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Increase in relativistic electron flux in the inner magnetosphere: ULF wave mode structure
~
Pergamon
www.elsevier.nl/locate/asr
Adv. Space Res. Vol. 25, No. 12, pp. 2327-2337, 2000 © 2000 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-1177/00 $20.00 + 0.00 PII: S0273-1177(99)00518-9
INCREASE IN RELATIVISTIC ELECTRON FLUX IN THE INNER MAGNETOSPHERE: ULF W A V E MODE STRUCTURE M. K. Hudson, S. R. Elkington and J. G. Lyon
Physics and Astronomy Department, Dartmouth College, Hanover, NH 03755 C. C. Goodrich
Astronomy Department, University of Maryland, College Park, MD 20742 ABSTRACT Pc 5 ULF waves are seen concurrently with the rise in radiation belt fluxes associated with CME magnetic cloud events. A 3D global MHD simulation of the 10-11 January, 1997 event has been analyzed for mode structure and shown to contain field line resonance components, both toroidal and poloidal, with peak power on the nightside during southward IMF conditions. A mechanism for inward radial transport and first-invariant conserving acceleration of relativistic electrons is assessed in the context of ULF mode structure analysis, and compared with groundbased and satellite observations. © 2000 COSPAR. Published by Elsevier Science Ltd.
INTRODUCTION The goal of this paper is to analyze the longitudinal and radial mode structure of ULF oscillations seen in the 3D global MHD simulation of the January 1997 magnetic cloud event [Goodrich et al., 1998]. This is the first such detailed analysis of ULF mode structure in MHD simulations driven by measured solar wind input parameters. The field time series from the simulations has been used to advance guiding center electron test particle trajectories in the equatorial plane [Hudson et aL, 1998], to model the rapid growth of outer zone electron flux observed for this event [Selesnick and Blake, 1998; Reeves et al., 1998a,b]. Magnetic and electric field time series from the MHD simulation have been extracted along the trajectory of four geosynchronous satellites: GOES 9, 1990-095, 1994-084 and 1991-080 (GOES 8 data was not available for comparison). Time series of total B, which would coincide with Bz for a dipole, azimuthal and radial electric field components E¢ and Er in the magnetic equatorial plane at L=6.6, and local times of respective satellites are shown in Figure 1. A comparison of the simulated and measured magnetic field data in the geographic equatorial plane at GOES 9 is shown in Figure 2. Location of the satellites at 0700 and 1300 UT is shown in Figure 3, against a snapshot of the MHD simulation electric field vectors in the magnetic equatorial plane at those times. Coherent ULF oscillations are evident during the time interval ~ 0500 - 1200 UT, depending on satellite location, from which information about longitudinal extent can be extracted. The oscillations are first seen in the simulations at the longitude of (a) GOES 9 around 0500 UT (2000 LT) and also at (b)1990-095 around 0500 UT (0230 LT). There is a clear compressional oscillation in B around 0600 UT at GOES 9, which is present in E¢ and grows to larger amplitude in Er by 0800 - 0900 UT. There is a spike in B around 1100 UT at (b)1990-095 associated with arrival of a solar wind pressure pulse detected at WIND [Li et al., 1998]. This compression is evident in the simulated magnetometer data at the location of all four geosynchronous spacecraft shown, but most prominent for 1990-095 on the dawn flank (there is no actual magnetometer on LANL spacecraft). Timing of simulated and measured GOES 9 magnetic field data following the very high density solar wind pressure pulse around 0100 UT on January 11 is in excellent agreement in Figure 2. 2327
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M.K. Hudson
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Figure 2. Btot observed by GOES 9 is compared with that from the MHD simulation at the location of GOES 9 in the geographic equatorial plane. The oscillations appear later and persist longer at (c)1994-084, which comes around to the nightside by 1200 UT (1900 LT). They appear latest at (d)1991-080, from around 0800 - 1200 UT (1240 - 1640 LT). Comparison of Figures 3a and 3b shows that ULF wave activity in the simulations has become quieter globally by 1300 UT. It is clear from the geosynchronous satellite locations and field time series that the ULF oscillations are more coherent on the nightside, and persist over at least a seven hour period from about 0500 - 1200 UT. The simulations allow examination of radial mode structure as well. A power spectrum of the model MHD fields has been produced for the various field components. The frequency domain analysis of the radial electric field component for the period 0900-1200 UT, centered on local midnight, is shown in Figure 4a; the azimuthal electric field (not shown) is weaker and dominated by the DC convection field. Spectra at 0800 LT (Figure 4b) and 1600 LT (Figure 4c) are displayed in the same format as Figure 4a. The radial component shows the most coherent structure of any field component, and moreso near midnight than at other local times. Assuming that the oscillations seen in the simulation are Alfv6nic in nature, the radial component of the electric field corresponds to a toroidal-mode field line resonance [Southwood, 1974]. However, the frequency range 0.5 - 2.5 mHz is lower than expected for the L values indicated (L=3-9), using either a dipole [Cummings et al., 1969] or Olson-Pfitzer [Singer et al., 1981] magnetic field model, and assuming a hydrogen plasma. The origin of these commonly observed low frequencies remains an outstanding issue [see Lessard et al., 1998, and references therein]. From Figure 4a, a concentration of power in regions of steep Alfv6n speed gradient is inferred, and confirmed by examining the time averaged Alfv6n speed profile at midnight LT
Relativistic Electrons in the Inner Magnetosphere
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Figure 3. Location of geosynchronous satellites in Fig. 1 at a) 0700 and b) 1300 UT, against a snapshot of the MHD simulation electric field vectors in the magnetic equatorial plane. Panel (a) is typical of ULF wave mode structure and activity level throughout the interval between 0500 - 1200 UT, quieter by the end of the interval (b).
