Simulations of radiation belt formation during storm sudden commencements

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. A7, PAGES 14,087-14,102, JULY 1, 1997 Simulations of radiation belt formation during storm sudden commencements M. K. Hudson, 1 S. R. Elkington, J. G. Lyon, 1 V. A. Marchenko, 1 I. Roth, 2 M. Temerin, 2 J. B. Blake, 3 M. S. Gussenhoven, 4 and J. R. Wygant 5 Abstract. MHD fields from globa] three-dimensiona] simulation of the gre t M rch 24, 1991, storm sudden commencement (SSC) re used to follow the trajectories of p rticles in guiding center test p rticle simulation of r di tion belt formation during this event. Modeling of less intense events during the lifetime of the CRRES s tellite, with similar morphology but less radial transport and energiz tion, is lso presented. In all c ses na]yzed, solar proton event w s followed by n SSC, le ding to the formation of new proton belt e rthw rd of solar proton penetration. The effect on p rticle energiz tion of v rying solar wind nd model pulse p r meters is investigated. Both seed population of solar protons nd the SSC shock-induced compression of the m gnetosphere re necessary conditions for the formation of new proton belt. The outer boundary of the inner zone protons c n be ffected by n SSC nd newly formed belt can be ffected by the ensuing or subsequent storm, which rn y occur in r pid succession, s was the c se in June nd July The cceler tion process is effective for both northward nd southward IMF, with more energiz tion nd inward r dia] transport for the southward c se for otherwise comparable solar wind p r meters, because of the initially more compressed m gnetop use in the southward c se. The inner boundary and stability of the newly formed belt depends on the rn gnitude of radial transport t the time of formation nd subsequent ring current perturbation of di b tic trapping. 1. Introduction Storm sudden commencement (SSC) compressions of the dayside magnetopause are driven by interplanetary shocks at 1 AU now generally attributed to coronal mass ejections (CMEs) [Gosling el al., 1990, 1991], rather than high-speed stream, corotation interaction regions which cause geomagnetic storms characteristic of the lite from July 25, 1990, to October 12, CRRES was placed in a low inclination (18.2 deg), geosynchronous transfer orbit with an apogee of 33,575 km and a perigee of 323 km, well instrumented for the study of energetic particle populations in the inner magnetosphere. Solar maximum produced solar energetic proton (SEP) events, defined as a > 10 parti- cles cm -2 s -x sr -x flux of > 10 MeV protons meadeclining phase of the solar ycle[tsurutani et al., sured by the geosynchronous GOES 7 spacecraft, during 1995]. A number of SSC events, including the great the 14-month lifetime of CRRES [Gussenhoven et al., March 24, 1991, SSC and ensuing geomagnetic storm, 1994]. Previous studies have focused on the formation of were observed during the lifetime of the CRRES satelnew radiation belts observeduring the March 24, 1991, storm [Mullen et al., 1991; Vampol and Korth, 1992; Blake et al., 1992a; Li et al., 1993; Hudson et al., 1995]. It is the purpose of this paper to examine the injection Department of Physics and Astronomy, Dartmouth College, of MeV particles on a drift timescale, as observed for Hanover, New Hampshire. the March event, for a range of parameters appropri- : Space Sciences Laboratory, University of California, Berkeley, ate for other SSC injection events during the lifetime California. s Space Sciences Department, The Aerospace Corporation, Los of CRRES. The March 24 storm was unique during the Angeles, California. CRRES mission for the magnitude of Dst (< -300 nt), 4 Phillips Laboratory, Hanscorn Air Force Base, Massachusetts. the flux and spectrum of energetic solar protons and in- 5School of Physics and Astronomy, University of Minnesota, ferred interplanetary shock speed, described below, and Minneapolis, Minnesota. the magnitude and short timescale of the SSC compressional magnetic pulse observed on the ground () 200 nt in less than I min) [Araki et al., 1997]. Each of the SEP Copyright 1997 by the American Geophysical Union. events defined by the above criteria had associated with Paper number 97JA it a subsequent SSC, which in some cases could be used /97/97JA to infer the interplanetary shock propagation speed. 14,087

2 14,088 HUDSON ET AL.: SIMULATIONS OF RADIATION BELT FORMATION In the next section we examine several smaller events, in addition to the March 24 SSC, in terms of their effects on MeV protons. We then introduce two types of numerical models for the electromagnetic fields associated with the SSC, along with simulations of the formation of new radiation belts and alteration of preexisting boundaries in the trapped proton population. We conclude with a discussion of the stability of such belts, brief mention of rapid electron radiation belt formation, described further elsewhere ILl et al., 1993], and consideration of the contribution which the drift time scale process analyzed here plays in radiation belt and geomagnetic storm dynamics. 2. March 24, 1991, and Weaker SSC Events In this section we present several examples of the formation of a new proton belt during the lifetime of the CRRES satellite which differ by the magnitude of the SSC, the flux and energy spectrum of accompanying solar protons, the radial location of the new belt, and its ensuing stability. The rapid formation of new radiation belts on a particle drift timescale due to SSC induced electric fields was well documented by observations from the CRRES satellite during the March 24, 1991, geomagnetic storm [Vampol and Korth, 1992; Blake et al., 1992a; Gussenhoven et al., 1993]. Plate i shows the fluence of > 30.9 MeV protons for orbits encompassing the March 24 event [Gussenhoven et al., 1994]. The Protel instrument on CRRES makes a 24-point spectral measurement covering the energy range MeV each second [Violet et al., 1993]. Plate i represents an average over L bins of 0.05 Rz width as the spacecraft sweeps through its 10-hour orbit. Note first the penetration of solar protons into L ~ 4 on the first two orbits (586 and 587) where they are prominent. The SSC occurred late in orbit 587 (measured perigee to perigee) when the spacecraft was inbound at L _ 2.5. A blue enhancement (reduced by spatial averaging) is just apparent on orbit 587 at this point, appearing much more prominent in an unaveraged format where the omnidirectional flux of > 20 MeV protons jumped by 3 orders of magnitude on the timescale of a few seconds [Blake et al., 1992a]. Next, note the formation of a new proton belt at L _ 2.5 extending well past the SEP event period, in fact lasting through the end of the CRRES mission [Blake et al., 1992b]. This event was unique during the CRRES mission in flux of such energetic solar protons, which reached almost 104 particles cm -2 sec -1 sr -1 at > 30 MeV on GOES 7. Plate 2 shows a second SEP event which began on January 31, Following the SSC at 1842 UT on February 1, which occurred when the spacecraft was outbound from perigee at L=1.65, a new radiation belt inside L=4 was seen in the 8.5 MeV Protel data (also in the 10.7 MeV Protel summary plot, Figure I of Gussenhoven et al. [1994]). In contrast with the March 24 event, the new proton belt does not extend much above 10 MeV. Also, the SEP source population as seen at GOES 7, shown in Figure lb, shows a much softer spectrum (steeper power law in flux vs. energy dependence) than the March 24 event (Figure la). The new proton belt persisted for over 35 days, through smaller SEP events evident in Plate 2. No upstream solar wind data were available for either the February i or March 24 event. An interplanetary shock speed of 1400 km s -x has been reported for the March 24 event, based on timing between the assumed solar precursor event and arrival of the SSC [$hea and Smart, 1993] and consistent with Ulysses observations at 2.5 AU [Phillips et al., 1992]. Similar timing considerations applied to the February i event and GOES X ray observations of a pair of flares on January 30 and 31 yield an interplanetary shock speed of order 1000 km s-1 for the pair of shocks producing the two spikes in > I MeV GOES protons on February 1. Because CRRES was at a low L value (1.65) at 17.6 MLT at the time of the SSC, the electric and magnetic field signatures were reduced even further for this smaller event, with essentially azimuthal GSE 5Ey ~ 5 mv m -x and compressional 5Bz ~-20 nt, as compared with the March 24, 1991, event where they were 20 mv m -x and 120 nt, respectively, at L-2.5 on the nightside [Wygant et al., 1994a]. Plate 3 shows a third SEP event which began on July 31, Following the SSC at 0741 UT on August 1, the formation of a new radiation belt between L=4-4.5 is apparent in the 10.7 MeV Protel data. Fol- lowing another moderate SEP event which occurred August 13-15, the newly formed belt disappeared. IMP 8 data are available for this event, showing a jump in the solar wind speed from 380 to 500 km s- x at the time of the SSC. June and July 1991 were extremely active periods at the sun, with a succession of flares which produced large fluxes of X rays at Ulysses [Kane et al., 1995], gamma rays detected by the Compton Gamma Ray Observatory [Trott. et et al., 1996] and SEP events seen by CRRES and GOES. The associated interplanetary shocks were of such intensity that they later produced radio emissions from the heliopause that were detected by Voyager [Gurnett et al., 1993]. Plate 4 shows the SEP events from May i to July 23, 1991, in the 10.7 MeV Protel data. A perturbation of the outer boundary of 10.7 MeV protons is apparent for the multiple SEP/SSC events in June and July [Gussenhoven et al., 1994]. SEP events can be identified in the GOES 7 data beginning on May 31, then on June 4, seen in Figure 2, followed by a pair of SSCs on June 7 and 9, and two more SEP events beginning on June 11 (SSC at 1012 UT on June 12) and June 15 (SSCs at 1019 and 1922 UT on June 17). All SSCs noted satisfy the NOAA A Quality criterion, defined as very remarkable, versus B Quality (unmistakable) and C Quality (doubtful). IMP 8 data available from the National Space Science Data Center for the discussed events are summarized in Table Analytic and MHD SSC Field Models A model for rapid acceleration of particles on the SSC and drift time scale has been applied to electrons ILl et

