The mechanism for formation of the Earth's radiation belts has been an outstanding issue for utilization of the geospace environment. We present a magnetic storm recovery phase that occurred from 10 to 19 October 1990, in which there is a clear correlation among continuous injection of hot electrons, generation of chorus, geomagnetic AE activity (all for ∼8 days) and the acceleration of electrons to relativistic energies. We propose a following scenario to explain the observations: the continuous injection of hot electrons associated with the continuous AE activity. The hot electrons with Tperp/Tpara > 1 temperature anisotropies excite whistler-mode chorus waves. The chorus interacts with energetic electrons accelerating them to MeV energies forming a flux of “killer electrons” in the outer radiation belt.
 Relativistic electrons in the Earth's Van Allen belt have been called “killer electrons” because of their hazardous influence on Earth-orbiting satellites and humans in space. The flux of the killer electrons in the MeV energy range shows dynamic variation during the magnetically disturbed period of magnetic storms and high speed solar wind streams [Paulikas and Blake, 1979; Reeves et al., 2003]. Summers et al.  have proposed that relativistic electrons of the outer belt are produced by acceleration with whistler-mode chorus [Tsurutani and Smith, 1974, 1977; Meredith et al., 2001, 2003; Miyoshi et al., 2003], which are observed in the dawn-side equatorial region during substorms and storms.
 The detailed variation of the outer radiation belt electrons during a magnetic storm “recovery” phase has been studied by Miyoshi et al.  and Horne et al. . They have shown that wave-particle interactions with chorus are important for large flux enhancements of the outer belt electrons. A statistical study using Akebono VLF wave data clarified that the generation region of chorus emissions during the recovery phase of magnetic storms is primarily located near the inner edge of the outer radiation belt (L-value ∼2.5), and gradually shifts outward (L-value ∼4) with time [Kasahara et al., 2004]. This outward motion of the chorus generation region is believed to be related to the expansion of the plasmasphere during its refilling process. Recent theoretical studies showed that nonlinear wave-particle interactions are important to generate relativistic electrons [Omura et al., 2007, 2008], so that it is necessary to consider not only large scale variations of chorus emissions during the storm main and recovery phases, but also the fine structure of the emissions. It is well-known that chorus consists of elements separated by noise intervals [Tsurutani et al., 2008].
 We report here a typical magnetic storm event which occurred from 9 to 19 October 1990. This magnetic storm was previously studied by Brautigam and Albert  using CRRES data. Summers et al.  have analyzed energization of outer-zone electrons by whistler-mode chorus during this storm. In the present paper simultaneous observation of VLF chorus, hot electrons of ∼30 keV, and the relativistic electrons of ∼2.5 MeV are presented. In addition we show the frequency characteristics of chorus elements that are important for nonlinear wave particle interactions.
2. Simultaneous Observations From 9 to 19 October 1990
Figures 1a, 1b, and 1c show ∼30 keV and relativistic ∼2.5 MeV electron fluxes and electric field component of VLF waves from 1 to 10 kHz for the magnetic storm, respectively. Figure 1 is a composite where Figure 1a is taken from the MEPED instrument onboard NOAA-10 [Raben et al., 1995]. Figures 1b and 1c are data taken from the RDM instrument [Takagi et al., 1993] and the multi-channel analyzer (MCA) [Kimura et al., 1990] onboard Akebono, respectively. The horizontal and vertical axes in each panel are universal time (UT) and the McIlwain L-value, respectively. The time resolution is 3 hrs. The Dst index is also shown by a solid line in Figures 1a–1d. Figure 1d shows the AE index.
 For this magnetic storm, the main phase occurred from the middle of day 9 and lasted through the beginning of day 10. The Dst index gradually recovers to quiet time values from day 10 through day 18. It should be noted that the Dst recovery was not monotonic. There are occasional small Dst decreases followed by increases. This is a particularly important point to note. It is assumed that magnetic reconnection between the southward component of the Alfvén waves and the magnetopause fields is taking place, leading to the plasma injections [Tsurutani et al., 1995]. Observations for showing close relationship Alfvén waves and large enhancement of outer belt electrons associated with chorus waves have been reported by Miyoshi et al.  for other storm events. It can be noted in Figure 1d that continuous AE activity occurs throughout the storm “recovery” phase from days 11 through 18. This type of activity is called a “high-intensity long-duration continuous AE activity” (HILDCAA) event [Tsurutani and Gonzalez, 1987] and relativistic electrons tend to increase during this continuous AE activity associated with high-speed streams [Iles et al., 2002; Miyoshi et al., 2007; Miyoshi and Kataoka, 2008].