M. K. H u d s o n et al.
2332
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Figure 4. Power spectrum of the radial component of the MHD simulation electric field for a two hour period centered at (a) 0000 LT, between 0900 UT and 1200 UT on 10 Jan 98. The ascending black lines indicate dipole drift frequency as a function of L for particles with energies shown in Figure 1. The descending lines between L = 4.2 and L = 6.6 give the dipole drift frequency of a particle moving radially through this range while conserving the relativistic adiabatic invariant. (b) Same as (a) centered on 0800 LT. (c) Same as (a) centered on 1600 LT. The descending lines between L=4.2 and 9 in Figure 4a indicate the drift frequency seen by a particle moving through this range of L shells at constant M, where M is the relativistic first adiabatic invariant [Schulz and Lanzerotti, 1974]. A 200 keV electron at L=8.4, diffusing or transported radially inward in the simulations (not shown) while conserving M, would arrive at L=4.2 with 1.6 MeV energy in the absence of any non-M conserving process. Such electrons would encounter significant power in the spectral range matching their drift frequency. This has led Hudson et al. [1998] to suggest a driftresonant acceleration mechanism to account for the rapid rise in electron flux around L=4 over several hours seen on January 10, both in satellite measurements [Selesnick and Blake, 1998; Reeves et aL, 1998; Buhler et al., 1998] and simulations [Hudson et al., 1998]. DISCUSSION The magnetic cloud observed to cross 1 AU on January 10 - 11 was embedded in a solar wind of moderate velocity ~ 400 km/s, compared to estimates as great as 1400 km/s for the March 24, 1991 event, where significant radiation belt flux enhancement occurred on the time scale of an MeV electron drift period following the SSC. Instead of a high speed interplanetary shock, the organizing feature of the event studied here was an extended period of southward IMF characterized by substorm activity preceeding the rise in relativistic electron fluxes after 0900 UT on January 10. In the period between about 9 and 12 UT, ground magnetometers located at College (L=5.5) and Gakona (L=4.9), Alaska, centered on midnight LT, recorded large amplitude (several hundred nT) oscillations in the magnetic
2334
M . K . Hudson et al.
/
....... . . . . . ...xI/. .......... Figure 5. Sketch of electron drift path and radial electric field orientation in a torroidal mode oscillation cycle. Solid arrows indicate electric field at t--0, and dashed as seen by an electron with wave frequency ¢O=C0D,the electron drift frequency, starting at dusk for an m=2 azimuthal mode number.
field coincident with the rise in electron flux observed by GPS spacecraft between 4.2 and 4.5 RE. These waves, also seen in riometer and scanning meridian photometer data, had periods of around 10 minutes corresponding to the drift frequency of 1.6 MeV electrons at L=4.2. The riometer data [see Hudson et al., 1998, Figure 1] showed further enhancement in activity around 11 UT when a moderate solar wind pressure pulse impacted the magnetosphere [Li et al., 1998]. However, this enhancement was embedded in ULF wave activity in the same frequency range over a three hour period at Gakona, during which significant electron flux increase was seen in the simulations at L = 4.2 [Hudson et al., 1998]. Figure 4a shows that a particle moving from just inside geosynchronous orbit to the radial distances covered by the GPS spacecraft would encounter significant power in the spectral range matching its drift frequency. Hence, a drift resonance between the particles and fields might be responsible for the energization observed in both in-situ measurements and in the simulation [Hudson et al., 1998]. The drift resonance between > 200 keV electrons and the torroidal oscillations apparent in the radial electric field component of the simulation data suggests the following coherent acceleration mechanism. Electron fluxes at geosynchronous were amplified by successive substorm injections throughout the period of steady southward IMF Bz beginning at 0440 UT [Reeves et al., 1998a]. Electrons with the fight drift phase are subjected to continuous acceleration by a radial electric field over a non-azimuthally symmetric drift path, given the electric field reversal on the fimescale of half an electron drift period, as sketched in Figure 5. Electrons with the opposite drift phase are continuously decelerated. Consider, for example, Er with azimuthal mode number m=2, indicated by solid arrows at t=0 in Figure 5. An electron
Relativistic Electrons in the Inner Magnetosphere
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with drift frequency tO=0~Dthe ULF wave frequency, drifting eastward from dusk (bottom) sees an electric field indicated by dashed arrows as it moves along its drift orbit. By the time it drifts around to dawn (top), half a drift period later, the electric field has reversed sign, but now dr/dt > 0 as it moves towards the dayside, vs. dr/dt < 0 as it moves towards the nightside, so such an electron experiences continuous -5 F_,tdr > 0, and is accelerated over its drift orbit. Examining an m=l mode, there would be acceleration all the way around the drift path if the wave frequency is twice the drift frequency. If the wave frequency is equal to the particle drift frequency, there is acceleration on one side and deceleration on the other which cancel for the m= 1 mode. There would be acceleration on one side of the orbit only (and no cancelling deceleration on the other) if the wave frequency is half the particle drift frequency, hence Er maximum at dawn would be zero at dusk. Other combinations abound for higher m and ULF wave frequencies. An estimate of the magnitude of the acceleration has been made using the maximum equatorial electric field strength seen in the simulations, 8 mV/m, assuming a radial drift path of ~ 