3 HUDSON ET AL.' SIMULATIONS OF RADIATION BELT FORMATION 14,089 PRO 30.9 te¾ Fmt,oas ?.,3 Plate 1. Proton fiuence in 30.9 MeV channel of Protel instrument on CRRES [Violet et al., 1993], averaged over 0.05 RE L bins for each 10-hour orbit from March 16 to April 10, 1991 [Gussenhoven et al., 1994]. Encompasses major solar energetic proton (SEP) event beginning on orbit 586 and SSC on orbit 587 (March 24, 1991), with formation of new radiation belt around L:2.5. ß al., 1993] and protons [Hudson ½t al., 1995], reproducing and neglects the radial component which is included many features of the new radiation belts formed around L 2.5 during the March 24 event, for example, drift echoes associated with acceleration over a limited range in the MHD model. Faraday's law determines B ( ), which is added to a background dipole magnetic field in the analytic model. The two exponentials in (1) deof longitude, a peaked energy spectrum for electrons scribe inbound and outbound pulses which superimpose around 15 MeV, and a broad fiat spectrum of protons to approximate compression and relaxation of the magfrom 20 to 40 MeV at the observed L values, within a netosphere. In equation (1) the phases of the inbound few drift periods of the injection. The primary source and outbound pulses are = [r + vo(t- tpa)]/d and for the new proton belt is the SEP population which rl = [r- vo(t- tra+ td)]/d, respectively, where v0 depenetrates into about L:4, ahead of the interplanetary notes the pulse propagation speed and d determines its shock producing the SSC. The source population for the width. c (> 0) describes the local time dependence new electron belt is the electron outer zone, which has a of the electric field amplitude, which is largest at much steeper power law energy spectrum than the solar tra = ti q-(care/vo)[1- cos( b- b0)] represents the protons. The induction electric field associated with shock compression of the dayside magnetosphere is responsible for the rise in fluxes of both protons and electrons at lower L values by several orders of magnitude on a drift timescale. The analytic form assumed for that electric field in the model of Liet al. [1993] is Ew-- E0[lq-cx cos( b- b0)] (e-ti2-c2e -n2) (1) where 4 is a unit vector pointing eastward. This model includes only the azimuthal electric field perturbation longitudinal time delay of the pulse from b0 to other local times where ca determines the magnitude of the delay; ca determines the partial reflection of the pulse, td = 2.1 RE/Vo indicates that the reflection occurs at r = 1.05 RE in Earth radii and ti is the initial reference time. At t=0 the pulse maximum is at about 25 RE at b0, and it reaches 10, 1.05, and 10 RE again at 48, 76, and 105 s, respectively. When the pulse is assumed to strike the magnetopause at 1500 MLT, in modelling the March 24, 1991, event, results are consistent with the arrival times of newly accelerated electrons and protons observed at CRRES [Blake et al.,

