Observation and model results accumulated in the last decade indicate that substorms can promptly inject relativistic ‘killer’ electrons (≥MeV) in addition to 10–100 keV subrelativistic populations. Using measurements from Cluster, Polar, LANL, and GOES satellites near the midnight sector, we show in two events that intense electric fields, as large as 20 mV/m, associated with substorm dipolarization are associated with injections of relativistic electrons into the outer radiation belt. Enhancements of hundreds of keV electrons at dipolarization in the magnetotail can account for the injected MeV electrons through earthward transport. These observations provide evidence that substorm electric fields inject relativistic electrons by transporting magnetotail electrons into the outer radiation belt. In these two events, injected relativistic electrons dominated the substorm timescale enhancement of MeV electrons as observed at geosynchronous orbit.
Energization can occur when particles are radially transported into a stronger magnetic field while conserving their first adiabatic invariant. Radial transport can be diffusive or prompt (nondiffusive) [Hudson et al., 2008]. Diffusive radial transport was first considered in 1960s [Kellog, 1959; Parker, 1960; Fälthammar, 1965]. In the magnetosphere, randomly varying electric fields and magnetic fields needed for radial diffusion are ULF waves with periods of 10 s–600 s, driven either by the solar wind or magnetospheric free energy sources [e.g., Takahashi and Ukhorskiy, 2007; Ukhorskiy et al., 2005; Claudepierre et al., 2008]. Different from that in diffusive radial transport, the electric field is intense and nonrandom during its interaction with particles in coherent radial transport. One example is the shock-induced electric field associated with magnetosphere compression [Wygant et al., 1994]. Analytical modeling and MHD simulations have shown that the shock-induced electric fields are capable of moving a portion of particles earthward and forming a new radiation belt on the drift timescale [Li et al., 1993; Hudson et al., 1995].
Substorm injection can be thought of as a form of coherent radial transport. Particle injections are manifested as rapid increases in the particle flux generally located at radial distances from 4 to 8 RE [Friedel et al., 1996; Reeves et al., 1990]. Injection of particles is associated with substorm dipolarization, a sudden reconfiguration of the nightside magnetosphere from a taillike configuration to a more dipolar-like configuration. Substorm dipolarization and the associated particle injections have been modeled in various approaches [Li et al., 1998; Birn et al., 1998; Elkington et al., 2005; Fok et al., 2001; Zhang et al., 2009; Yang et al., 2011]. The energy of injected particles is usually from tens to hundreds of keV.
Recent studies, both theoretical and observational, have indicated that substorm dipolarization can directly inject MeV ‘killer’ electrons. Test particle simulation [Kim et al., 2000] with MHD model-based fields [Birn and Hesse, 1996] showed that substorm dipolarization can transport the plasma sheet population earthward and contribute to MeV electrons enhancements in the outer radiation belt. Observations from GPS and geosynchronous satellites provided evidence that repeated strong substorms inject MeV electron to the geosynchronous altitude during a geomagnetic storm [Ingraham et al., 2001]. The kinetic radiation belt model developed by Fok et al.  identified substorm electric fields as being responsible for rapid enhancements of MeV electrons during dipolarization. Observations from the Akebono spacecraft found rapid enhancements of >2.5 MeV electrons in the outer belt associated with storm time substorm dipolarizations [Nagai et al., 2006]. MHD and kinetic model have shown rapid enhancement of relativistic electron flux due to dipolarization in agreement with Akebono observations [Glocer et al., 2011].
Although the importance of substorm electric fields has been recognized in the modeling of Mev electron injections, detailed observations of the electric fields during such substorm injection have not been made. Using measurements from multiple spacecraft at different radial distances (Cluster∼18 RE, Polar∼8 RE, LANL and GOES satellites∼6.6 RE) near the midnight sector, we present the first observations of intense substorm electric fields associated with the injections of MeV electrons.
The organization of the paper is as follows. Section 2 presents two case studies of substorm electric fields injecting relativistic electrons into the outer radiation belts. Section 3 discusses the physics of the energization process and implications of the observation results. Section 4 presents the summary and conclusions.