1.5 RE. A 100 keV electron at geosynchronous takes approximately one hour to drift around the earth and increase its energy to 200 keV for the assumed parameters, in another hour it increases its energy to 400 keV, and in two more hours it exceeds 1.6 MeV. Starting at 200 keV, its energy exceeds 1.6 MeV in less than 3 hours. These estimates, which assume continuous acceleration over a drift path, may be optimistic by a factor of two, but are supported by the relativistic test particle results [Hudson et al., 1998]. Thus, it seems reasonable to conclude that the observed increase in relativistic electron flux in the simulations, and measured for the January 1997 event, can be explained in part by drift resonant acceleration in the radial electric field of torroidal eigenmodes which show enhanced power during the period of rise in electron fluxes seen by GPS and other spacecraft. A poloidal mode component (E~) in the same frequency range will also contribute to inward radial transport [Li et al., 1993], however the amplitude above 0.5 mHz is weaker in the F~ than Er component throughout most of the ULF oscillations evident in Figures 1a - 1d. Evidence for ULF wave correlation with relativistic electron acceleration has been examined for two other CME-magnetic cloud events, 27 May 1996 and 15 May 1997, as well as 10-11 January 1997 [Baker et al., 1998a; 1998b]. The presence of significant ULF wave power (50 - 100 nT) at, e.g. 2 mHz, is correlated with the rise in relativistic electron flux for the latter two events, and absent for the first event which showed no comparable rise in flux. CONCLUSIONS
Hudson et al. [1998] have used the MHD simulation data to advance relativistic guiding center electron trajectories in the equatorial plane, simulating the rise in flux by several orders of magnitude seen by numerous spacecraft to peak near L=4.2 - 4.5 by early January 11, 1997 [GPS, Reeves et al., 1998b; Polar, Selesnick and Blake, 1998; STRV-lb, Buhler et al., 1998]. The rise in flux occurred over several hours in the 1.6-3.2 MeV energy channel of GPS, beginning around 1100 UT on January 10 [Li et al., 1998] and continuing to increase until 0200 UT on January 11 [Reeves et al., 1998b]. The January 1997 event was characterized by an extended period of steady southward IMF up until 1630 UT, which produced a sequence of substorms [Reeves et al., 1998a]. Simultaneous groundbased measurements in Alaska and Canada, which were situated postmidnight in local time at 1100 UT, indicated enhanced ULF wave power coincident with the rise in relativistic electron flux. GOES 9 observed enhanced ULF wave activity beginning around 0500 UT, several hours ahead of the rise in flux first seen at GPS [Li et al., 1998]. Evidence for ULF wave correlation with relativistic electron acceleration has been examined for two other CME-magnetic cloud events, 27 May 1996 and 15 May 1997, as well as 10-11 January 1997 [Baker et al., 1998a; 1998b]. The presence of significant ULF wave power (50-100 nT) at - 2 mHz, as seen by the Canopus magnetometer chain, is correlated with the rise in relativistic electron fluxes for the latter two events, while the absence of comparable ULF wave power for the first event correlates with the lack of relativistic electron response.
2336
M.K. Hudson et al.
The global MHD simulations provide an opportunity for ULF wave mode structure analysis not possible with a limited set of spacecraft, while at the same time enabling comparison with spacecraft and ground measurements. Thus far, we have examined the UT, LT and radial extent of the ULF waves, as well as identified the dominant toroidal mode structure in equatorial plane analysis of the simulation data at the time of initial increase in observed relativistic electron fluxes. There is evidence for poloidal mode power as well in the same frequency range at earlier times, e.g. around 0600 UT (2100 LT) at GOES 9, in both the compressional B and azimuthal E~ components (Figure l a). We plan next to examine in more detail the azimuthal mode number, which is evidently low from snapshots of the equatorial plane electric field vectors (Figure 3a). The acceleration mechanism proposed here is distinct from that attributed to rapid compressions of the magnetopause on the electron drift timescale, such as occurred for the March 24, 1991 CME-driven SSC [Li et al., 1993; Hudson et al., 1997]. In the latter case, it was shown that electrons drift eastward synchronously with a magnetosonic pulse launched within the magnetosphere by the dayside SSC shock compression. It is the azimuthal electric field component which transports electrons (and protons) radially inward in this case, increasing their energy as the first adiabatic invariant is conserved. The pulse spreads around the flanks of the magnetosphere at a characteristic magnetosonic speed determined by the plasma density and magnetic field, with maximum effect on those electrons drifting eastward at a comparable velocity. Lower energy electrons are not efficiently transported inward by such a pulse, which is mainly bipolar after reflection from the ionosphere [see Hudson et al., 1997, Figure 3]. Electrons in drift coherence with the magnetosonic pulse as it spreads around the flanks of the magnetosphere become drift-phase bunched in less than one drift period, as observed for the March 1991 event [Blake et al., 1992]. By contrast, the ULF-wave drift-coherent mechanism proposed here requires multiple drift orbits to increase electron energies from the hundred keV to MeV range, and drift echo features are not expected. Nonetheless, because it is a coherent process, it is much more efficient and rapid than acceleration by standard radial diffusion, based on incoherent electric or magnetic fluctuations. The January 1997 event is noteworthy for the lack of 1 - 2 day delay typically observed for outer zone electron flux buildup associated with high speed solar wind stream