4 14,090 HUDSON ET AL.: SIMULATIONS OF RADIATION BELT FORMATION PP I, ley Fmt, n,s m nil m &, m,, '9m{ n m in in m[ ' n an..1 m m m m m I I - m -- m I.- -m m m - 4C0 47o 480,t ,.5{' ' _50 Orbit Plate 2. Proton fluence in 8.5 MeV channel of Protel instrument on CRRES, same format as Plate 1, for orbits 455 to 555, encompassing an SEP event, SSC and formation of new proton belt on February I (orbit 465). 1992a]. Only the drift phase of accelerated particles is affected by a different choice of 0 in the analytic model. The pulse parameters used by Liet al. [1993] for electrons and Hudson et al [1995] for protons for this event were E0-240 mv m -, Cl - 0.8, c2-0.8, ca - 8.0, v km s - ti=80 s q50-45 ø and d-30,000 km. The amplitude E0:240 mv m - assumed for the March 24 event was based on extrapolation of the measured electric field on the nightside at the location of the CRRES satellite [Wygant et al., 1994a], and their suggestion that this magnitude was required to explain particle energy gain by tens of MeV for outer zone electrons initially in the 1-9 MeV range. This model, including time-varying B 0, reproduced the electron drift echoes observed on CRRES [Blake et al., 1992a] in remarkable detail, while Hudson et al. [1995] reproduced observed proton drift echoes in the MeV channel reported by Blake et al. [1992a] using the same field model and a combination of solar and inner zone proton source populations. In section 4, we will show results from varying parameters of the analytic model to simulate weaker proton belt formation events such as seen in Plates 2 and 3. Electromagnetic fields from MHD simulations of interplanetary shock impact on the magnetosphere [Lyon et al., 1994] have now been used to push particles in the equatorial plane using guiding center equations of motion [Hudson et al., 1996a]. Figure 3 shows the az- imuthal electric field time history from two MUD simulations at four radial locations for northward (Figure 3a) and southward (Figure 3b) IMF conditions, and a solar wind speed of 1000 km/s. The MIlD simulations begin with a steady solar wind speed of 400 km s - and density of 5 cm -a. A shock is introduced with a jump in solar wind speed to 1000 km s - (directed 15 ø off the Sun-Earth line, producing a shock front at 20ø), a density increase to 20 cm -a and jump in Bz from-2 to -8 nt in the southward case and, likewise by a factor of four, from 5 to 20 nt in the northward case. In both cases there is about a factor of 25 increase in solar wind pressure. An equilibrium magnetosphere was formed by running the MIlD simulation for 20 min of real time at the nominal solar wind values before introducing the shock parameters at the upstream simulation boundary of 25 RE, with parameters chosen to satisfy Rankine-Ilugoniot conditions for a strong shock, whence the factor of four jump in solar wind density and magnetic field strength [Kantrowitz and Petchek, 1966]. A smaller magnitude of Bz is assumed in the southward case because the initial location of the magnetopause would be further compressed relative to the northward case for larger values. A Kp:3 model plasmasphere is included [Moore et al., 1987], which produces the initial Alfvdn speed profiles shown in Figure 4, just prior to shock arrival at the magnetopause. The steep decrease in Alfvdn speed between L=4 and 6 is due to

5 HUDSON ET AL.' SIMULATIONS OF RADIATION BELT FORMATION 14,091 SSC o: 542 UT ! 10o MAR 19 MAR 20 MAR 21 MAR 22 MAR 23 MAR 24 MAR 25 MAR SSC 1847_ UT 103, 102 1oo 10-!! 1',!11 "1 I 28 JAN 29 JAN 30 JAN $1 JAN 01 FEB 02 FEB 03 FEB 04 FEB Figure 1. GOES 7 energetic proton differential flux at geosynchronous orbit foi 1991 dates shown, with threshold detectors at energies indicated. (a) Note rise in SEP flux on March 23 and at time of storm sudden commencement (SSC) on March 24, (b) Weaker SEP event with rise in flux on January 31, followed by pair of SSCs on February 1, 1991, with NOAA A Quality SSC occurring at 1842 UT. plasmaspheric density. The spatial grid of the fields is interpolated to 0.2 Rz by 7.50 in the equatorial plane, with a time step of 1 s in the MHD code. The inner boundary is at L=1.8, with field-aligned currents mapped to an ionosphere with uniform conductance of 5 mhos [Fedder and Lyon, 1995]. MHD fields plotted in Figures 3 and 4 illuminate some short_comings of the analytic model, which assumes a constant pulse velocity and largest amplitude at highest L values, with a reduced amplitude at lower L values due to interference between the incident pulse and the pulse reflecting at r RE. The MHD simulation incorporates a plasmasphere, affecting both the pulse velocity which tracks the Alfvdn speed profile shown in Figures 4a and 4b and pulse amplitude as a function of L shown in Figures 3a and 3b. The main effect on am- plitude is due to focusing as the pulse moves from weak to strong background, predominantly dipolar magnetic field. However, the plasmasphere provides some shielding with a reduction in electric field amplitude at L-5 and increase again at L=3 due to focusing. Wygant et al. [1996] have shown a statistical tendency for storm associated electric fields directly measured by CRRES to be larger for L-2-4 than at higher L values. Other features of the analytic model can be varied by changing parameters, for example, fixed pulse velocity, width,' and maximum amplitude E0. We have varied the latter in section 4 in modeling weaker events where protons remain outside the plasmapause. The analytic model produces a bipolar azimuthal electric field pulse due to the compression and relaxation of Bz (dipole direction in the equatorial plane) inside the magnetopause. Figure 3 shows that in the MHD simulations the magnetopause moves inside geosynchronous orbit for the chosen parameters, with the electric field assuming the interplanetary Vsw x B value at L0-7 and 9 (also at L0--6, not shown) after a single versus bipolar oscillation. The azimuthal field E produces inward (and outward) (de)acceleration when applied to a test particle, changing the particle energy while conserving the first adiabatic invariant. The damped oscillations within the plasmasphere have roughly the same period as seen on CRRES for the March 24 event [Wygant et al., 1994a] and may correspond to a characteristic (cavity mode) oscillation of the region between the ionosphere and plasmapause, with n--1 and m--2 radial and azimuthal mode numbers apparent in the simulation [Hudson et al., 1996b].

6 , r 14,092 HUDSON ET AL.' SIMULATIONS OF RADIATION BELT FORMATION $$C 0337 UT $$C 2228 UT S$C 0040 UT, z 10! 10o 10-! 0.'5 JUN 04 JUN 05 JUN 06 JUN 07 JUN 08 JUN 09 JUN 10 JUN S$C 1716 UT $SC UT o! 10 o 10-] 10 JUN 11 JUN ]2 JUN 13 JUN 14 JUN 15 JUN 16 JUN 17 JUN Figure 2. GOES 7 energetic proton differential flux, same format as Figure 1: (a) June 3 to June 10, 1991, and (b) June 10 to June 17, NOAA A Quality SSCs are indicated universal time. 4. Guiding Center Test Particle Guiding center test particle simulations have been Simulations performed using the analytic model for a smaller induction electric field value than E0=240 mv/m used to simulate the March 24 event [Liet al., 1993; Hudson The relativistic guiding center equation of motion, et al., 1995]. While the March 24 event was characsetting vii=0 in the equatorial plane, is [Northrop, 1963] terized by a very fiat spectrum for solar protons (Figure la), the August 1, 1990, and February 1, 1991, - x (-ce + M CvB, events were characterized by a W -x to W -2 power law by the time the SSC hit the magnetosphere (see Figwhere Ew is the wave induction electric field given either ure lb). The spectrum is flatter at earlier times for these weaker events, since the most energetic protons by (1) or MHD simulation output, x = BIB is a unit vector along B, B is the total magnetic field strength, appear to be accelerated when the shock is closer to the 7 = (W + moc2)/moc 2 is the relativistic energy factor, Sun, and have flushed through the magnetosphere by the time of the SSC, in contrast to the March 24 event. W is the particle's kinetic energy, Mr - p}/2mob is the The power law of the source population is imposed afrelativistic adiabatic invariant and pñ - 7mov is the ter protons are accumulated in L energy bins at the particle's perpendicular momentum. The smaller radial end of the simulations. Plate 5a shows a W -2 input electric field component neglected in the analytic model solar proton source population which is used to simuis one fourth to one third the value of E outside the late the weaker events (contrast with Figure 2 of Hudplasmasphere in the MHD simulation. The adiabatic son et al. [1995], which simulates the March 24 event change in energy along the ion trajectory R(t) is mc with a W ø'3 solar proton spectrum). A different source times the relativistic factor population is used than of Hudson et al. [1995], to in- 7(t) mo c2. (3) sure a smoother variation in flux with L. Energy values in the simulation are binned in 5 % increments starting from 0.25 MeV for the analytic field runs and from

