Three superposed epoch analyses of plasma data from geosynchronous orbit are compared to infer relative distributions of electromagnetic ion cyclotron (EMIC)- and whistler-mode wave instabilities. Both local-time and storm-time behaviours are studied with respect to dynamics of relativistic electrons. Using LANL-GEO particle data and a quasi-linear approximation for the wave growth allows us to estimate the instability of the two wave modes. This simple technique can allow powerful insights into wave–particle interactions at geosynchronous orbit. Whistler-wave activity peaks on the dayside during the early recovery phase and can continue to be above normal levels for several days. The main phase of all storms exhibits the most EMIC-wave activity, whereas in the recovery phase of the most radiation-belt-effective storms, a significantly suppressed level of EMIC activity is inferred. These key results indicate new dynamics relating to plasma delivery, source and response, but support generally accepted views of whistlers as a source process and EMIC-mode waves as a major loss contributor at geosynchronous orbit.
Understanding high-speed solar wind streams (HSSs) and their interactions with the magnetosphere are critical for understanding many of the key issues of radiation-belt dynamics. High-speed streams peak in the declining phase of the solar cycle, and although they cause relatively small excursions of Dst, their effect on radiation belts is surprisingly strong. Why high-speed streams cause this response is an active area of research. Periods of high-speed solar wind correlate with the growth of MeV (‘killer’) electrons in the outer radiation belt to a higher degree than other geophysical parameters (O’Brien et al. 2001). In the recent deep solar minimum of cycle 23, recurrent high-speed streams have caused significant energization of radiation belts (Baker & Kanekal 2008).
In addition to adiabatic effects, several competing wave–particle interactions are contenders for producing large-scale changes in observed electron flux in the outer-electron radiation belt (e.g. Liemohn & Chan 2007; Summers et al. 2007a,b). In this paper, two significant classes of wave–particle processes, whistler-mode and electromagnetic ion cyclotron (EMIC)-mode waves, are addressed. Whistler-mode waves are important for radiation-belt particles, both as an acceleration mechanism and as a loss mechanism (Friedel et al. 2002; Bortnik et al. 2008). Whistlers generated by anisotropic, hot plasma-sheet electrons can parasitically resonate with near-relativistic electrons, accelerating them to yet higher energies (e.g. Horne & Thorne 2003). High-latitude whistler chorus waves can also propagate and cause loss, though high-latitude mechanisms are not relevant to this study (Bortnik et al. 2008). Relativistic electrons can also resonate with EMIC waves produced by anisotropic, hot plasma-sheet ions, resulting in pitch-angle scattering and precipitation loss to the atmosphere (e.g. Spasojevic et al. 2004; Millan & Thorne 2007). In this paper, we use geosynchronous observations of the unstable plasma-sheet ion and electron populations that produce whistler and EMIC waves to infer the probable occurrence properties of such waves in association with high-speed stream events. The ‘inference technique’ has been well established (MacDonald et al. 2008; Blum et al. 2009a), and is based on an extensive theoretical and modelling framework (e.g. Gary 1993; Gary et al. 1994; Gary & Wang 1996). Experimental tests have served to validate the quasi-linear approximations used (Anderson et al. 1996; Gary et al. 2005).
Recently, Borovsky & Denton (2009) examined a carefully chosen set of HSS events between 1993 and 2006. They showed that HSSs deliver a superdense plasma from the solar wind that are observable in the magnetosphere shortly after magnetospheric-convection onset (Denton & Borovsky 2009). The occurrence of this superdense plasma is strongly correlated with a dropout in the outer-electron radiation-belt flux, as measured at geosynchronous orbit, and with the occurrence of a plasmaspheric drainage plume (Borovsky & Denton 2009).
In brief, our study uses a superposed epoch analysis to reveal the wave properties inferred from this plasma as a function of storm phase. This analysis technique has reliably illuminated the global distribution of plasma particles at geosynchronous orbit (e.g. Denton et al. 2005, 2006; Lavraud et al. 2005). The superposed epoch technique is combined with the simple wave-inference technique for the full set of HSSs used in the previous Denton and Borovsky studies. In addition, these results are compared with previous work, in which a set of storms with high radiation-belt flux response are contrasted with those with lower response (O’Brien et al. 2001; Smith et al. 2004; MacDonald et al. 2008; Blum et al. 2009a). According to the convention of previous work, these sets of storms are called ‘events’ and ‘non-events’, respectively. By examining these three cases, the effects of competing wave–particle acceleration and loss mechanisms as a function of local time and storm progression can be disentangled with respect to the relativistic electron-flux behaviour.