interactions [Blake et al., 1997], as well as for moderate solar wind velocity (< 500 km/s), until after passage of the magnetic cloud on January 11 [Burlaga et al., 1998]. While the correlation between solar wind speed and outer zone electron fluxes is well documented [Paulikas and Blake, 1979], the additional factor of steady southward IMF Bz [Blake et al., 1997] clearly played a role in the January 1997 case. It appears that such steady southward IMF Bz, well known to facilitate substorms, may affect the relativistic electron population in two ways. First, it provides an enhanced seed population in the hundred keV energy range due to substorm injections. Second, the ULF wave activity in the 10 minute period range is enhanced. Further investigation of what we have interpreted as torroidal oscillations, based on analysis of the MHD simulation data, will be pursued. In summary, we have analyzed the ULF wave mode structure in the 3D global MHD simulation of the January 10 - 11, 1997 magnetic cloud event. The increase in the ULF wave activity on the nightside in the simulations occurs in a frequency range comensurate with electron drift periods. Solar wind parameters from the WIND spacecraft were used to drive this simulation, and output fields have been used to push guiding center relativistic electron trajectories in the equatorial plane. Power enhancement in the radial electric field component of the simulations coincident with the electron drift period suggests drift-resonant acceleration over multiple electron drift periods. As electrons move inward, gaining energy from this radial electric field while conserving the first invariant, the flux peak moves inward to L=4 on a time scale of several hours, during a time interval both of enhanced ULF wave activity as seen by ground instrumentation on January 10, and the rise in relativistic electron fluxes seen by numerous spacecraft. Analysis of azimuthal mode structure in the simulations is underway, along with consideration of multiple resonant interactions. ACKNOWLEDGMENTS We thank J. B. Blake for providing Polar as well as HEO data, which motivated initial work on this event, G. D. Reeves for preprints and discussion of this event and for providing GPS and
Relativistic Electrons in the Inner Magnetosphere
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geosynchronous data for comparison with the simulations, R. Denton, I. Roth and M. Temerin for helpful discussions, and X. Li and R. Selesnick for preprints and discussion of their work on this event. This work is supported by NASA grants NAG5-7442, NAG5-6427 and NAGS-2252 to Dartmouth College. The work at the University of Maryland has been carded out with support received from NASA grant NAG5-101. REFERENCES Baker et al., Coronal mass ejections, magnetic clouds, and relativistic magnetospheric electron events: ISTP, J. Geophys. Res., 103, 17279 (19988). Baker et al., A strong CME-related magnetic cloud interaction with the Earth's magnetosphere: ISTP observations of rapid relativistic electron acceleration on May 15, 1997, Geophys. Res. Lett., 25, 2975 (1998b). Blake et al., Injection of electrons and protons with energies of tens of MeV into L - 3 on March 24, 1991, Geophys. Res. Lett., 19, 821 (1992). Blake et al., Correlation of changes in the outer-zone relativistic-electron population with upstream solar wind and magnetic field measurements, Geophys. Res. Lett., 24, 927 (1997). Buhler et al., The outer radiation belt during the 10 January, 1997 CME event, Geophys. Res. Lett., 25, 2983 (1998). Budaga et al., A magnetic cloud containing prominence material: January, 1997, J. Geophys. Res., 103, 277 (1998). Cummings et al., Standing AlfvEn waves in the magnetosphere, J. Geophys. Res., 5, 207 (1969). Goodrich et al, An overview of the impact of the January 10 - 11, 1997 magnetic cloud on the magnetosphere via global MHD simulation, Geophys. Res. Lett., 25, 2537 (1998). Hudson et al, MHD/particle simulations of radiation belt formation during a storm sudden commencement, in Radiation Belts: Models and Standards, edited by J. F. Lemaire, D. Heynderickx, and D. N. Baker, Geophys. Momogr. Ser., vol. 97, p. 57, AGU, Washington, D. C. (1996). Hudson et al., Simulations of radiation belt formation during storm sudden commencements, J. Geophys. Res., 102, 14,087 (1997). Hudson et al., Simulation of radiation belt dynamics driven by solar wind variations, AGU Yosemite Monograph, in press, (1998). Lessard et al., Simultaneous satellite and ground-based observations of a discretely driven field line resonance, J. Geophys. Res., in press, (1998). Li et al., Simulation of the prompt energization and transport of radiation belt particles during the March 24, 1991, SSC, Geophys. Res. Lett., 20, 2423 (1993). Li et al., Energetic electron injections into the inner magnetosphere during the January 10-11, 1997, magnetic storm, Geophys. Res. Lett., 25, 2561 (1998). Paulikas, G. A., and J. B. Blake, Effects of the solar wind on magnetospheric dynamics: Energetic electrons at the synchronous orbit, Quantitative Modeling of Magnetospheric Processes, 21, Geophys. Monograph Series (1979). Reeves et al., The relativistic electron response at geosynchronous orbit during the January 10, 1997, magnetic storm, J. Geophys. Res., 103 17559 (1998a). Reeves et al., The global response of relativistic radiation belt electrons to the January 1997 magnetic cloud, Geophys. Res. Lett., 25, 3265 (1998b). Schulz, M., and L. J. Lanzerotti, Particle Diffusion in the Radiation Belts, Springer-Verlag, Berlin (1974). Selesnick, R. S., and J. B. Blake, Radiation belt electron observations from January 6 to 20, 1997, Geophys. Res. Lett., 25, 2553 (1998). Singer et al., Standing hydromagnetic waves observed by ISEE 1 and 2: radial extent and harmonic, J. Geophys. Res., 97, 3519 (1982). Southwood, D. J., Some features of field line resonances in the magnetosphere, Planet. Space Sci., 36, 503 (1974).