 In Figure 1a, it is noted that ∼30 keV electrons are injected into the magnetosphere throughout the storm “recovery” phase. Thus this storm “recovery” is not simply a loss of the ring current particles from the storm main phase injection, but the ring current is sustained by frequent injections of these new particles. Immediately after each fresh ∼30 keV electron injection, the Dst index decreases slightly. During each AE increase within the HILDCAA event, Dst decreases, indicating that fresh energetic particle injection contributes to the global ring current intensification [Miyoshi et al., 2003, 2007; Soraas et al., 2004; Miyoshi and Kataoka, 2005; Tsurutani et al., 2006]. This continuous particle “pumping” into the ring current is what maintains the storm recovery for ∼8 days.
Figure 2 shows an example of wave activity observed during the magnetic storm, from 9 to 19 October 1990. Figure 2a shows the Akebono trajectory from 01:30 to 03:30 UT on Oct. 10, 1990. Akebono's orbit goes from the southern hemisphere to the northern hemisphere, crossing the geomagnetic equator at 03:06 UT. The magnetic local time (MLT) was 10.2 at 02:00 UT and 11.1 at 03:00 UT. Figure 2b shows a 1-hr VLF wave spectrogram for the electric field and magnetic field components measured by the MCA. Solid lines in the spectrogram indicate the lower hybrid frequency (top line), the H+ (middle line) and He+ (bottom line) ion cyclotron frequencies, respectively. The telemetry reception for the MCA was unfortunately interrupted from 02:29 to 02:40 UT due to a satellite ranging operation. Stripes in the magnetic field below 200 Hz from 02:00 to 02:26 UT are caused by instrument interference. Intense chorus is observed at L-values from 8.4 down to 3.5 (shown in the red circle in Figure 2b). The chorus frequency becomes higher as the L-value decreases. Another band of emission observed in the frequency range 200 Hz to 2 kHz (from 02:18 to 03:00 UT) is plasmaspheric hiss. Plasmaspheric hiss is usually observed inside the plasmasphere. In this event, the intensity is much lower than the one for chorus. It should also be noted that equatorial noise detected at frequencies below the lower hybrid frequency is sometimes observed in the equatorial region, but equatorial noise is generally confined inside L-value < 2.5 because of the orbital effect of Akebono [Kasahara et al., 1994].
Figure 2c shows a 30-second plot of the VLF wave spectrogram for magnetic fields measured by the WBA [Kimura et al., 1990]. The WBA is an analogue waveform receiver, and the color scales are given by the relative values at the right. A series of rising chorus elements is observed around 6–9 kHz. We have carefully checked the data and confirmed that the dominant wave activity during magnetic storm shown in Figure 1c is chorus. That is, chorus is present throughout the entire 8 days of storm recovery.
 It is noted that the enhancement of the AE index (Figure 1d) and occurrence of chorus are well correlated. This is expected because chorus emissions are believed to be generated by hot electron injected during substorms [Meredith et al., 2002; Lyons et al., 2005; Miyoshi et al., 2007]. It is also noted that there is a clear correlation between the inner edges of hot plasma injections and occurrence of VLF chorus emissions. This is presumably due to the fresh injections of ∼30 keV electrons with a high temperature anisotropy (Tperp/Tpara > 1) [Kennel and Petschek, 1966; Tsurutani and Lakhina, 1997] leading to the generation of the chorus emissions [Katoh and Omura, 2007; Omura et al., 2008]. Once generated, these waves can then trap a fraction of the hot electron population and energize them to MeV energies as discussed below.
3. Electron Acceleration by Whistler-Mode Chorus Emissions
 The relativistic ∼2.5 MeV electrons, noted in Figure 1b, become intensified throughout the 8 days. The greatest intensities occur at the end of the interval. Brautigam and Albert  using CRRES observations have concluded that the gradual increase of relativistic electrons throughout the storm “recovery phase” is inconsistent with the radial diffusion model, and suggested that an acceleration mechanism inside the radiation belts is needed. Evidence from phase space density profiles [Iles et al., 2006] is also in agreement with the in situ acceleration argued here.