HSS events were chosen on the identification of typical high-speed stream parameters in the solar wind, e.g. east–west shear flow (the signature of the boundary between fast and slow wind), sustained increase in solar wind speed and so on (R. McPherron 2005, personal communication). This initial list was expanded to 124 events based on the same criteria (see Denton & Borovsky 2008 for full details). For their superposed epoch analysis, the zero epoch time was chosen as the time of magnetospheric-convection onset, following the arrival of each HSS at the magnetosphere (via examination of the Kp index). The exact time of the zero epoch was derived at higher time resolution than the 3 h Kp index by identifying the time of equatorward expansion of the midnight boundary index (MBI; Madden & Gussenhoven 1990). As shown by Thomsen (2004), the Kp index and the MBI are highly correlated with the magnetospheric convection onset. It is also noted that previous studies have identified that the MBI provides a cleaner comparison basis for these small HSS-driven storms than the Dst index. The mean minimum Dst for HSS storms is only approximately 20 nT (Denton & Borovsky 2008). Dst is not used in the selection criteria for the HSS storms.
As described by MacDonald et al. (2008), events and non-events were selected ‘based on whether or not the ‘noon-reconstructed’ 1.8–3.5 MeV electron flux measured by Los Alamos National Laboratory geosynchronous satellites 48–72 hours after the Dst minimum exceeds 0.5 e− (cm2 s sr keV)−1. As described by O’Brien et al. (2001) the noon-reconstructed flux is based on a statistical technique to remove the local time variations in radiation belt particles, and normalize the fluxes to that of a virtual geosynchronous spacecraft located at noon’. About 138 event storms (enhanced post-storm MeV electron response) and 183 non-event storms (non-enhanced MeV electron response) make up these two groups. A minimum Dst criterion of −50 nT was used; therefore, these storms may include the most geoeffective high-speed streams.
In the present analysis, particle observations are available at an 86 s cadence from seven LANL satellites over a total time period from 1989 to 2005. Geosynchronous orbit is a convenient place to observe electron and ion fluxes at all energies, including higher energies where relativistic effects become important. The Magnetospheric Plasma Analyzer (MPA) instrument measures three-dimensional distributions of ions and electrons from 1 eV to 45 keV, whereas the Synchronous Orbit Particle Analyzer (SOPA) instrument measures higher energy flux (Belian et al. 1992; Bame et al. 1993). The ion and electron moments are calculated using the MPA instrument according to the methods described in Thomsen et al. (1999). Electron moments are from 30 eV to 45 keV, and ions are separated into two ranges: ‘cold ions’ with energies less than 100 eV and ‘hot ions’ with energies from 100 eV to 45 keV. Calculations of plasma parallel beta using the dynamic T89 model (Tysganenko 1989) as in situ measurements of magnetic-field strength were not available. SOPA data were processed as described by Borovsky & Denton (2008) to construct a clean multi-spacecraft average flux as a function of time. Separate analyses were carried out for the HSS, event and non-event sets of storms. Hourly averages were used for the epoch time and local time in the superposed epoch analyses.