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Adv. Space Res. Vol. 25, No. 12, pp. 2327-2337, 2000 © 2000 COSPAR. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0273-1177/00 $20.00 + 0.00 PII: S0273-1177(99)00518-9
INCREASE IN RELATIVISTIC ELECTRON FLUX IN THE INNER MAGNETOSPHERE: ULF W A V E MODE STRUCTURE M. K. Hudson, S. R. Elkington and J. G. Lyon
Physics and Astronomy Department, Dartmouth College, Hanover, NH 03755 C. C. Goodrich
Astronomy Department, University of Maryland, College Park, MD 20742 ABSTRACT Pc 5 ULF waves are seen concurrently with the rise in radiation belt fluxes associated with CME magnetic cloud events. A 3D global MHD simulation of the 10-11 January, 1997 event has been analyzed for mode structure and shown to contain field line resonance components, both toroidal and poloidal, with peak power on the nightside during southward IMF conditions. A mechanism for inward radial transport and first-invariant conserving acceleration of relativistic electrons is assessed in the context of ULF mode structure analysis, and compared with groundbased and satellite observations. © 2000 COSPAR. Published by Elsevier Science Ltd.
INTRODUCTION The goal of this paper is to analyze the longitudinal and radial mode structure of ULF oscillations seen in the 3D global MHD simulation of the January 1997 magnetic cloud event [Goodrich et al., 1998]. This is the first such detailed analysis of ULF mode structure in MHD simulations driven by measured solar wind input parameters. The field time series from the simulations has been used to advance guiding center electron test particle trajectories in the equatorial plane [Hudson et aL, 1998], to model the rapid growth of outer zone electron flux observed for this event [Selesnick and Blake, 1998; Reeves et al., 1998a,b]. Magnetic and electric field time series from the MHD simulation have been extracted along the trajectory of four geosynchronous satellites: GOES 9, 1990-095, 1994-084 and 1991-080 (GOES 8 data was not available for comparison). Time series of total B, which would coincide with Bz for a dipole, azimuthal and radial electric field components E¢ and Er in the magnetic equatorial plane at L=6.6, and local times of respective satellites are shown in Figure 1. A comparison of the simulated and measured magnetic field data in the geographic equatorial plane at GOES 9 is shown in Figure 2. Location of the satellites at 0700 and 1300 UT is shown in Figure 3, against a snapshot of the MHD simulation electric field vectors in the magnetic equatorial plane at those times. Coherent ULF oscillations are evident during the time interval ~ 0500 - 1200 UT, depending on satellite location, from which information about longitudinal extent can be extracted. The oscillations are first seen in the simulations at the longitude of (a) GOES 9 around 0500 UT (2000 LT) and also at (b)1990-095 around 0500 UT (0230 LT). There is a clear compressional oscillation in B around 0600 UT at GOES 9, which is present in E¢ and grows to larger amplitude in Er by 0800 - 0900 UT. There is a spike in B around 1100 UT at (b)1990-095 associated with arrival of a solar wind pressure pulse detected at WIND [Li et al., 1998]. This compression is evident in the simulated magnetometer data at the location of all four geosynchronous spacecraft shown, but most prominent for 1990-095 on the dawn flank (there is no actual magnetometer on LANL spacecraft). Timing of simulated and measured GOES 9 magnetic field data following the very high density solar wind pressure pulse around 0100 UT on January 11 is in excellent agreement in Figure 2. 2327
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Relativistic Electrons in the Inner Magnetosphere
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Figure 2. Btot observed by GOES 9 is compared with that from the MHD simulation at the location of GOES 9 in the geographic equatorial plane. The oscillations appear later and persist longer at (c)1994-084, which comes around to the nightside by 1200 UT (1900 LT). They appear latest at (d)1991-080, from around 0800 - 1200 UT (1240 - 1640 LT). Comparison of Figures 3a and 3b shows that ULF wave activity in the simulations has become quieter globally by 1300 UT. It is clear from the geosynchronous satellite locations and field time series that the ULF oscillations are more coherent on the nightside, and persist over at least a seven hour period from about 0500 - 1200 UT. The simulations allow examination of radial mode structure as well. A power spectrum of the model MHD fields has been produced for the various field components. The frequency domain analysis of the radial electric field component for the period 0900-1200 UT, centered on local midnight, is shown in Figure 4a; the azimuthal electric field (not shown) is weaker and dominated by the DC convection field. Spectra at 0800 LT (Figure 4b) and 1600 LT (Figure 4c) are displayed in the same format as Figure 4a. The radial component shows the most coherent structure of any field component, and moreso near midnight than at other local times. Assuming that the oscillations seen in the simulation are Alfv6nic in nature, the radial component of the electric field corresponds to a toroidal-mode field line resonance [Southwood, 1974]. However, the frequency range 0.5 - 2.5 mHz is lower than expected for the L values indicated (L=3-9), using either a dipole [Cummings et al., 1969] or Olson-Pfitzer [Singer et al., 1981] magnetic field model, and assuming a hydrogen plasma. The origin of these commonly observed low frequencies remains an outstanding issue [see Lessard et al., 1998, and references therein]. From Figure 4a, a concentration of power in regions of steep Alfv6n speed gradient is inferred, and confirmed by examining the time averaged Alfv6n speed profile at midnight LT
Relativistic Electrons in the Inner Magnetosphere
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Figure 3. Location of geosynchronous satellites in Fig. 1 at a) 0700 and b) 1300 UT, against a snapshot of the MHD simulation electric field vectors in the magnetic equatorial plane. Panel (a) is typical of ULF wave mode structure and activity level throughout the interval between 0500 - 1200 UT, quieter by the end of the interval (b).