7 HUDSON ET AL.' SIMULATIONS OF RADIATION BELT FORMATION 14, PR0 10.? MeY Fmt.ot s l 1.5.,... œ- Orbit. Plate $. Proton fluence in 10.7 MeV channel of Protel instrument on CRRES, same format as Plate 1, for orbits 10 through 75 (July 29 through August 25, 1990), encompassing an SEP event, SSC, and formation of a new proton belt on August 1, 1990 [Gussenhoven et al., 1994]. 1.5 MeV for the MHD field driven simulations (shown to the March 24 event [Gussenhoven e! al., 1993]. The in Plate 5a). Three source populations corresponding source spectrum is cutoff at 25 MeV since more enerto more energetic solar protons which penetrate deeper into the magnetosphere, less energetic solar protons and inner zone protons are described by different energy spectra and cutoffs. The inner zone protons are simgetic protons do not contribute to the new proton belts seen in Plates 1, 2, or 3. An induction electric field amplitude of 240 mv/m, decreasing as the pulse spreads azimuthally along the ulated with energy W < (4.5/L) 5 in MeV. Inside this flanks of the magnetosphere according to (1), produces energy range, the flux is a W -5 power law in energy a proton belt extending into L _ 2.5 in the energy range and depends on a radial distance as 10 -ø'9œ. The solar MeV, as observed on CRRES for the March 24 protons are characterized by two cutoff energies used to model the energy dependent penetration to lower L values, with the bulk concentrated above L=5.5 for enevent [Hudson et al., 1995]. Plates 5b and 5c show results from the analytic model for E0=20 and 40 mv m-1 respectively, with other parameters the same as given ergies > 10 MeV. The highest flux population is initial- above for simulations of the March 24 event. Plate 5 ized with W > (8.5/L) 7, and the remaining (lower L penetrating) protons are simulated with W > (6.5/L) 6. The difference between the two solar proton fluxes is indicates that an E0=40 mv m -1 field can move solar protons inside L=4 from L=5-6 and produce enhancements up to energies of around 10 MeV. A key fea- one order of magnitude. The flux of both solar proton populations is assumed to have a W -2 spectral dependence, in contrast with the flatter spectrum used to simulate the March 24 event. There is a numerical factor x 105 to insure that the inner zone flux is stronger in absolute numbers than the solar proton flux, consistent with average CRRES observations prior ture of the energization process is the azimuthal propagation of the pulse, which synchronizes with proton or electron drift motion over a limited range of particle energy [Hudson et al., 1996a]. Brautigam et al. [1995] have varied the preceding pulse model parameters in studying a weaker electron injection event in August 1991, finding good agreement with MeV

8 14,094 HUDSON ET AL.: SIMULATIONS OF RADIATION BELT FORMATION Plate 4. Proto.n flu ence in 10.7 MeV channel of Protel instrument on CRRES, same format as Plate 1, for orbits 680 to 880 (May 1 through July 23, 1991). There is a decrease in maximum L.of 10.7 MeV pr~tons on orbi~ 7.65 (June 4-5)_, and i~crease on orbit 783 (June 12), coincident with SSCs noted m text. A s1m1lar decrease m maximum L was seen on orbit 856 (July 13) [Guss enhoven et al., 1994]. electron measurements by reducing the pulse velocity, as well as amplitude, and increasing pulse width relative to the parameters used to model the stronger March 24 event. 5. MHD Field Driven Simulations Following particle trajectories in the MHD fields requires interpolation of field quantities to the location of the guiding center, which is carried out using a threepoint quadratic spline [Press et al., 1986]. Unlike the analytic model, the MHD fields extend to a magnetopause where B reverses for the southward IMF case. A stopping criterion has been applied to.protons when B becomes so small that the guiding center equations of motion are invalidated. The stopping criterion fol-. lows from the gyrocenter approximation requirement that the Larmor radius be smaller than the magnetic field gradient scale length, (\7 ln B)- 1. Expanding this inequality, a proton is removed from the simulation if the following condition is not satisfied: ~W(W + 2mc 2 ) < eb(\7 ln B)- 1. (4) Plates 6a and 6b show the flux of protons at the end of the time series shown in Figure 3, driven by MHD fields for northward and southward IMF cases. The relative flux versus energy and L shell is plotted from an intial population of 459,360 protons, with a flux accumulation time in a given energy-l bin which exceeds one full drift period for the minimum energy plotted (1.5 MeV), normalized by the drift period at that energy. Thus flux is drift averaged in this plot. In weighting particle flux j (cm- 2 s- 1 ) based on initial energy, we assume that the distribution function is conserved along the trajectory, therefore that flux divided by energy is conserved according to Liouville's theorem. Each test particle which remains in the simulation domain contributes more or less to the final distribution depending on whether it was initially at lower or higher energy, as well as its initial L value, according to the flux weighting scheme described in section 4, imposed at the end of the run. Thus one test particle represents many, and how many is a function of its initial location in energy-l space. Since some particles are stopped by the nonadiabaticity criterion ( 4), absolute flux is not determined, but mapping factors such as the L- 2 increase in flux due to spatial focusing are preserved, along with the first adiabatic invariant. Most of the acceleration occurs during the first (negative) oscillation of Eq,, as is apparent in single particle trajectory plots [Hudson et al., 1995,