3. Proxy technique
In fundamental terms, anisotropy upper bounds in collisionless plasmas arise from wave–particle interactions. If a species’ anisotropy (perpendicular divided by the parallel temperature) is sufficiently large, it will drive one or more plasma instabilities. Growing waves scatter the particles in the sense of reducing the driving anisotropy, thereby moving the species’ velocity distribution towards isotropy, analogous to the isotropization role of particle–particle interactions in collision-dominated plasmas and fluids. If one solves the linear kinetic-dispersion equation for a particular instability and for a particular value of growth rate, the solutions can be written as functions of the species’ beta and temperature anisotropy as3.1where n signifies either species in an idealized electron–proton collisionless plasma, in which both species are represented by bi-Maxwellian velocity distributions. and Sn and αn are constant parameters that are obtained by a fit to the linear theory for a given growth rate (e.g. Gary & Wang 1996). For instance, whistler-mode waves, in which the electron population is anisotropic at a growth rate of 0.001 Ωe, correspond to constant values of Se=0.21 and αe=0.6, defining the ‘threshold’ of the anisotropy versus beta relationship (Gary et al. 2005). Both computer simulations and space-plasma observations have shown that if the temperature anisotropy exceeds the threshold condition represented by equation (3.1), the instability will be excited and will reduce the anisotropy below the threshold values. If wave–particle scattering rates are sufficiently fast, observations will show few, if any, anisotropy values above the threshold condition, so that equation (3.1) becomes a statistical upper bound on the observations. Our analysis technique uses this relation to infer how near the distributions are to being unstable at a certain growth rate. We define the observational parameter as3.2where T||n, T⊥n and nn are measured by the plasma instrument, and αn is determined from the fit that results in equation (3.1). We refer to Σe as the whistler-wave growth parameter. Generally, for the magnetospheric ion and electron populations used in this study, a maximum growth rate of 0.001 is appropriate to choose (e.g. MacDonald et al. 2008; Blum et al. 2009a).
EMIC-mode waves are excited by the free energy in the hot (keV) plasma-sheet ions. The coexistence of a cold-ion population (such as plasmaspheric material) makes it easier to excite the instability. Therefore, the formalism for EMIC-mode waves is more complex owing to the presence of both cold-plasma and multiple-ion species. The MPA instrument cannot easily distinguish between different ion species, and it is typically assumed that all positive ions are protons when calculating moments of distribution (Thomsen et al. 1999), and the same procedure is carried out in the subsequent calculations. However, although the details of the instability (including the range of unstable frequencies) depend on the composition, the heavier ion population does not actually change the maximum growth rate significantly, thus limiting the effect of this assumption on the technique used here (Gendrin et al. 1984). Future instrumentation that could measure all the heavy ions would ameliorate the uncertainties of the present situation significantly. For EMIC waves, the same simple form as equation (3.1) can be used, although Sn and αn now become weak functions of the ratio of cold-to-hot ion density as3.3aand3.3bwhere nh is the hot-ion portion of the population and ne is the total electron density. Using linear theory to determine how these two fitting parameters vary with the relative hot-proton density leads to the forms of these equations. Assuming γm/Ωp=10−3, we obtain σ0=0.429, σ1=0.124, σ2=0.0118, a0=0.409, a1=0.0145 and a2=0.00028 (Blum et al. 2009a). The proxy technique established by Blum et al. (2009a) then calculates the observational magnitude of the EMIC growth parameter Σp using equation (3.2), and compares it with the computed values of the threshold Sh for a given growth rate. Then, the percentages of the observations when the growth parameter exceeds the threshold anisotropy are evaluated.
Examples of proxy calculations are shown in figure 1 for both whistler and EMIC waves in the HSS events. Results for events and non-events can be found in MacDonald et al. (2008) and Blum et al. (2009a), for whistler and EMIC waves, respectively. The whistler growth parameter plotted corresponds to Σe for a growth rate of 0.001. In each hourly bin, the values are averaged and thus considerably lower than the threshold value. The enhanced growth probability for whistler waves extends across the dawn side from just before midnight to nearly noon. This is consistent with the global picture inferred from wave measurements from the CRRES mission and more recently from the THEMIS satellites (Meredith et al. 2003a; Li et al. 2009). The superposed epoch technique also shows the distribution as a function of storm phase. Whistler-mode waves peak in the post-midnight sector at all times during the storm, except for the main phase when they extend more broadly towards dawn. More waves are inferred in the recovery phase of high-speed stream storms than in the pre-storm days. This is consistent with the very quiet pre-storm conditions typically found prior to the majority of high-speed stream events (Borovsky & Steinberg 2006).
For EMIC waves, the quantity plotted in figure 1 corresponds to the percentage of waves inferred in each hourly bin, in which the observational EMIC growth parameter Σp exceeds the theoretical anisotropy limit Sh corresponding to a growth rate of 0.001. Most of the waves are seen in the post-noon sector, consistent with the location of the plasmaspheric plume as sometimes observed at geosynchronous orbit and with the global picture built up by the CRRES mission (Meredith et al. 2003b). The instability is most easily excitable where the cold plasmaspheric material coexists with the hot anisotropic plasma-sheet material. These waves peak during the main phase of storms. This is consistent with recent observations by Fraser et al. (2010) and Blum et al. (2009a), although inconsistent with most ground-based observations (e.g. Engebretson et al. 2008). Fewer EMIC waves are inferred in the recovery phase, compared with those before the storm. Waves are also inferred at other local times, consistent with the coexistence of cold plasma and anisotropic hot plasma and some in situ observations.