 The wave-particle interactions leading to the electron acceleration up to ∼2.5 MeV takes place gradually through continuous generation of chorus emissions. In the wave-particle interaction process, the ratio of the wave frequency to the local electron cyclotron frequency is a critical parameter for the acceleration process. Noting that the Lorentz factor γ corresponds to an energy 0.51 (γ − 1) MeV, we find that 2.5 MeV corresponds to γ ∼ 6. The cyclotron resonance velocity VR = (ω − Ωe/γ) k becomes 0 when γ = Ωe/ω. It has been hypothesized that there is a very effective mechanism called “relativistic turning acceleration (RTA)” when VR = 0 [Omura et al., 2007] in the presence of a coherent whistler-mode wave packet like a chorus element. For even higher energies with VR > 0, there occurs another effective mechanism called “ultra-relativistic acceleration (URA)” [Summers and Omura, 2007] because the resonant electrons move in the same direction with a whistler-mode wave packet ensuring a longer period of interaction. Figure 3 shows the ratio of the chorus frequency F at the observation point to the local electron cyclotron frequency FH0 at the magnetic equator. We selected 59 chorus events which were observed by the WBA from October 1990 to November 1991, and carefully selected the highest and lowest frequencies of the 130 chorus elements. These events were not always in storm “recovery” phases, but also in relatively quiet intervals. Figure 3 shows the results. We calculated FH0 by tracing the magnetic field line to the magnetic equator for a dipole model rather than the Tsyganenko model, because no solar wind data were available for the period of 1990–1991. It should also be noted that these chorus events are basically observed in the off-equatorial region because the apogee of Akebono is ∼10,300 km. VLF chorus elements, however, basically propagate along the magnetic field lines with frequencies at the generation point [Omura et al., 2008]. The ratio F/FH0 is plotted as a function of L-value, and it gives the energy range of relativistic electrons trapped near the magnetic equator that can undergo the RTA process. Very effective acceleration can take place for energetic electrons with γ satisfying the condition F/FH0 = ω/Ωe = 1/γ. For example, waves with F/FH0 = 0.2 can effectively accelerate γ = 5 particles, i.e., ∼2 MeV electrons.
 The range of chorus frequencies corresponds to the range of the unstable whistler-mode frequencies at the equator [Omura et al., 2008]. It is noted that at low L-value, the chorus relative frequency range is lower. This feature may indicate that the temperature anisotropy of the energetic electrons becomes smaller as they are transported into the inner magnetosphere. Another possibility is that chorus with earthward inclined wave vectors propagate from the equator to lower altitudes where the magnetic fields are larger, decreasing the ratio F/FH0 [Santolik, 2008]. There are other possible explanations as well. As discussed above, a wider range of chorus frequencies starting from 0.1∼0.2 FH0 is necessary for acceleration of hot electrons to MeV energy. Therefore, in the lower L region, chorus emissions with the lower and narrower range of frequency cannot accelerate particles in the range of several hundred keV (γ ∼ 2) by the RTA process explaining why relativistic electrons are not observed during this storm.
 What causes the sporadic electron injections sustaining the ring current/electron radiation belt causing the unusually long storm “recovery” phase? Unfortunately, the solar wind data are not available during the storm, but the Dst decreases and AE increases, and continuous injections of hot electrons suggest that this storm “recovery” phase would be driven by Alfvén waves in the high speed stream (see Tsurutani et al.  for review). From statistical studies, it has been shown that CIR/high speed stream-driven storms tend to cause large flux enhancement of the outer belt electrons [Miyoshi and Kataoka, 2005]. Interplanetary Alfvén waves associated high speed coronal hole streams cause substorms and enhanced convection, leading to these sporadic plasma injections from the plasma sheet [Miyoshi et al., 2007]. The electrons injected into the inner magnetosphere develop high temperature anisotropies, which in turn causes the whistler-mode instability. When the waves grow to sufficient amplitude for nonlinear wave trapping of resonant electrons, chorus emissions with rising frequency are effectively induced via the nonlinear growth mechanism [Omura et al., 2008] as evidenced in the present event. The waveform analysis of chorus emissions observed at the time of a magnetic storm [Santolík et al., 2004] clearly shows that chorus emissions consists of coherent waves with amplitudes 50–150 pT, and the observed amplitudes could correspond to even higher amplitudes ∼300 pT (Santolik  and Tsurutani et al.  for reviews). The large amplitudes of coherent chorus elements are important for the acceleration of relativistic electrons. A recent test particle simulation study assuming chorus elements with such large amplitudes shows that chorus emissions can energize a fraction of hot electrons via the RTA and URA mechanisms, and that the repeated occurrence of the emissions results in a gradual formation of high energy tails of the velocity distribution function that extends to several MeV energy [Furuya et al., 2008]. In our scenario low frequency interplanetary waves carried by the fast solar wind cause magnetic reconnection, sporadic plasma injections, excitation of chorus emissions, and the production of relativistic electrons flux in the outer radiation belt.
 The authors wish to thank T. Nagai for providing the RDM data, and his helpful comments and suggestions. Energetic electron fluxes from NOAA-10 were obtained from the WDC database for Aurora at the National Institute of Polar Research, Japan. The AE and Dst indices were obtained from World Data Center at Kyoto University. Portions of this work were performed at the Jet Propulsion Laboratory, California Institute Technology under contract with NASA.