9 HUDSON ET AL' SIMULATIONS OF RADIATION BELT FORMATION 14,095 Table 1. A Summary of the IMP 8 Data for the NOAA "A" Quality SSCs Discussed in the Text Storm Sudden Commencement Date Time, UT V,,, km s - n, cm -3 AB, nt Kp Dst, nt August 1, August 15, 1990 ~ February 1, na na na March 24, na na na May 31, June 4, June 12, na na June 17, June 17, June 30, July 6, na na na July 8, na na July 12, na na na July 19, na na na 4-50 August 18, Solar wind velocity V w, ion density n, change in the magnetic field amplitude over the SSC, AB, and geomagnetic index Kp are given at the time of the SSC, while minimum Dst for the ensuingeomagnetic storm is given. In a number of cases, the data were not available (na). 1996a, b]. Substantially more protons are stopped for Plate 6b to reproduce the March 1991 event, while Plate the southward IMF case (40.6 % due to nonadiabatic- 6c corresponds to a stronger event. We have restricted ity, unweighted by choice of power law, while another 6 % leave the simulation spatial domain of L= ) the particle simulation domain to L > 2.3, 0.5 RE outside the inner boundary of the MHD simulation at. than for the northward IMF fields (21.8% and 15.7 % L-1.8, where the MHD fields are well behaved. This in the same categories). Of those stopped, almost all limits the contribution of inner zone protons to the inoriginate outside L=7. Those protons lost from the sim- ner edge of the new proton belt, thus proton drift echoes ulation spatial domain are primarily lost from the outer reported by Blake et al. [1992a] are not yet well reproboundary, well outside the final magnetopause location. duced by the MHD field model. However, the new pro- Comparing the northward and southward IMF cases, ton belt structure beyond L=2.5 seen in Plates 6b and more protons are accelerated into the 20 to 40 MeV 6c is more consistent with Protel measurements from range in the southward case, with peak flux between the orbit following injection [Hudson et al., 1996a, b, L=3-4, than in the northward case. Increasing the solar 1997] than results from the analytic model [Hudson et wind velocity in the MHD simulations (1400 km s -1), with other field parameters the same as for Plate 6b, al., 1995]. It is most likely that the IMF was southward for the and a power law appropriate for the March 24 solar March 1991 event because of the strength of the ensuproton source spectrum, W ø'a, yields results plotted in ing geomagnetic storm, which reached a Dst of-300 nt. Plate 6c (see Hudson et al. [1996a] for corresponding Comparing Plates 6a and 6b for a solar wind speed of field data). Protons are accelerated inside L=2.5 in this 1000 km s -, note that the outer boundary extends to a extreme case, to higher energies than seen in Plate 6b, higher L value in the case of northward IMF, primarily with 56.8 % stopped due to the nonadiabaticity crite- because of the nonadiabaticity criterion (4) which rerion (4) and 4.9 % lost from the simulation spatial do- moves a larger fraction of protons at higher L values in main. The reason for the much larger number of nona- the southward case. Finally, the gap between inner zone diabatic protons in the case of greater solar wind speed and solar protons, and the energy dependent decrease and southward IMF is that the magnetopause is more in flux with L in the source population (Plate 5a), is compressed both by greater solar wind speed and by apparent in all three final flux plots shown, as well as enhanced reconnection for southward IMF. Thus more Plates 5b and 5c. protons find themselves in a weak magnetic field region during the course of the southward IMF or greater solar wind speed simulation. Comparison with CRRES Protel data indicates that the March event was intermediate between Plates 6b and 6c in strength of induction electric field produced by the SSC (E4 reached 250 mv m- at L-4.5 on the dayside for the MHD fields 6. Discussion 6.1. Injection Mechanism The March 24, 1991, SSC demonstrated that new radiation belts can form on the MeV particle drift used to produce Plate 6c, see Hudson et al. [1996a, timescale, which coincides with the SSC timescale, or Figure 2]). Protons are not transported to low enough tens to a few hundred seconds, in contrast to the hours L values and correspondingly high enough energies in to days of the geomagnetic storm. Other smaller scale

10 14,096 HUDSON ET AL.' SIMULATIONS OF RADIATION BELT FORMATION L = 3 _ 0.05 o.oo-.,... L =9 - i',.i... '... '" '" [i; i. _ , I, I I ; I ;,,, i... I O time (s)...,...,/,,,,...,...,...,... =3 _ = =. -=- ' _ 't t.,'...' _..." / _ - I".j - -o.:o -,,,/, I,,, I I I,, I... I... ' O time (s) ' alent energy. A similar plot has been made for the analytic model of Li ei al. [1993] for electrons [Ginei et al., 1994]. There is a range of optimum Mr for minimum L (maximum energization) for both protons and electrons. Protons (electrons) which are drifting westward (eastward) at a speed which optimizes the interaction time with the pulse undergo the greatest acceleration. The pulse simply pushes cold plasma in and then out again, while very energetic particles (> 25 MeV protons and > 50 MeV electrons) are hardly affected by the pulse as they pass through it [Liet al., 1993, 1996; Ginei et al., 1994]. The particle drift includes both gradient B and E x B contributions in the equatorial plane. The electric field component E s produces inward (and outward) radial motion, while the generally smaller Er component, neglected in the analytic model, produces azimuthal acceleration. The gradient B drift actually reverses direction where the pulse magnetic field gradient exceeds that of the primarily dipolar background field, allowing more energetic particles whose drift motion is dominated by this energy-dependent drift component to stay longer in the region where the pulse amplitude is large [Hudson ei al., 1996b]. Note in Figure 5 the concentrated final L range for both protons and electrons undergoing maximum acceleration. This produces the greatly enhanced fluxes observed immediately following the SSC [Blake et al., 1992a], which cannot be accounted for simply by accelerating particles on nearby drift shells, for example, inside L=5 [Li ei al., 1993]. Figure 3. Azimuthal electric field component versus time at four radial locations at noon in MHD simulations ES, qb0 = 0 ø for (a) northward and (b) southward interplanetary magnetic field (IMF) cases described in text. In both cases the solar wind speed was increased from a nominal value of 400 to 1000 km s- x to produce an interplanetary shock which impacts and compresses the dayside magnetosphere = ' ' T 12 T ß.. 2,,, 4,,, 6,,, 8,.. 10.,. events during the lifetime of the CRRES satellite show radml distance (Re) 12 similar morphology, with less radial transport and energization. The induction electric field which accompanies magnetopause compression transports particles radially inward, increasing energy with conservation of the first adiabatic invariant. Protons which undergo maximum radial transport and acceleration stay well ahead of the magnetopause as it moves inward, and thus remain adiabatic, as described by equation (4). The mechanism is resonant over a range of initial energies, or equivalent magnetic moments, such that protons (or electrons) f ''' -- T= b t gradient-drifting either too slowly or to too fast relative to the azimuthal spreading of the pulse do not spend 0 an optimum amount of time in the region of maximum rodml dis t6o nce (Re) 8 pulse amplitude. This effect is seen in Figure 5, a plot of the minimum L value reached by any proton (Figure 5a) Figure 4. Alfvdn speed versus radial location at three or electron (Figure 5b) pushed by the MHD fields used different local times indicated, after shock parameters to produce Plate 6c (1400 km/s solar wind shock speed), have been introduced but before the shock hits the magstarting with a ring distribution in longitude, all at the netopause for (a) northward and (b) southward IMF same intial L shell and magnetic moment Mr, or equiv- cases described in text.