2 Case Studies
Figure 1 is a schematic view of the magnetic field configuration and spacecraft positions projected in the xz-GSM plane before substorm dipolarization for the events we show. The magnetotail is stretched during the growth phase of substorms, and dipolarization occurs as the substorm proceed to the expansion phase. The blue arrows in Figure 1 indicate the inferred motion of the magnetic field in the dipolarization when the taillike magnetic field geometry become more dipole-like. The locations of the spacecraft were very similar in the two events. Cluster, Polar, LANL-90, and GOES 10 were near magnetic midnight. Four Cluster spacecraft were closely separated (∼200 km). Cluster and Polar were at the radial distances of ∼18 RE and 9 RE, respectively.
2.1 Event of 8 August 2003
2.1.1 The Substorm Dipolarization
Figure 2 presents observations of electric field, magnetic field, and energetic electrons from Cluster, Polar, LANL 90, and GOES 10 during a dipolarization during a substorm event on 8 August 2003 at 05 UT, which was the middle of three consecutive substorms. Figures 2a and 2b show a 20–30 min increase in Bz-GSM by ∼17 nT at Cluster and ∼30 nT at Polar, a characteristic signal of a change of field line configuration in the dipolarization. The increases in Bz were accompanied by an increase in AE index, consistent with the well-known phenomenon that the dipolarization occurs in the substorm expansion phase. The timescale of the Bz increase is much longer than that of the “dipolarization front” (tens) [Runov et al., 2009]. It has been suggested that the dipolarization front is related to but distinct from the dipolarization associated with a global change in the magnetic field configuration [Nakamura et al., 2011; Birn et al., 2011].
Both Cluster and Polar observed current sheet thinning before the dipolarizations. Cluster transversed from the central plasma sheet to the plasma sheet boundary layer (PSBL) around 0420–0440 UT and then to the tail lobe around 0510 UT, indicated by an increase of magnetic field strength and decrease of keV plasma sheet electrons. Polar transversed into the PSBL from 0425 UT to 0440 UT and remained in the PSBL until dipolarization. As dipolarization occurred and the current sheet expanded, Cluster and Polar reentered the plasma sheet and observed intense electric fields. Cluster observed a positive 21 mV/m Ey pulse associated with an earthward ion fast flow. Polar observed impulsive electric fields of ∼10–20 mV/m. The strong Ez-GSM observed at Polar corresponds to an azimuthal E×B flow, which is likely due to the deflection of the earthward flow related to the flux pileup. Ey-GSM at Polar (not shown) is mostly aligned with the spin axis and less accurate due to the short boomlength.
2.1.2 Substorm Electric Fields and the MeV Electron Injection
Figure 2c shows the observation of substorm electric fields and energetic electron injection. The top two panels show the magnitude of spin plane electric fields from Cluster (xy-GSE) and Polar (xz-GSE). Cluster was in the tail lobe in the early stage of dipolarization, which is likely the reason that the electric field signature was delayed. Cluster observed several orders of magnitude increase in hundreds of keV electrons at the dipolarization. In the near-Earth magnetotail, Polar observed the enhanced energetic electrons and substorm electric fields at the very beginning of the dipolarization. At geosynchronous altitude, both LANL-90 and GOES 10 observed a flux enhancement in relativistic electrons and subrelativistic electrons which can be identified as the substorm injection. This injection is a so-called “dispersionless injection,” characterized by a simultaneous enhancement over a broad range of energy. The flux of relativistic electrons increased by a factor ∼2 to 3 in the timescale of dipolarization at geosynchronous distance. These observations together provide evidence that dipolarization electric fields are associated with high-energy electrons injected into the outer radiation belt. Notice that the relativistic electron flux decreased after 0545 UT at GOES 10. This temporal decrease (0545–0555 UT) of MeV electrons at GOES 10 may reflect either a temporal decrease or an earthward spatial gradient in the electrons that were transported to geosynchronous orbit.