This technique exploits multi-point measurements at geosynchronous orbit to infer the in situ statistical distribution of waves. Other in situ observations or modelling is required to understand how measurements at geosynchronous orbit are related to the global morphology. Globally measuring waves is extremely difficult, and our inference technique can add to the nebulous picture by exploiting the long-time basis of geosynchronous data to build up a clearer picture of distributions at geosynchronous orbit as a function of local time. Next, wave inferences and radiation-belt responses are plotted together to highlight the differences between the three types of events. Local time averages over the local time sectors of peak inferred wave growth are made for easier discernment of the gross trends. Figure 2 contains plots of the MeV electron fluxes, EMIC-wave proxy and whistler-wave proxy for the HSS, events and non-events (blue, black and red traces, respectively), as described previously. Figure 2a shows fluxes measured by the SOPA instrument on LANL-GEO satellites in the energy range of 1–1.5 MeV electrons. Figure 2b shows the EMIC-mode proxy as averaged over the peak local times from 12.00 to 18.00 local time. The proxy indicates the per cent of time waves above a growth rate of 0.001 are expected to grow in a given hourly bin. Figure 2c shows the magnitude of the whistler-wave mode proxy as averaged for all local times between midnight and noon. Taken together, the comprehensive view enables comparison of relative strengths of various wave modes and the fluxes of relativistic electrons.
In comparing the events/non-events storms, one can see that the relativistic electron fluxes begin at similar flux levels and yet have a large difference in flux post storm. These events were indeed chosen solely based on their differing post-storm response. The set of non-events also has a larger magnitude dropout than events. In terms of EMIC waves, both events and non-events show an increase in the abundance of waves for 1 day before minimum Dst. The recovery-phase comparison is significantly different. EMIC waves during events are suppressed below ‘typical’ levels from 0.5 to approximately 4 days into the recovery, whereas non-events quickly recover to a ‘normal’ level of EMIC-wave activity. Inferred whistler-wave activity also differs between events and non-events. During the storm main phase, whistler waves are apparently less unstable for both events and non-events. Examining the plasma distributions, this is attributable to reduced plasma-sheet electron anisotropy, which has been interpreted as a signature of the rapid delivery of nearly isotropic plasma-sheet material during the strong convection of the main phase (Denton et al. 2005; MacDonald et al. 2008). Also for both events and non-events, the highest concentration of whistler-wave activity appears strongest in the early recovery phase, with a gradual decline towards pre-event levels throughout the recovery phase. However, throughout the gradual decline, events have higher levels of whistler activity than non-events do from approximately 1 to 4 days after minimum Dst.
In summary, the primary differences between events and non-events (similar events with differing post-storm levels of relativistic fluxes) are that the events display both relatively reduced EMIC and enhanced whistler-wave activity over several days in the recovery phase. These results may inform some of the delicate balance between wave–particle interactions, leading to net growth and loss, and also show the power of a global superposed epoch-analysis study using data from multiple geosynchronous satellites. These results suggest the interesting possibility that a net increase in radiation-belt fluxes may be as much due to the suppression of loss processes as to an enhancement of growth processes.
The corresponding results for the HSS are shown by blue curves in figure 2. However, because we have followed Denton & Borovsky (2008) in organizing these events by the onset of convection as measured by the MBI rather than the Dst minimum, the zero epoch for the HSS is not the same as that for the event/non-event sets. For comparison purposes, the HSS events were shifted back by half a day in figure 2. For HSS events, the onset of convection is expected to correspond to the time of storm onset. Minimum Dst defines the time generally referred to as the end of the main phase and start of the recovery phase.