11 ß ß,, HUDSON ET AL.' SIMULATIONS OF RADIATION BELT FORMATION 14, ,, i... i... i,, M,. (10'MeV/O) Figure 5. Plot of minimum L value reached by any (a) proton and (b) electron in a ring initially distributed uniformly in longitude, all at the same initial L shell and magnetic moment Mr. the March event, inner zone protons were also affected and underwent drift phase bunching and radial redistribution [Hudson et al., 1995]. In the absence of an adequate source population, Gussenhoven et al. [1994] have suggested that the SSC may simply perturb the outer boundary of inner zone protons. Examination of Dst for the active June-July 1991 period leads to the following alternative interpretation of the boundary variations seen in Plate 4. A drop in flux inside L-3 occurred on June 5 (orbit 767) when the magnetic field was disturbed by buildup of the ring current reflected in Dst. This depletion in flux was filled in by the SSC injection event on June 12 associated with the highest solar wind speed shock of injection events found during the lifetime of CRRES (850 km s- ), excluding March 24, Subsequent depletion events in Plate 4 were associated with the ring current injections indicated by Dst buildup on July 9 and 13 [Gussenhoven et al., 1994, Figure 6]. As noted by Gussenhoven et al. [1994], there was no significant solar proton source population for the July 8 SSC, which might otherwise have led to injection. Variation in the trapped proton outer boundary in Plate 4 is due to a combination of SSC produced injections and ring current associated depletions. Hudson et al. [1997] have suggested that ring current buildup perturbs the curvature gradient scale length sufficiently to destroy adiabatic trapping as the ratio of ion gyroradius to the magnetic scale length becomes ~ 20 % (a) analytic model The analytic model demonstrates the basic mechanism and electric field amplitude required (E0-40 mv m - ) for radial transport by i to 2 Rs inside the SEP penetration boundary. Plate I shows radial transport from a cutoff at L=4 into L=2.5 for the March event at 30.9 MeV. For the February I event, the SEP source population is less energetic, as seen in Figure 1, than the March event. Consequently, it does not extend radially inward as far as the March source population before the SSC occurs, and the weaker SSC results in less radial transport to produce the new belt. A similar scenario can be inferred for the August 1, 1990, event. The correlation between magnitude of SEP events for very energetic solar protons (> 30 MeV) and interplanetary shock speed, both inferred and measured, has been well established [Cliver et al., 1990]. Overall, a high-speed interplanetary shock acts as a double hammer on the magnetosphere, first in preloading an energetic, low L- penetrating solar proton population, then with further acceleration in perpendicular energy to form a trapped population when the SSC arrives Boundary Perturbations A seed population of MeV particles is a necessary condition for the formation of a new radiation belt, with outer zone electrons [Liet al., 1993] and SEP protons [Hudson et al., 1995] satisfying the resonance criterion apparent in Figure 5. In the extreme case of F "' time (seconds) 10 "-"." : ' :.' 10 " 2o! lo o (b) mhd model time (seconds) ß :,, -," o' 10.. Figure 6. Plot of proton energy I/V and trajectory in the equatorial plane (a) for analytic field model and (b) for 1400 km s - solar wind shock velocity MHD fields, with intial W=2 MeV at L=9.

12 14,098 HUDSON ET AL- SIMULATIONS OF RADIATION BELT FORMATION [Schulz, 1991; Chirikov, 1987]. Thus a proton population trapped at L=3-4, as in Plates 2 and 3, near the peak of the stormtime ring current, may survive the in- jection (SSC triggered) storm, only to be removed by a later storm. A comparison of Plates 5b and 5c shows the dependence of the penetration depth of solar protons on the induction electric field amplitude, also evident in com- paring the MHD simulation results for southward IMF in Plates 6b and 6c. In simulations using the analytic fieid model, E0 is varied explicitly, while in MHD simulations the solar wind shock velocity increase (from 1000 km s - to 1400 km s -, in caseshown) produces a corresponding increase in the maximum azimuthal electric field amplitude from 110 mv m- in the 1000 km s -x case (Figure 3b) to 250 mv m -x in the 1400 km s -x case [see Hudson et al., 1996a, Figure 2]. Other parameters of the analytic field model have been varied in studying a weaker electron injection event on August 18, 1991 [Brautigam, 1995]. Good agreement was obtained with MeV electron measurements on CRRES by reducing the model magnetosonic pulse speed in the magnetosphere from the value used by Liet al. [1993] of 2000 km s - to 1250 km s -x, increasing the pulse width d to 60,000 km, reducing the reflected pulse amplitude determined by the parameter c2 in equation (1) from 0.8 to 0.45, reducing E0 to 8 mv m -x and assuming that the shock hit the magnetosphere at noon Comparison of MHD and Analytic Models Figure 6 compares both the trajectory and energy time history of a proton starting at the same energy W=2 MeV and L=9 in the analytic field model (c2=0.8, along with other parameters the same as Liet al. [1993]) and pushed by the MHD fields of the 1400 km s -x simulation (Plate 6c). In the MHD case (Figure 6b) one sees minor oscillations in energy at the same period as the fields, which extend in time beyond the bipolar phase modelled by equation (1), with no net energy loss as seen in the analytic case (Figure 6a). Proton simulations of the March event have been performed with a reduced reflection coefficient c2 [Hudson et al., 1994], however the protons appear to be better modelled at L ) 2.5 for E0 > 100 mv m - with the MHD simulations than with the analytic field only approximated by superposition of incident and reflected solitons of opposite polarity in equation (1). The MHD simulations include the secondary oscillations and radial dependence of the magnetosonic pulse velocity (cf. Figure 4) and amplitude (Figure 3). The analytic model assumes a constant pulse velocity and decreasing amplitude with decreasing L due to interference between the incident and reflected pulse near the inner boundary. Figure 3 shows that the pulse amplitude at L-3 can be as large as at L--7 in the MHD simulations, primarily due to geometric focusing of wave energy into a smaller volume superimposed on partial reflection off the plasmapause density gradient. For the smaller values of E Conclusion and 40 mv m -x used in simulating weaker events with the analytic model in Plates 5b and 5c, protons remain outside the model plasmasphere where significant change in MHD pulse velocity and amplitude occurs. Further, the excellent agreement between the analytic model field simulations of both strong [Liet al., 1993] and weak [Brautigam, 1995] electron acceleration events demonstrates the overall utility of this model for electron simulations. Electron simulations using he same input spectrum as used by Li et al. [1993] and the MHD fields described here have been performed and will be described separately. Overall, they are consistent with the analytic model results Distinguishing SSC Proton and Electron Injection and Ring Current Buildup A distinction between proton and electron acceleration by the SSC induced electric field comes from conservation of the first adiabatic invariant and the fact that electrons are relativistic while protons are not. Consequently, proton energy increases as L -3 while electron energy increases L - / moving radially inward. Thus protons gain more energy than electrons for a given decrease in L. Figure 5b shows a minimum L value for electrons of about L--2.3, slightly lower in L than for protons in Figure 5a, and consistent with particle measurements for the March event [Blake et al., 1992a]. The effect of the MHD pulse fields on electrons is essentially monotonic in L for those transported radially inward by the main SSC compression, and less so for protons which interact with the reflected component on the dayside where its amplitude is larger. Thus the new electron belt extends to slightly lower L values without significant outward transport due to a weaker interaction than protons with the reflected pulse component. This study focuses on the acceleration of radiation belt protons in the MeV energy range on their drift timescale measured in minutes, and contrasts with the build up of the storm time ring current on the time scale of hours, with peak flux in the hundred kev range [Chen et al., 1993, and references therein]. The ensuing radiation belt modification can last much longer than the ring current buildup and recovery cycle of several days. Thus it brackets in time the event defined as a geomagnetic storm, with its associated Dst perturbation [Tsuritani et al., 1995]. The newly trapped population may survive the injection storm, but not a subsequent one with larger Dst buildup [Hudson et al., 1997]. What was significant about the March 1991 event from the standpoint of space weather was the persistence of the new electron and proton radiation belts over many months. Once at such low L values, subsequent SSCs and ring current perturbations have a

