JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 104, NO. A7, PAGES 14,571-14,581, JULY 1, 1999

Electron pitch angle distributions following the dipolarization phase of a substorm: Interball-Tail observations and modeling

3 j A Sauvaud, 4 and P. Koperski 5 R. Smets, 1,2 D. Delcourt, . .

Abstract. We investigate Interball-Tail observations of electron pitch angle distributions after the dipolarization phase of a substorm. For 10 keV electrons we observe beamlike, coniclike, and perpendicularly peaked distributions at L -• 11, L • 9, and L • 7, respectively. We examine the efficiency of betatron heating and Fermi acceleration associated with adiabatic transport of the electrons during the substorm dipolarization phase. This dipolarization phase was modeled using transition between different Kp levels within a realistic magnetic field model. The calculations reproduce well the evolution of the high-energy electron flux in the parallel and perpendicular directions. They also reproduce well the pitch angle distribution observed by Interball-Tail at 10 keV, after the dipolarization phase. It is shown that Fermi acceleration is the leading process, compared to betatron heating. The production of the coniclike distributions is narrowly linked to the existence of a transition region between dipolelike and taillike magnetic fields, at about L • 9.

1. Introduction

A large amount of observations both from space and from the ground has been collected during substorm events. If magnetotail dynamics during substorms is now very well documented, the mechanism responsible for substorm onset is still unclear. Lui [1991] reviewed different theoretical models proposed so far and put for- ward a synthesis model. Up to now, even if the origin of reconnection in a collisionless plasma is not identified, the Near Earth Neutral Line (NENL) model of Hones [1979] is the most consensual one, and the one able to explain the largest set of observations. Analyzing more than 100 substorm events observed in the midtail by the Geotail spacecraft, Nagai and Machida [1998] placed the reconnection region between XGSM = --22 RE and XGSM =--30 RE in the premidnight plasma sheet.

One of the most impressive phenomena during sub- storms is the energetic electron precipitation in the au- roral ionosphere. These precipitations, observed dur- ing the expansion phase of substorms, must find their

•Centre d'•tude des Environnements Terrestre et Plan6taires, V61izy, France.

2Now at Laboratory for Extraterrestrial Physics, NASA Goddard Space Hight Center, Greenbelt, Maryland.

3Centre d'6tude des Environnements Terrestre et Planetaires, Saint- Maur des Foss6s, France.

4Centre d'6tude Spatial des Rayonnements, Toulouse, France. '•Space Research Center of Polish Academy of Sciences, Warsaw.

Copyright 1999 by the American Geophysical Union.

Paper number 1998JA900162. 0148-0227/99/1998 JA900162$09.00

origin in energization and/or pitch angle diffusion pro- cesses occuring inside the plasma sheet. Several mech- anisms have been proposed to fill the loss cone and en- sure these auroral precipitations. Kennel and Petschek [1966] showed that whistler mode noise leads to high- energy (above 40 keV) electron pitch angle diffusi6n in the near-Earth region, below L = 10 (L being the dimensionless parameter defined by Roedeter [1970]). Damping of the particle pitch angle can be responsible for their injection inside the loss cone, and precipita- tion in the auroral oval. Johnstone et al. [1993] re- visited the results of Kennel and Petschek [1966] and showed that there is no energy threshold limiting this wave-particle interaction. They accordingly proposed this mechanism as being responsible for the diffuse au- rora. On the other hand, discrete aurora associated with substorms are nonstationary and localized phe- nomena. Pitch angle diffusion stimulated by whistler mode noise can also occur but cannot be the only mech- anism responsible for discrete aurora. As dipolarization of magnetic field lines occurs on a very short timescale (a few minutes), Mauk [1986] put forward the enhanced dawn-dusk electric field and associated convection surge as an efficient ion energization mechanism in the mag- netic field direction. Taking into account nonadiabatic effects, Delcourt et al. [1990] demonstrated even larger energization rates. Using a self-consistent approach, Mauk [1989] showed that field-aligned potential drops of a few kiloelectronvolt can be generated. The exis- tence of such potential drops induces further parallel energization and can hence lead to particle precipita- tion in the auroral oval.

