acceleration event in the storm recovery phase [Horne et al., 2003].

[42] Hence both radial diffusion and local stochastic acceleration are likely to contribute to electron acceleration in the outer radiation belt [e.g., O'Brien et al., 2003]. However, further work, beyond the scope of the present study, is required to determine the relative roles of radial diffusion and local stochastic acceleration in the energization process. In particular, studies of the temporal evolution of the energetic electron phase space density as a function of L during storms and PSALMSS events would be particularly appropriate with local peaks being supportive of local acceleration driven by whistler mode chorus.

6. Conclusions

[43] We present plasma wave and particle data from the CRRES satellite during 26 geomagnetically disturbed periods to investigate the viability of a local stochastic electron acceleration mechanism to relativistic energies driven by resonant interactions with whistler mode chorus. Our main conclusions are as follows:

[44] 1. Relativistic electron flux enhancements tend to be confined to the region outside of the plasmapause and the most significant flux enhancements are associated with (1) periods of prolonged substorm activity (tAE>100 > 2 days; tAE>300 > 0.7 days), (2) enhanced fluxes of seed electrons (e.g., J⟂,seed > 1.5 × 104 cm−2s−1sr−1keV−1 at L = 4.5; J⟂,seed > 8000 cm−2s−1sr−1keV−1 at L = 6), (3) periods of enhanced lower-band chorus activity (IB,int > 500 pT2 day).

[45] 2. At a given L there is a general trend for larger flux enhancements to be associated with longer durations of prolonged substorm activity, larger fluxes of seed electrons, and higher lower-band chorus wave power.

[46] 3. Moderate or strong storms may affect the whole outer zone (3 < L < 7) with flux enhancements typically peaking in the range 4 < L < 5. Weak storms and periods of prolonged substorm activity lacking a magnetic storm signature (PSALMSS) are typically only effective in the regions 4 < L < 7 and 4.5 < L < 7, respectively.

[47] 4. No significant relativistic electron flux enhancements are seen in the heart of the outer radiation belt for any event, regardless of storm strength and seed level, during events associated with low levels of substorm activity (tAE>100 < 1 day; tAE>300 < 0.4 days) and low levels of lower-band chorus activity (IB,int < 100 pT2 day).

[48] These results are consistent with a local, stochastic, chorus-driven electron acceleration mechanism involving the energization of a seed population of electrons with energies of a few hundred keV to relativistic energies operating on a time-scale of the order of days. Such interactions are likely to contribute to the reformation of the relativistic outer zone population following prolonged substorm activity.

Acknowledgments

[49] We thank Al Vampola and Daniel Heynderickx for providing the MEA data used in this study and for many helpful discussions. We also thank the World Data Centre C1 for STP at the Rutherford Appleton Laboratory and the NSSDC Omniweb for providing the geomagnetic indices used in this paper. This research was funded in part by NASA grant NAG5-11922. D. S. acknowledges support from the Natural Sciences and Engineering Research Council of Canada under grant A-0621.

[50] Lou-Chuang Lee thanks one reviewer for the assistance in evaluating this paper.

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