13 HUDSON ET AL.- SIMULATIONS OF RADIATION BELT FORMATION 14,099 Proton Source Population 2 o 1o Energy (MeV) Solar proton flux 4O Total Proton Flux Total Proton Flux e Energy, MeV Energy, MeV E 0 = 20 mv/m; solar proton flux ~ W -2 E 0 = 40 mv/m; solar proton flux ~ W -2 Plate 5. Relative proton flux versus energy and L shell: (a) for input source population. There are two solar proton source populations described by energy cutoffs in the text, which model the energy dependent radial penetration depth of solar proton flux versus L; a third population models the inner zone. A W -2 power law is superimposed on the solar proton source populations, while a W - power law is used for the inner zone. (b) Flux versus energy and L shell after 300 s, averaged over AL=0.1 and AW=0 using input source population in Plate 5a and analytic field model described in text, with E0= 5 mv rn-l (c) Same as Plate 5b with E0=40 rnv m -1. smaller effect, so > 10 MeV electrons and tens of MeV protons are longlived. The primary loss mechanism at low L values appears to be radial diffusion and colligoing effect on restructuring radiation belt boundaries, spectra, and fluxes. Future work will include the consideration of off-equatorial mirroring particles in the MHD sional losses to the atmosphere for the protons [Schulz field simulations, which is expected to be of greater imand Lanzerotti, 1974], while slot region wave-particle portance for protons since the SEP source population interactions [L lons et al.; 1972; Albert, 1994] undoubt- is essentially isotropic, in contrast to the outer zone edly contributed to the more rapid decay at higher L seen for the electrons for the March event [Vampol and Korth, 1992]. The overall effect of smaller events on rasource population assumed in electron simulations [Li et al., 1993]. The significance of this mechanism for outer zone electron variability must also be examined diation belt dynamics over the long term remains to be relative to other mechanisms which characterize the inievaluated. However, it is clear both from the CRRES observations and modeling that moderate events which are quite common around solar maximum have an ontial decrease and subsequent enhancement of outer zone fluxes over the longer time scale of Dst evolution in a geomagnetic storm.

14 14,100 HUDSON ET AL.' SIMULATIONS OF RADIATION BELT FORMATION Total Proton Flux Energy (MeV) Northward IMF; Solar proton flux ~ W '2 Total Proton Flux Total Proton Flux 2 0 ' c Energy (MeV) Energy (MeV) Southward IMF; Solar proton flux ~ W '2 MHD fields; Solar proton flux ~ W ø'3 Plate 6. Flux versus energy and L shell after 500 s using input proton source population in Plate 5a and MHD fields in Figure 3, for (a) northward IMF case and (b) southward IMF case, with a solar wind shock speed of 1000 km s -. (c) Southward IMF case for a solar wind shock speed of 1400 km s- t and a W -ø'3 solar proton power law weighting, appropriate for the March 1991 event [Hudson et al., 1995]. Energy axis has been extended to 100 MeV for this case to coincide with the full range of the Protel instrument on CRRES. Acknowledgments. Work at Dartmouth was supported by AFOSR grant F , and at Dartmouth and Berkeley by NASA grants NAG and NAGW Work at the Aerospace Corporation was supported by the Air Force under contract Fo C Computations were performed on the SDSC and PSC Grays. We would like to thank NOAA SEC for providing the GOES 7 data and A Quality SSC list. The Editor thanks the referees for their assistance in evaluating this paper. References Albert, J. M., Quasi-hnear pitch angle diffusion coefficients: Retaining high harmonics, J. Geophys. Res., 99, 23,741, Araki, T., et al., The anomalous sudden commencement on March 24, 1991, J. Geophys. Res., in press, Blake, J. B., W. A. Kolasinski, R. W. Fillius, and E.G. Mullen, Injection of electrons and protons with energies of tens of MeV into L < 3 on March 24, 1991, Geophys. Res. Lett., 19, 821, 1992a. Blake, J. B., M. S. Gussenhoven, E.G. Mullen, and R. W. Filhus, Identification of an unexpected space radiation hazard, IEEE Trans. Nucl. $ci., 39, 1761, 1992b. Brautigam, D. H., Radiation belt electron dynamics dur- ing a magnetospheric compression event (abstract), Eos Trans. AGU, 76(d6), Fall Meet. Suppl., F945, Chen, M. W., M. Schulz, L. R. Lyons, and D. J. Gorney, Stormtime transport of ring-current and radiation-belt ions, J. Geophys. Res., 80, 690, 1975.