2.1.3 The Electron Phase Space Density
Figure 3 compares the phase space density (PSD) of electrons at different radial distances. The differential flux is converted to the PSD in the GEM (Geospace Environment Modeling) unit (c/MeV/cm)3 as f=(3.325×10−11)j/p2c2, where j is the differential flux in cm−2s−1sr−1MeV−1, f is the PSD, and p is the amplitude of momentum. PSD from Polar is calibrated according to Chen et al. . Figure 3a presents the PSD, as a function of the first adiabatic invariant μ, of 90° pitch angle electrons at Cluster and LANL-90 from 0528 UT to 0536 UT during the dipolarization. Both Cluster and LANL-90 spacecraft were close to the equatorial plane during the dipolarization. The 90° pitch angle electrons at these two spacecraft can be considered as near-equatorial mirroring electrons. The first adiabatic invariant μ is calculated using the dipole model field B∼100 nT at the LANL-90 and the observed Bz∼20 nT at Cluster. During active solar wind conditions such as interplanetary shocks, the magnetic field at geosynchronous orbit can be perturbed and the field strength is better addressed with models [e.g, Wang et al., 2009, 2010]. We use omnidirectional flux to approximate the flux at 90° pitch angle. Energetic electrons can be very isotropic at L=6.7 [Ni et al., 2011] and are quite isotropic at Cluster (data not shown) in this event. As shown in Figure 3a, the PSD spectrum at Cluster is in good agreement with the PSD of injected electrons observed at LANL-90. The agreement is an indication of sufficient source at Cluster to account for the injected electrons through earthward transport conserving μ and J (the second adiabatic invariant). Liouville's theorem states that the PSD is conserved along the particle trajectory in the phase space. If all electrons at midtail (Cluster) are adiabatically transported to the geosynchronous orbit (LANL-90), the PSD at LANL-90 would be exactly the same as that of Cluster. In reality, not all electrons at Cluster could make their way to the place of the geosynchronous orbit (LANL-90). However, the agreement in the slope and the magnitude of the PSD spectrum between Cluster and LANL-90 strongly suggested that midtail provide sufficient source electrons for relativistic electron injection in this event.
In Figure 3b we compare the PSD between Polar and LANL-90. Unlike Cluster, Polar was at some distance from the neutral sheet plane during the dipolarization (Bx >Bz). The 90° pitch angle electrons at Polar are not near-equator mirroring particles. Because the time and spatial variation of the magnetic field between geosynchronous orbit and the Polar location is not known, it is not possible to determine the change in the pitch angle of an electron observed at Polar after it is transported to geosynchronous orbit. For this reason, the pitch angle of electrons at LANL-90 is determined as a parameter. We found that PSD of 90° pitch angle electrons at Polar matches the PSD of 27° pitch angle at LANL-90 as shown in Figure 3c. The excellent similarity between two PSD spectra indirectly suggests that off-equator mirroring electrons at Polar may account for injection of relativistic electrons with small pitch angles at LANL-90.
2.2 Event of 20 September 2003
The event on 20 September 2003 is in many aspects similar to the event on 8 August 2003. As can be seen in Figure 4, Cluster observed consistent negative Bz (−5 nT) and tailward flow (10–100 km/s) from 0400 UT to 0415 UT. This may correspond to a neutral line formation in the plasma sheet earthward of the spacecraft. The subsequent reversal of Bz and strong earthward flow after 0415 UT is consistent with the scenario of the neutral line moving tailward and passing the spacecraft [e.g., Hones Jr., 1976].
Due to the plasma sheet thinning, Polar and Cluster were not inside the central plasma sheet in the early stage of dipolarization. Larger electric fields were observed in the later stage of dipolarization in the center of the plasma sheet. Impulsive electric fields from 2 mV/m to 5 mV/m in good agreement with the −V×B field obtained from the fast ion bulk flow continued for approximately 40 min at Cluster. Polar observed a spin plane electric field as large as 20 mV/m. The dipolarization electric fields are associated with earthward flow and expected to move earthward. After the Cluster observed large electric field in the plasma sheet around 0430 UT, however, Polar did not see a large electric field. This counterintuitive observation, which also appeared in the 8 August 2002 event, may be attributed to different vertical positions of spacecraft in the plasma sheet. While Cluster (Bz>>Bx) was close to the plasma sheet center, Polar (Bx>Bz) was relatively far away from the neutral plane at the dipolarization. As Cluster observed large dipolarization electric fields in the tail, Polar continued moving away from the plasma sheet center in these two events. Because of their different vertical distances from the plasma sheet center, Polar and Cluster did not observe the same part of the structured dipolarization electric fields. If the dipolarization electric fields decrease with the vertical distance from the plasma sheet center, Polar might not see a large electric field while Cluster could observe a large one. In addition, dipolarization also progresses azimuthally. Cluster and Polar were apart by 4 RE in the y-GSE. The timing between Cluster and Polar might be partially attributed to azimuthal propagation in addition to radial propagation.