14,571

14,572 SMETS ET AL.' PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL

December 2, 1995

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Figure 1. (a)(b) and (c) X,Y,Z components and (d)total magnetic field as a function of time (between 0630 UT and 0930 UT) on December 2, 1995. GSM coordinates of the spacecraft are indicated at bottom. Substorm onset occurs at 0708 UTo

Nonadiabatic effects have also been shown to be an

efficient mechanism to ensure pitch angle scattering and fill the loss cone [see $ergeev et al., 1983; Chen and Pal- madesso, 1986; B•'chner and Zelenyi, 1989; Zelenyi et al., 1990; D½lcourt et al., 1996]. This essentially con- cerns the ions even if in highly stretched magnetic field topology like in the far tail, nonadiabatic effects can also modify the electron pitch angle distribution (PAD) [e.g., Schriver et al., 1998; Smets et al., 1998].

In this paper we present electron observations from the Interball-Tail spacecraft following the dipolarization phase of a substorm. We focus on the December 2, 1995, pass and examine the energetic (10 keV) electron flux evolution. We will show that at L ~ 11, the bulk of the plasma is observed along the magnetic field direction. At L ~ 9, energetic electrons are preferentially observed at intermediate pitch angles of about 30 ø . Closer to Earth, at L ~ 7, electrons are essentially observed in the

SMETS ET AL' PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL 14,573

direction perpendicular to the magnetic field. We pro- pose the adiabatic heating/acceleration occurring dur- ing field line dipolarization as being responsible for this anisotropy. This interpretation is supported by numer- ical calculations which reproduce well the Interball-Tail observations.

2. Observations

The Interball-Tail spacecraft was launched from Ple- setsk (Russia) on August 3, 1995. Its eccentric orbit allows exploration of the geomagnetic tail until 20 Re. With the orbit plane of Interball-Tail making a full rev- olution around Earth in 1 year, the satellite is located in the midnight sector every December of each year.

Figure 1 presents the evolution of the X, Y, and Z components and total magnetic field measured by the MIFM instrument (see Klimov et al. [1997] for a de- scription of the instrument) between 0630 UT and 0930 UT on December 2, 1995. In this paper we use the geocentric solar magnetospheric (GSM) coordinate sys- tem. From the beginning of the observation period until 0708 UT the total magnetic field is increasing, largely because of the enhancement of the X component. This corresponds to the end of a substorm growth phase dur- ing which the magnetic field lines become increasingly taillike. Substorm onset then occurs at 0708 UT. On a

timescale of a few minutes the X component of the mag- netic field sharply decreases, whereas the Z component increases. Equivalently, local magnetic field lines are rapidly dipolarized. The subsequent observation period corresponds to expansion (i.e., field line dipolarization

farther out in the magnetotail) and recovery phases of the substorm. Note the decrease of the X component of the magnetic field until 0820 UT and, after changing sign, the increase of this component due to spacecraft crossing of the magnetic equator. The Z component of the magnetic field is increasing from 0708 UT until about 0750 UT, and from then on smoothly varies un- til the end of the observation period. It must be noted that the characteristic evolution of the magnetic field components during substorms (i.e., stretching followed by relaxation) is here tempered by the spatial displace- ment of the spacecraft, from XGSM = 11.5 Re down to XGSM = 6.5 Re, Z•SM remaining approximately equal to 3

A notable feature of the substorm expansion phase is the earthward injection of energetic particles [see, e.g., $auvaud and Winckler, 1980]. Figure 2 presents the time evolution of 10 keV electron flux in the parallel (dotted line), and perpendicular (solid line) directions to the magnetic field measured by the ELECTRON in- strument (see $auvaud et al. [1997] for a description of the instrument). From 0630 UT until 0708 UT the magnetic field fluctuates, and, the electron flux in the three directions being approximately the same, there is no anisotropy. At the onset of the substorm (0708 UT) the three components of the electron flux drastically increase by about two orders of magnitude during the few minutes of the local dipolarization. This increase is observable at all energies above 500 eV even though it is most pronounced at the highest energies. From 0820 UT until approximately 0850 UT one can note that even if flux is noisy, its level in the parallel direction is larger

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Figure 2. Parallel (dotted line) and perpendicular (solid line) flux of 10 key electrons observed by Interball-Tail between 0630 UT and 0930 UT.