We see in figure 2a that the relativistic electron fluxes during HSS events start from a base level higher than that of the other groups. They also peak higher and slightly later (approx. 1.5 days) than the set of events. Both differences probably result from the inherently repeatable and long duration nature of HSS storms, i.e. the radiation belts are heated to a comparatively higher level by the recurrent fast solar wind that accompanies previous HSSs. In addition, the dropout for HSS storms is similar in magnitude to non-event storms, i.e. quite large, although the flux levels for HSS storms begin much higher.
Relative to the other two categories, the HSS events have the highest inferred EMIC-wave activity in the main phase of storms, with a full 20 per cent of observations exceeding a growth rate of 0.001, consistent with the largest observed ‘dropout’. In the recovery phase, the level of EMIC-wave activity during HSSs looks similar to that of the events storms, namely that it is suppressed below ‘normal’ levels. This is consistent with a suppressed loss mechanism and hence a net gain of relativistic electrons. For whistler waves during the HSS events, there is a prolonged, but not dramatic, enhancement throughout the main and recovery phases, i.e. during the times of fast solar wind and enhanced magnetospheric convection. In the pre-storm period for HSS events, whistler waves are significantly reduced below ‘normal’ levels for either event or non-event storms. Compared with events, HSS events have significantly reduced levels of whistler waves pre-storm, and although there is an increase during the storm, the overall magnitudes are still reduced.
The proxy technique employed here has been validated in comparison to ground or in situ wave observations. The event/non-event lists analysed by MacDonald et al. (2008) were also analysed by Smith et al. (2004). The whistler proxy was consistent with whistler waves observed at the Halley station (MacDonald et al. 2008). In addition, Blum et al. (2009b) have compared the EMIC-wave mode proxy with in situ GOES Pc1-2 high-resolution magnetic-field data. Statistically, the proxy and the wave observations agree quite consistently. Both the proxy and the space-based wave observations indicate an abundance of EMIC-wave activity in the storm main phase (Fraser et al. 2010). In addition, Blum et al. (2009b) found good agreement for some events when GOES and LANL satellites were relatively close to each other. Converting the proxy output (i.e. per cent of waves present in a given time bin above a certain growth rate) to the approximate power of waves will be explored in future work.
Recent efforts (e.g. Huang et al. 2009) have shown that magnetopause shadowing may be responsible for the observed major dropout of relativistic electron fluxes at the main phase. The results outlined in this paper and presented in figures 1 and 2 indicate that conditions are ripe for intense EMIC waves around storm onset as well. The relative importance of adiabatic and non-adiabatic effects on losses during the main phase of storms thus remains open and a subject of future research.
The superposed epoch analysis and inferences of wave properties allow us to form a picture of global wave distributions at geosynchronous orbit during different types of storms. This analysis, while informative in that it shows quantities not easily imaged by single spacecraft, has numerous caveats and is obviously not intended to present a complete picture. Major restrictions to this work stem from its limitation to electron and ion fluxes (from eV to 45 keV) at equatorial geosynchronous orbit, which may lie outside the main region for radiation-belt loss and acceleration. Also quasi-linear theory is used, and only whistler and EMIC-mode waves are tractable with this technique. However, this simple technique illuminates local times and time frames when waves are active during typical storms. This may prove instructive in physics-based or reanalysis-type modelling efforts (e.g. O’Brien & Lemon 2007; Varotsou et al. 2008).
In summary, we have shown global distributions of inferred whistler- and EMIC-mode wave activity at geosynchronous orbit during high-speed streams and other storms. Radiation-belt electron fluxes are lowest for the storms exhibiting the most EMIC activity and the least whistler-wave activity in the recovery phase. This is consistent with the current interpretation that whistler waves are primarily an acceleration mechanism, whereas EMIC waves are primarily a loss process for relativistic radiation-belt electrons. The inclusion of HSS events in this comparison leads to the interesting possibility that the relative suppression of EMIC activity in the recovery phase may be more important for radiation-belt regrowth than the enhanced whistler activity. This study has revealed the delicate competition and differences in local time and storm phase distributions of waves that may be sensed from this simple but powerful technique. Such information should be used for inputs to simulations of the radiation-belt response. Further work is required to clarify to what degree the global electron energization that occurs results from these and other processes.
One contribution of 8 to a Special feature ‘Geospace effects of high-speed solar wind streams’.
- Received February 9, 2010.
- Accepted May 18, 2010.
- © 2010 The Royal Society