Figure 4c shows the simultaneous occurrence of substorm electric fields, enhancement of energetic magnetotail electrons, and injection of relativistic electrons into the outer radiation belt during the 40 min substorm dipolarization. All of these together provide evidence that the intense substorm electric field is responsible for injecting relativistic electrons.
An enhancement of electrons from tens of keV to 1 Mev during the dipolarization was clearly observed in the near-Earth and middle magnetotail. Event on 20 September 2003 was during moderate magnetic storm (Dst from −30 to −45) and much more intense than the event on 8 August 2003 in terms of the relativistic electron flux. At geosynchronous distance, the presubstorm 1 MeV electron flux (∼100/cm2· s· sr · keV) and its increase (a factor of 2 or more) are much larger than the quiet time flux level and comparable to the enhanced flux in storm time in other studies [e.g., Kim and Chan, 1997]. Figure 5 shows the comparison of PSD at different radial distances during the dipolarization. The format of Figure 5 is the same as Figure 3. A dipole magnetic field of 100 nT and an assumption of isotropic distribution are used to obtain the PSD at LANL-90. The similarity between the PSD spectrum of the injected populations and the PSD at midtail suggests that energetic magnetotail electrons provide the source electrons for MeV electron injection.
3.1 The Physics of the Energization Process
Under the condition of conserving μ, the rate of kinetic energy gain for particles is dW/dt=qVd·E+(μ/γ)∂B/∂t [Northrop, 1963], where W is the total kinetic energy, Vd is the guiding center drift velocity plus electron parallel velocity, and γ is the relativistic factor. The first term on the right side corresponds to energy increases due to the guiding center drift in the electric field. The second term is called the “betatron acceleration” term, caused by the curl of E associated with ∂B/∂t acting on the electron gyromotion [Northrop, 1963].
Guiding center drift along the dawn-dusk electric field may explain the results of energization in our observations. For simplicity, consider the near-equator-mirroring electrons with drifts of E×B and ∇B. These two drifting together can energize electrons as large as the cross-tail potential. Based on a calculation in a dipole field, Ingraham et al.  argues that a 23 mV/m induction electric field with an azimuthal span of 60° can move electrons from L=15 to L=6.7, resulting adiabatic energization from 100–200 keV to 0.8–1.3 MeV. In our observations, the simultaneous occurrence of injection at GOES10 and LANL-90 suggests an injection region spanning more than 6 h in MLT. The dawn-dusk electric fields associated with substorm dipolarization are 10–20 mV/m at radial distances from 6.7 RE to 18 RE. Assuming that a drifting electron encounters an average of 10 mV/m dawn-dusk electric field, such an electron can gain energy ∼0.6–1.5 MeV during its drift from midtail to geosynchronous distance.
Betatron acceleration with conservation of μ could occur in the dipolarization [Li et al., 1998, 2003; Zaharia et al., 2004; Ashour-Abdalla et al., 2011]. The amount of energization does not depend on the cross-tail potential but is related to the change of the magnetic field as electrons drift toward Earth. In one theoretical study, the dipolarization is modeled as propagating electromagnetic pulses in betatron acceleration and energizes plasma sheet electrons up to hundreds of keV [Li et al., 1998]. Both the initial energy of midtail electrons and the electric field of the pulse in the dipolarization model of Li et al.  are a fraction of those observed in our events. With proper conditions of substorm electric fields and source electron population, the betatron acceleration model is capable of energizing electrons to relativistic energy as well (X. Li, private communication, 2012).
Both acceleration mechanisms, guiding center drift and Betatron acceleration, may operate in the observations presented. More studies are necessary to clarify the relative importance of the various mechanisms.