14,574 SMETS ET AL.: PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL

than in the perpendicular direction. However, at the end of the observation period this anisotropy reverses, the flux in the perpendicular direction becoming larger than the flux in the parallel direction.

The O- ß spectrograms, where O is the polar an- gle and ß is the azimuthal or spin an. ale, show the whole solid angle around the ELECTRON instrument on board Interball-Tail and allow us to study the evolu- tion of the electron PAD in detail. Plates la-lc present O- ß spectrograms obtained at 0828 UT, 0838 UT, and 0918 UT , respectively. In Plate 1, the logarithmic value of the flux at constant energy (10 keV) is color- coded, and the white crosses represent the +B and -B directions. Note that the time required to build ©- ß spectrograms is the spin period of Interball-Tail, which is about 2 min. In Plate l-a, at 0828 UT, the bulk of the electron plasma is observed along the direction of the magnetic field, giving a beamlike distribution. Plate l- b shows the O- <I> spectrogram measured at 0838 UT. It is clear that the direction parallel to the magnetic field is somewhat depleted, and the bulk of the electron population is observed at an intermediate pitch angle of about 30 ø, giving a ring-type distribution. Plate 1-c presents the O- • spectrogram measured at 0918 UT. The direction along the magnetic field is now totally depleted, and electrons are observed essentially in the direction perpendicular to the magnetic field.

This evolution in pitch angle is observed on a timescale of about 2 hours after the dipolarization of the magnetic field lines. Other Interball-Tail passes exhibit a similar evolution on a timescale of about 1-2 hours. In all cases

the transition to ring-like distributions is observed near L = 8. This suggests that these features are not tem- poral but are due to the spatial displacement of the spacecraft.

The behavior obtained at 10 keV in Plate i differs

from that observed at lower energy (500 eV). In the latter case, beamlike distributions are observed just af- ter the dipolarization of the magnetic field lines and persist during the whole observation period. Similar beamlike distributions are observed by CRRES [e.g., Johnstone et al., 1996] after the dipolarization of mag- netic field lines. In almost all the cases studied with

Interball-Tail data in December 1995, low-energy beams are observed from a geocentric distance of 6 RE up to 15 RE. Figure 3 presents a cut of the distribution function along the direction of the magnetic field for the December 2, 1995, pass (0800 UT). One can no- tice shoulders in the distribution function, which are indicative of mixing of different populations. The low- energy part of the distribution appears to be of iono- spheric origin, whereas the high-energy tail of the dis- tribution is composed of magnetospheric electrons (the high density value at very low energies corresponding to photo electrons produced at the surface of the space- craft). This assertion is supported by former studies of the ionosphere-magnetosphere coupling, which put for- ward the existence of such electron beams [see, e.g., Kan

et al., 1988]. In the following, we will not address the production mechanism of these low-energy beams and will focus on the highenergy part of the distribution (10 keV).

3. Modeling Approach

The Interball-Tail observations presented in section 2 were recorded close to Earth and after the dipolar- ization phase of a substorm. In this region the curva- ture radius of magnetic field lines is much larger than the electron Larmor radius, and electrons behave in an adiabatic manner. Note that using a large set of spa•cecraft data, Pulkkinen et al. [1992] showed that in some instances, the curvature radius of the magnetic field lines may become so small at XGSM "-• --15 RE (in the midnight sector) that the adiabatic approxi- mation is violated even for electrons. This hypothe- sis, however, remains highly controversial, and on the basis of numerous substorm observations, Lui [1996] ar- gued that in most cases the electron transport is adi- abatic. Moreover, since magnetic field lines are dipo- larized on a timescale of a few minutes and the bounce

period of 10 keV electrons is of a few seconds, mag- netic field lines remain nearly identical during one elec- tron bounce, and the longitudinal invariant is likely to be conserved during dipolarization. In the following we thus assume that the two first adiabatic invariants

are conserved for electrons during the substorm. Using an approach somewhat similar to that of Cowley and Ashour-Abdalla [1975] in a dipolar field, we investigate how the betatron heating (resulting from conservation of the first adiabatic invariant) and the Fermi accelera- tion (resulting from conservation of the second adiabatic invariant) affect the electron distribution functions.