M. K. H u d s o n et al.
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Figure 4. Power spectrum of the radial component of the MHD simulation electric field for a two hour period centered at (a) 0000 LT, between 0900 UT and 1200 UT on 10 Jan 98. The ascending black lines indicate dipole drift frequency as a function of L for particles with energies shown in Figure 1. The descending lines between L = 4.2 and L = 6.6 give the dipole drift frequency of a particle moving radially through this range while conserving the relativistic adiabatic invariant. (b) Same as (a) centered on 0800 LT. (c) Same as (a) centered on 1600 LT. The descending lines between L=4.2 and 9 in Figure 4a indicate the drift frequency seen by a particle moving through this range of L shells at constant M, where M is the relativistic first adiabatic invariant [Schulz and Lanzerotti, 1974]. A 200 keV electron at L=8.4, diffusing or transported radially inward in the simulations (not shown) while conserving M, would arrive at L=4.2 with 1.6 MeV energy in the absence of any non-M conserving process. Such electrons would encounter significant power in the spectral range matching their drift frequency. This has led Hudson et al. [1998] to suggest a driftresonant acceleration mechanism to account for the rapid rise in electron flux around L=4 over several hours seen on January 10, both in satellite measurements [Selesnick and Blake, 1998; Reeves et aL, 1998; Buhler et al., 1998] and simulations [Hudson et al., 1998]. DISCUSSION The magnetic cloud observed to cross 1 AU on January 10 - 11 was embedded in a solar wind of moderate velocity ~ 400 km/s, compared to estimates as great as 1400 km/s for the March 24, 1991 event, where significant radiation belt flux enhancement occurred on the time scale of an MeV electron drift period following the SSC. Instead of a high speed interplanetary shock, the organizing feature of the event studied here was an extended period of southward IMF characterized by substorm activity preceeding the rise in relativistic electron fluxes after 0900 UT on January 10. In the period between about 9 and 12 UT, ground magnetometers located at College (L=5.5) and Gakona (L=4.9), Alaska, centered on midnight LT, recorded large amplitude (several hundred nT) oscillations in the magnetic
2334
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/
....... . . . . . ...xI/. .......... Figure 5. Sketch of electron drift path and radial electric field orientation in a torroidal mode oscillation cycle. Solid arrows indicate electric field at t--0, and dashed as seen by an electron with wave frequency ¢O=C0D,the electron drift frequency, starting at dusk for an m=2 azimuthal mode number.
field coincident with the rise in electron flux observed by GPS spacecraft between 4.2 and 4.5 RE. These waves, also seen in riometer and scanning meridian photometer data, had periods of around 10 minutes corresponding to the drift frequency of 1.6 MeV electrons at L=4.2. The riometer data [see Hudson et al., 1998, Figure 1] showed further enhancement in activity around 11 UT when a moderate solar wind pressure pulse impacted the magnetosphere [Li et al., 1998]. However, this enhancement was embedded in ULF wave activity in the same frequency range over a three hour period at Gakona, during which significant electron flux increase was seen in the simulations at L = 4.2 [Hudson et al., 1998]. Figure 4a shows that a particle moving from just inside geosynchronous orbit to the radial distances covered by the GPS spacecraft would encounter significant power in the spectral range matching its drift frequency. Hence, a drift resonance between the particles and fields might be responsible for the energization observed in both in-situ measurements and in the simulation [Hudson et al., 1998]. The drift resonance between > 200 keV electrons and the torroidal oscillations apparent in the radial electric field component of the simulation data suggests the following coherent acceleration mechanism. Electron fluxes at geosynchronous were amplified by successive substorm injections throughout the period of steady southward IMF Bz beginning at 0440 UT [Reeves et al., 1998a]. Electrons with the fight drift phase are subjected to continuous acceleration by a radial electric field over a non-azimuthally symmetric drift path, given the electric field reversal on the fimescale of half an electron drift period, as sketched in Figure 5. Electrons with the opposite drift phase are continuously decelerated. Consider, for example, Er with azimuthal mode number m=2, indicated by solid arrows at t=0 in Figure 5. An electron
Relativistic Electrons in the Inner Magnetosphere
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with drift frequency tO=0~Dthe ULF wave frequency, drifting eastward from dusk (bottom) sees an electric field indicated by dashed arrows as it moves along its drift orbit. By the time it drifts around to dawn (top), half a drift period later, the electric field has reversed sign, but now dr/dt > 0 as it moves towards the dayside, vs. dr/dt < 0 as it moves towards the nightside, so such an electron experiences continuous -5 F_,tdr > 0, and is accelerated over its drift orbit. Examining an m=l mode, there would be acceleration all the way around the drift path if the wave frequency is twice the drift frequency. If the wave frequency is equal to the particle drift frequency, there is acceleration on one side and deceleration on the other which cancel for the m= 1 mode. There would be acceleration on one side of the orbit only (and no cancelling deceleration on the other) if the wave frequency is half the particle drift frequency, hence Er maximum at dawn would be zero at dusk. Other combinations abound for higher m and ULF wave frequencies. An estimate of the magnitude of the acceleration has been made using the maximum equatorial electric field strength seen in the simulations, 8 mV/m, assuming a