3.2 The Electric Field of Substorm Dipolarization
The property of the dipolarization electric fields is one important issue for understanding injections of MeV electrons. Measurements of the substorm electric field can be a diagnostic tool to assess the possible energy gain of electrons. In the steady convection, the cross-tail potential maps to the polar cap potential (about 100 keV) and corresponds to a small electrostatic dawn-dusk electric field (0.2–0.5 mV/m). In a substorm dipolarization, dawn-dusk electric fields are associated with the change of magnetic field configuration and the cross-tail potential does not map to the polar cap potential. Electric fields of substorm dipolarization can be from several mV/m to tens of mV/m in observations [Cattell and Mozer, 1984; Fairfield et al., 1998; Tu et al., 2000; Nishimura et al., 2008] and modeling [Birn and Hesse, 1996; Birn et al., 1998; Zhang et al., 2009], much larger than those in steady convection. In our events, the substorm electric fields are in the range from several mV/m to 20 mV/m. These electric fields are comparable to the enhanced large-scale electric field (6 mV/m) during active geomagnetic storms [Wygant et al., 1998]. One interesting question is what fraction of the time MeV electron injection may be explained by intense substorm electric fields. The ongoing Radiation Belt Storm Probes (RBSP) mission combined with Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft enables measurements of substorm electric fields from the inner radiation belt to the near-Earth magnetotail and will facilitate further studies.
3.3 PSD at Different Radial Distances
The source population of the MeV electron injection is generally expected to be the high-energy tail of the plasma sheet population, normally modeled as a kappa distribution based on the statistic study of Christon et al. . By examining the PSD over an interval of a geomagnetic storm, Taylor et al.  have shown that the electron phase space density (PSD) is highly variable in the midtail plasma sheet (18 RE) and appears sufficient to supply relativistic electrons in the radiation belts in certain cases. While studies of the electron PSD at different radial distance have been generally focused on a timescale from days (storm time) to years, our study focused on PSD variations on relatively short substorm timescales. The enhancement of 100 keV electrons at substorm dipolarization, which is much higher than the presubstorm plasma sheet population level, suggests a source of energetic electrons produced within the substorm timescale.
4 Summary and Conclusions
We present the first simultaneous observations of the substorm dipolarization electric fields and the injection of relativistic electrons. These observations were made by LANL, GOES, Polar, and Cluster near the midnight sector during moderate substorm dipolarizations. The electric fields are associated with the rapid magnetic field reconfiguration during the substorms and occur as structured pulses with a timescale of ∼tens of minutes. The electric field amplitude varies from several mV/m to 20 mV/m, comparable to those seen in other substorm studies [Cattell and Mozer, 1984; Cattell et al., 1986; Fairfield et al., 1998; Tu et al., 2000; Nishimura et al., 2008] and much larger than that expected from a steady convection. The observed substorm electric fields were associated with relativistic electron injection at the geosynchronous distance. We showed that the observed enhancements of magnetotail energetic electrons at dipolarization can account for the injected relativistic electrons through earthward transport and conservation of the first adiabatic invariant. These observations together support the scenario that intense substorm electric fields promptly (within timescales of tens of minutes) inject relativistic electrons into the outer radiation belt through earthward transport of less energetic magnetotail electrons.
In our events, injected relativistic electrons dominate the substorm timescale enhancement of MeV electrons as observed at geosynchronous orbit. The long-time (storm time) influence of such injections depends on the occurrence frequency and how deep the electric field penetrates into the heart of the radiation belt (L∼4–5). The occurrence frequency and the radial extent of relativistic electron injections are subjects of further investigation. Based on studies of electric field penetration from CRRES [Rowland, 2002] and a survey of Electric Field and Waves Instrument (EFW) data from early RBSP mission (S. Thaller, private communication, 2013), we anticipate that such injections can operate as close as 3–4 RE from Earth.
This research was supported by NASA grants NNG04GG83G, NNH13ZDA001N, NNX08AF28G, NAG5-12765, and NNX13AE16G and a contract from APL for the development of RBSP/EFW. We would like to thank Cluster Active Archive and instrument teams EFW, FGM, RAPID, CIS, and PEACE for providing Cluster data. We thank Forrest Mozer for Polar EFI data, Christopher Russell for Polar MFE data, and Dot DeLapp for providing LANL particle data. GOES EPS and Polar HYDRA data are made available by NASA's Goddard Space Flight Center at CDAWeb. L.Dai thanks Steve Monson for proofreading the manuscript.
The Editor thanks Jiannan Tu and an anonymous reviewer for their assistance in evaluating this paper.