To describe the magnetic field geometry, we use the Tsyganenko [1989] model and consider two different Kp levels. The low Ifp value is intended to describe the magnetic field after dipolarization, while the high value describes the magnetic field before dipolarization. The algorithm used to reconstruct the PAD is the fol- lowing:

1. We first consider a velocity V• and pitch angle at a given point P1 after dipolarization, at which we want to know the phase space density fl.

2. We integrate the magnetic field line from P1 up to the ionosphere in the post-dipolarization configuration (i.e., considering the low Ifp level).

3. Considering that magnetic field lines are anchored in the ionosphere during the few minutes of the dipo- larization [see, e.g., Birmingham and Jones, 1968], the invariant latitude after dipolarization is identical to that before dipolarization. Accordingly, from the iono- spheric foot obtained above, we integrate the field line down to the equator but in the predipolarization (high Ifp level) configuration. We thus describe the stretch- ing of the magnetic field lines before dipolarization. For L = 7, 9, and 11 at P1, we obtain L = 9.7, 28.5, and 34.0 at P2, respectively.

SMETS ET AL- PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL 14,575

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14,576 SMETS ET AL.: PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL

10

lO 9

ionosoheric popula,ion

-electrons

10 8 magnetospheric poputafion

-2 10/* 0 210/+ /+10 z+ V//(km/sec)

Figure 3. Cut of the electron distribution function along the direction of the magnetic field.

4. At the position P2 obtained at the equator, we assume an equilibrium distribution before dipolariza- tion. Using the Liouville theorem, we have equality of phase space densities before and after dipolarization. The phase space density after dipolarization can thus be calculated from its predipolarization value, which depends on the velocity and pitch angle (V2;c•2) at P2. This couple (V2;c•2) is determined assuming conserva- tion of both magnetic moment tt and longitudinal in- variant J.

5. Knowing the magnetic field magnitude at position P2, we calculate the electron perpendicular velocity by conservation of

6. To determine the parallel velocity Vii 2 which en- sures conservation of J, we use a dichotomy algorithm. Two extreme values of Vii 2 are prescribed, one mini- mizing the longitudinal invariant and one maximizing it. J is then calculated from the average value of these two limiting velocities. The longitudinal invariant be- ing an increasing function of the parallel velocity, this average velocity becomes the new upper (respectively lower) limit if the resulting J value is smaller (respec- tively larger) than the one expected. Iteration is per- formed until J approaches the expected value within an error less than 0.1%.

7. With Vii 2 and Vñ2, we deduce (V2;o•2) and hence f2(V2;c•2). By application of the Liouville theorem we derive f• = f2 at the observation point P1 after dipo- larization.

By doing so, we implicitly take into account the large- scale perpendicular electric field existing during dipolar- ization. On the other hand, there may exist a parallel electric field accelerating the particles along the mag-

netic field. In this regard, measurements at low energies (500 eV) systematically reveal beamlike distributions along the whole Interball-Tail pass, even when perpen- dicularly peaked distributions are observed at high en- ergies (Plate 1-c). If a parallel electric field is at work, it thus affects essentially the low-energy electron popula- tion. Because it has a minor incidence at high energies, this parallel electric field was not accounted for in the present calculations.

The calculations require us to consider two different Kp values, before and after dipolarization. A paramet- ric analysis reveals that the computation results do not depend much on the Kp values as such but rather on the difference between the two Kp values. In the following, we chose Kp = 3 and I•p : 1 before and after dipo- larization, respectively, these values being determined from best fit with Interball-Tail observations.

Finally, from the field variations in Figure i which display a reversal of the Bx component, it is clear that the spacecraft is traveling not far from the magnetic equator. Still, in the following calculations, because the spacecraft does not sit exactly at the equator, we were led to consider some difference between the magnetic field magnitudes at the observation point and at the equator. The ratio between these two magnitudes was then used to project the distributions from the equator to the observation point.