radial drift path of ~ 1.5 RE. A 100 keV electron at geosynchronous takes approximately one hour to drift around the earth and increase its energy to 200 keV for the assumed parameters, in another hour it increases its energy to 400 keV, and in two more hours it exceeds 1.6 MeV. Starting at 200 keV, its energy exceeds 1.6 MeV in less than 3 hours. These estimates, which assume continuous acceleration over a drift path, may be optimistic by a factor of two, but are supported by the relativistic test particle results [Hudson et al., 1998]. Thus, it seems reasonable to conclude that the observed increase in relativistic electron flux in the simulations, and measured for the January 1997 event, can be explained in part by drift resonant acceleration in the radial electric field of torroidal eigenmodes which show enhanced power during the period of rise in electron fluxes seen by GPS and other spacecraft. A poloidal mode component (E~) in the same frequency range will also contribute to inward radial transport [Li et al., 1993], however the amplitude above 0.5 mHz is weaker in the F~ than Er component throughout most of the ULF oscillations evident in Figures 1a - 1d. Evidence for ULF wave correlation with relativistic electron acceleration has been examined for two other CME-magnetic cloud events, 27 May 1996 and 15 May 1997, as well as 10-11 January 1997 [Baker et al., 1998a; 1998b]. The presence of significant ULF wave power (50 - 100 nT) at, e.g. 2 mHz, is correlated with the rise in relativistic electron flux for the latter two events, and absent for the first event which showed no comparable rise in flux. CONCLUSIONS
Hudson et al. [1998] have used the MHD simulation data to advance relativistic guiding center electron trajectories in the equatorial plane, simulating the rise in flux by several orders of magnitude seen by numerous spacecraft to peak near L=4.2 - 4.5 by early January 11, 1997 [GPS, Reeves et al., 1998b; Polar, Selesnick and Blake, 1998; STRV-lb, Buhler et al., 1998]. The rise in flux occurred over several hours in the 1.6-3.2 MeV energy channel of GPS, beginning around 1100 UT on January 10 [Li et al., 1998] and continuing to increase until 0200 UT on January 11 [Reeves et al., 1998b]. The January 1997 event was characterized by an extended period of steady southward IMF up until 1630 UT, which produced a sequence of substorms [Reeves et al., 1998a]. Simultaneous groundbased measurements in Alaska and Canada, which were situated postmidnight in local time at 1100 UT, indicated enhanced ULF wave power coincident with the rise in relativistic electron flux. GOES 9 observed enhanced ULF wave activity beginning around 0500 UT, several hours ahead of the rise in flux first seen at GPS [Li et al., 1998]. Evidence for ULF wave correlation with relativistic electron acceleration has been examined for two other CME-magnetic cloud events, 27 May 1996 and 15 May 1997, as well as 10-11 January 1997 [Baker et al., 1998a; 1998b]. The presence of significant ULF wave power (50-100 nT) at - 2 mHz, as seen by the Canopus magnetometer chain, is correlated with the rise in relativistic electron fluxes for the latter two events, while the absence of comparable ULF wave power for the first event correlates with the lack of relativistic electron response.
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The global MHD simulations provide an opportunity for ULF wave mode structure analysis not possible with a limited set of spacecraft, while at the same time enabling comparison with spacecraft and ground measurements. Thus far, we have examined the UT, LT and radial extent of the ULF waves, as well as identified the dominant toroidal mode structure in equatorial plane analysis of the simulation data at the time of initial increase in observed relativistic electron fluxes. There is evidence for poloidal mode power as well in the same frequency range at earlier times, e.g. around 0600 UT (2100 LT) at GOES 9, in both the compressional B and azimuthal E~ components (Figure l a). We plan next to examine in more detail the azimuthal mode number, which is evidently low from snapshots of the equatorial plane electric field vectors (Figure 3a). The acceleration mechanism proposed here is distinct from that attributed to rapid compressions of the magnetopause on the electron drift timescale, such as occurred for the March 24, 1991 CME-driven SSC [Li et al., 1993; Hudson et al., 1997]. In the latter case, it was shown that electrons drift eastward synchronously with a magnetosonic pulse launched within the magnetosphere by the dayside SSC shock compression. It is the azimuthal electric field component which transports electrons (and protons) radially inward in this case, increasing their energy as the first adiabatic invariant is conserved. The pulse spreads around the flanks of the magnetosphere at a characteristic magnetosonic speed determined by the plasma density and magnetic field, with maximum effect on those electrons drifting eastward at a comparable velocity. Lower energy electrons are not efficiently transported inward by such a pulse, which is mainly bipolar after reflection from the ionosphere [see Hudson et al., 1997, Figure 3]. Electrons in drift coherence with the magnetosonic pulse as it spreads around the flanks of the magnetosphere become drift-phase bunched in less than one drift period, as observed for the March 1991 event [Blake et al., 1992]. By contrast, the ULF-wave drift-coherent mechanism proposed here requires multiple drift orbits to increase electron energies from the hundred keV to MeV range, and drift echo features are not expected. Nonetheless, because it is a coherent process, it is much more efficient and rapid than acceleration by standard radial diffusion, based on incoherent electric or magnetic fluctuations. The January 1997 event is noteworthy for the lack of 1 - 2 day delay typically observed for outer zone electron flux buildup