15 HUDSON ET AL.: SIMULATIONS OF RADIATION BELT FORMATION 14,101 Chirikov, B. V., Particle dynamics in magnetic traps, in Reviews of Plasma Physics, vol. 13, edited by B. B. Kadomstev, p. 1, Consult. Bur., New York, Cliver, E. W., J. Feynman, and H. B. Garrett, An estimate of the maximum speed of the solar wind, , O r. Geophys. Res., 95, 17,103, Fedder, J. A., and J. G. Lyon, The Earth's magnetosphere is 165 Rr long: Self-consistent currents, convection, mag- netospheric structure, and processes for northward interplanetary magnetic field, J. Geophys. Res., 100, 3623, Ginet, G. P., W. J. Burke, and J. Albert, An analysis of electron energization seen in simulations of the March 24, 1991, SSC (abstract), Eos Trans. A GU, 75(16), Spring Meet. Suppl., 305, Gosling, J. T., S. J. Bame, D. J. McComas, and J. L. Phillips, Coronal mass ejections and large geomagnetic storms, Geophys. Res. Lett., 17, 901, Gosling, J. T., D. J. McComas, J. L. Phillips, and S. J. Bame, Geomagnetic activity associated with Earth passage of interplanetary shock disturbances and coronal mass ejections, J. Geophys. Res., 96, 7831, Gurnett, D. A., W. S. Kurth, S.C. Allendoff, and R. L. Poynter, Radio emission from the heliopause triggered by an interplanetary shock, Science, œ6œ, 199, Gussenhoven, M. S., E.G. Mullen, C. Hein, J. Bass, and D. Madden, CRRES high energy proton flux maps, IEEE Trans. Nucl. Sci.,.iO, 1450, Gussenhoven, M. S., E.G. Mullen, and M.D. Violet, Solar particle events as seen on CRRES, Adv. Space Res., 1.i Hudson, M. K., A.D. Kotelnikov, X. Li, I. Roth, M. Ternerin, J. Wygant, J. B. Blake, and M. S. Gussenhoven, Modelling formation of new radiation belts and response to ULF oscillations following March 24, 1991, SSC (abstract), Eos, Trans. A GU, 75(.i.i), Fall Meet. Suppl., 538, Hudson, M. K., A.D. Kotelnikov, X. Li, I. Roth, M. Ternerin, J. Wygant, J. B. Blake, and M. S. Gussenhoven, Simulation of proton radiation belt formation during the March 24, 1991, SSC, Geophys. Res. Lett., œœ, 291, Hudson, M. K., S. R. Elkington, J. G. Lyon, V. A. Marchenko, I. Roth, M. Ternerin, and M. S. Gussenhoven, MHD/particle simulations of radiation belt formation during storm a sudden commencement, in Radiation Belts: Models and Standards, edited by J. F. Lemaire, D. Heynderickx, and D. N. Baker, Geophys. Monogr. Set., vol. 97, p. 57, AGU, Washington, D.C., 1996a. Hudson, M. K., et al., Modeling formation f new radiation belts and response to ULF oscillations following March 24, 1991, SSC, in Workshop on the Earth's Trapped Particle Environment, AIP Cony. Proc., vol. 383, p. 119, AIP Press, Woodbury, NY, 1996b. Hudson, M. K., V. A. Marchenko, I. Roth, M. Ternerin, J. B. Blake, and M. S. Gussenhoven, Radiation belt forma- tion during storm sudden commencements and loss during main phase, Adv. Space Res., in press, Kane, S. R., K. Hurley, J. M. McTiernan, M. Sommer, M. Boer, and M. Niel, Energy release and dissipation during giant solar flares, Astrophys. J., 6, 147, Kantorwitz, A., and H. E. Petchek, MHD characteristics and shock waves, in Plasma Physics in Theory and Application, p. 148, edited by W. B. Kunkel, McGraw Hill, New York, Li, X., I. Roth, I., M. Ternerin, J. R. Wygant, M. K. Hudson, and J. B. Blake, Simulation of the prompt energization and transport of radiation belt particles during the March 24, 1991, SSC, Geophys. Res. Lett., œ0, 2423, Li, X., M. K. Hudson, J. B. Blake, I. Roth, M. Ternerin, and J. R. Wygant, Observation and simulation of the rapid formation of a new electron radiation belt during March 24, 1991, SSC, Workshop on the Earth's Trapped Particle Environment, AIP Cony. Proc., vol. 383, p. 109, AIP Press, Woodbury, NY, Lyon, J. G., M. K. Hudson, J. A. Fedder, and C. C. Goodrich, Global MHD simulation of the March 24, 1991, SSC (abstract), Eos Trans. A GU, 75(.i.i), Fall Meet. Suppl., 539, Lyons, L. R., R. M. Thorne, and C. F. Kennel, Pitch-angle diffusion of radiation belt electrons within the plasmasphere, J. Geophys. Res., 77, 3455, Moore, T. E., D. L. GaJ]agher, J. L. Horwitz, and R. H. Comfort, MHD wave breaking in the outer plasmasphere, Geophys. Res. Lett., 1, 1007, Mullen, E.G., M. S. Gussenhoven, K. Ray, and M. Violet, A double-peaked inner radiation belt: Cause and effect as seen on CRRES, IEEE Trans. Nucl. Sci., 38, 1713, Northrop, T. G., The Adiabatic Motion of Charged Particles, Interscience, New York, Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, Cambridge Univ. Press, New York, Phillips, J. L., S. J. Bame, J. T. Gosling, D. J. McComas, B. E. Goldstein, E. J. Smith, A. Balogh, and R. J. Forsyth, Ulysses plasma observations of corona] mass ejections near 2.5 AU, Geophys. Res. Lett., 19, 1239, Schulz, M., The magnetosphere, in Geomagnetism, vol. 4, edited by J. A. Jacobs, p. 87, Academic, San Diego, Calif., Schulz, M., and L. J. Lanzerot ti, Particle Diffusion in the Radiation Belts, Springer, New York, Shea, M. A., and D. F. Smart, March 1991 Solar-terrestrial phenomena and related technological consequences, in Proc. Int. Conf. Cosmic Rays, œ3rd, Trottet, G., C. Barat, R. Ramaty, N. Vilmer, :I. P. Dezalay, A. Kuznetsov, N. Mandzhavidze, R. Syunyaev, R. TMon, and O. Terekhov, Thin target 7 ray line production during the June 1, 1991 flare, in Proc. High Energy Solar Physic Workshop, edited by R. Ramaty, N. Mandzhavidze, and X.-M. Hua, Am. Inst. of Phys., College Park., Md., Tsurutani, B. T., W. D. Gonzales, A. L. C. Gonzales, F. Tang, J. K. Arballo, and M. Okada, Interplanetary origin of geomagnetic activity in the declining phase of the solar cycle, J. Geophys. Res., 100, 21717, Vampola, A. K., and A. Korth, Electron drift echoes in the inner magnetosphere, Geophys. Res. Lett., 19, 625, Violet, M.D., K. Lynch, R. Redus, K. Riehl, E. Boughan, and C. Hein, Proton telescope (PROTEL on the CRRES spacecraft), IEEE Trans. Nucl. Sci., 0, 242, Wygant, J. R., F. Mozer, M. Ternerin, J. B. Blake, N. Maynard, H. Singer, and M. Smiddy, Large amplitude electric and magnetic field signatures in the inner magnetosphere during injection of 15 Mev electron drift echoes, Geophys. Res. Lett., œ1, 1739, 1994a. Wygant, J. R., J. B. Blake, M. Hudson, I. Roth, M. Ternerin, and H. Singer, Observations of global compressional MHD fluctuations in the inner magnetosphere by the CRRES electric and magnetic field instruments (abstract), Eos Trans. AGU, 75(.i), Fall Meet. Suppl., 538, 1994b. Wygant, J., M. Ternerin, F. Mozer, H. J. Singer, and M. K. Hudson, Experimental evidence on the role of the large spatial electric field in creating the ring current, paper presented at Chapman Conference on Magnetospheric Storms, AGU, Pasadena, Ca]if., 1996.

16 14,102 HUDSON ET AL.: SIMULATIONS OF RADIATION BELT FORMATION J. B. Blake, Space Sciences Department, The Aerospace Corporation, Los Angeles, CA S. R. Elkington, M. K. Hudson, J. G. Lyon and V. A. Marchenko, Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH ; e-maih M. S. Gussenhoven, Phillips Laboratory, Hanscorn Air Force Base, MA I. Roth and M. Ternerin, Space Sciences Laboratory, University of California, Berkeley, CA J. R. Wygant, School of Physics and Astronomy, University of Minnesota, Minneapolis, MN (Received May 1, 1996; revised October 30, 1996; accepted November 18, 1996.)