associated with high speed solar wind stream interactions [Blake et al., 1997], as well as for moderate solar wind velocity (< 500 km/s), until after passage of the magnetic cloud on January 11 [Burlaga et al., 1998]. While the correlation between solar wind speed and outer zone electron fluxes is well documented [Paulikas and Blake, 1979], the additional factor of steady southward IMF Bz [Blake et al., 1997] clearly played a role in the January 1997 case. It appears that such steady southward IMF Bz, well known to facilitate substorms, may affect the relativistic electron population in two ways. First, it provides an enhanced seed population in the hundred keV energy range due to substorm injections. Second, the ULF wave activity in the 10 minute period range is enhanced. Further investigation of what we have interpreted as torroidal oscillations, based on analysis of the MHD simulation data, will be pursued. In summary, we have analyzed the ULF wave mode structure in the 3D global MHD simulation of the January 10 - 11, 1997 magnetic cloud event. The increase in the ULF wave activity on the nightside in the simulations occurs in a frequency range comensurate with electron drift periods. Solar wind parameters from the WIND spacecraft were used to drive this simulation, and output fields have been used to push guiding center relativistic electron trajectories in the equatorial plane. Power enhancement in the radial electric field component of the simulations coincident with the electron drift period suggests drift-resonant acceleration over multiple electron drift periods. As electrons move inward, gaining energy from this radial electric field while conserving the first invariant, the flux peak moves inward to L=4 on a time scale of several hours, during a time interval both of enhanced ULF wave activity as seen by ground instrumentation on January 10, and the rise in relativistic electron fluxes seen by numerous spacecraft. Analysis of azimuthal mode structure in the simulations is underway, along with consideration of multiple resonant interactions. ACKNOWLEDGMENTS We thank J. B. Blake for providing Polar as well as HEO data, which motivated initial work on this event, G. D. Reeves for preprints and discussion of this event and for providing GPS and
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geosynchronous data for comparison with the simulations, R. Denton, I. Roth and M. Temerin for helpful discussions, and X. Li and R. Selesnick for preprints and discussion of their work on this event. This work is supported by NASA grants NAG5-7442, NAG5-6427 and NAGS-2252 to Dartmouth College. The work at the University of Maryland has been carded out with support received from NASA grant NAG5-101. REFERENCES Baker et al., Coronal mass ejections, magnetic clouds, and relativistic magnetospheric electron events: ISTP, J. Geophys. Res., 103, 17279 (19988). Baker et al., A strong CME-related magnetic cloud interaction with the Earth's magnetosphere: ISTP observations of rapid relativistic electron acceleration on May 15, 1997, Geophys. Res. Lett., 25, 2975 (1998b). Blake et al., Injection of electrons and protons with energies of tens of MeV into L - 3 on March 24, 1991, Geophys. Res. Lett., 19, 821 (1992). Blake et al., Correlation of changes in the outer-zone relativistic-electron population with upstream solar wind and magnetic field measurements, Geophys. Res. Lett., 24, 927 (1997). Buhler et al., The outer radiation belt during the 10 January, 1997 CME event, Geophys. Res. Lett., 25, 2983 (1998). Budaga et al., A magnetic cloud containing prominence material: January, 1997, J. Geophys. Res., 103, 277 (1998). Cummings et al., Standing AlfvEn waves in the magnetosphere, J. Geophys. Res., 5, 207 (1969). Goodrich et al, An overview of the impact of the January 10 - 11, 1997 magnetic cloud on the magnetosphere via global MHD simulation, Geophys. Res. Lett., 25, 2537 (1998). Hudson et al, MHD/particle simulations of radiation belt formation during a storm sudden commencement, in Radiation Belts: Models and Standards, edited by J. F. Lemaire, D. Heynderickx, and D. N. Baker, Geophys. Momogr. Ser., vol. 97, p. 57, AGU, Washington, D. C. (1996). Hudson et al., Simulations of radiation belt formation during storm sudden commencements, J. Geophys. Res., 102, 14,087 (1997). Hudson et al., Simulation of radiation belt dynamics driven by solar wind variations, AGU Yosemite Monograph, in press, (1998). Lessard et al., Simultaneous satellite and ground-based observations of a discretely driven field line resonance, J. Geophys. Res., in press, (1998). Li et al., Simulation of the prompt energization and transport of radiation belt particles during the March 24, 1991, SSC, Geophys. Res. Lett., 20, 2423 (1993). Li et al., Energetic electron injections into the inner magnetosphere during the January 10-11, 1997, magnetic storm, Geophys. Res. Lett., 25, 2561 (1998). Paulikas, G. A., and J. B. Blake, Effects of the solar wind on magnetospheric dynamics: Energetic electrons at the synchronous orbit, Quantitative Modeling of Magnetospheric Processes, 21, Geophys. Monograph Series (1979). Reeves et al., The relativistic electron response at geosynchronous orbit during the January 10, 1997, magnetic storm, J. Geophys. Res., 103 17559 (1998a). Reeves et al., The global response of relativistic radiation belt electrons to the January 1997 magnetic cloud, Geophys. Res. Lett., 25, 3265 (1998b). Schulz, M., and L. J. Lanzerotti, Particle Diffusion in the Radiation Belts, Springer-Verlag, Berlin (1974). Selesnick, R. S., and J. B. Blake, Radiation belt electron observations from January 6 to 20, 1997, Geophys. Res. Lett., 25, 2553 (1998). Singer et al., Standing hydromagnetic waves observed by ISEE 1 and 2: radial extent and harmonic, J. Geophys. Res., 97, 3519 (1982). Southwood, D. J., Some features of field line resonances in the magnetosphere, Planet. Space Sci., 36, 503 (1974).