4. Results and Discussion

Figure 4 presents the time evolution of the 10 keV electron flux using the same format as in Figure 2 (solid and dotted lines depicting the perpendicular and par-

SMETS ET AL.' PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL 14,577

10 4

10 3

10 2

101

10 ø

L - 11.5 L - 6.5 \/

0930

• • I [ I • ] I • • I • • I ,

0630 0700 0730 0800 0830 0900

UT

Figure 4. Computed parallel (dotted line) and perpendicular (solid line) flux of 10 keV electrons as function of time. Dipolarization starts at 0710 UT.

allel fluxes, respectively). Interball-Tail traveling to- ward Earth during the observation period, the time pre- sented along the horizontal axis is directly proportional to Interball-Tail geodistance, assuming that the space- craft is moving at constant speed from L = 11.5 (0630 UT) down to L = 6.5 (0930 UT). In Figure 4, dipolar- ization occurs at 0710 UT. We can clearly see a jump of more than two orders of magnitude in the flux in- tensity at the onset of dipolarization. Moreover, from 0710 UT until 0840 UT the flux in the parallel direction is larger than that in the perpendicular direction, this anisotropy being reversed after 0840 UT.

These computed features are in good agreement with those observed (Figure 2). It must be noted that the flux intensity directly depends on the parameters of the equilibrium distribution function before dipolarization. We considered an isotropic Maxwelltan with a density of 4 x 103 m -3 and a temperature of 1 keV. In the Maxwelltan distribution, density and temperature ap- pear as a multiplicative term and as an exponent ar- gument, respectively. Thus, in their logarithmic val- ues, density and temperature appear as additive and multiplicative factors, respectively. Decreasing (or in- creasing) the temperature would lead to decreasing (or increasing) the jump in the flux intensity (homothetic transformation of the two flux profiles), whereas chang- ing the density would add some offset (translation of the two profiles).

Previous studies reported the existence of anisotropies in electron PADs during both growth and expansion

phase of substorms [see, e.g., West et al., 1978a,b, Baker et al., 1978, West, 1979]. These types of anisotropy have not been observed by Interball-Tail among the cases studied in December 1995. Even when Interball-Tail

was located in the inner plasma sheet, there was no significant anisotropy in electron PADs below 10 keV. Differences with previous observations may be due to the distinct energy range considered (above 40 keV for the referenced paper hereinafter).

To examine the robustness of the numerical results, we have considered the influence of anisotropy in the initial distribution. It appears that an anisotropy T[i= 2 x T_L (that is, a fairly beamlike distribution prior to substorm onset) leads to fairly similar results. The structures displayed in Figures 4, 5, and 6 and in Plate 2 are still observed, at the same L value, even if their location in phase space slightly changes. This is mainly due to the off-equator position of the observation point: As the electron PADs are built away from equator, the pitch angle range of interest is small enough to be weakly affected by such anisotropy.

Figure 5 presents the computed flux intensity after dipolarization as a function of pitch angle. Flux profiles are shown at three different locations of the spacecraft: L = 11, L = 9, and L: 7. At L = 11 we obtain a bell- shaped curve with a maximum flux at a very small pitch angle (-., 4ø). At L: 9 we still have a bell-shaped curve, the maximum being shifted toward larger pitch angles. Note also the weaker flux gradient achieved. At L: 7 we obtain a rather monotonic evolution, flux gradually

14,578 SMETS ET AL' PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL

O2

-04

o lo 2o 3o

a•.• (degree) Figure 15. Computed intensity of the electron flux after dipolarization as a function of pitch angle at three different L values.

increasing with pitch angle. In order to compare these results with Interball-Tail observations, Plate 2 presents the ©- <I, spectrograms obtained using a convolution of the profiles in Figure 5 with the relationship giving the observed pitch angle for a given ©- (I) couple. As discussed above, these O-<I, spectrograms are built out- side of the equator, the pitch-angle at the observation point being related to the equatorial pitch angle using conservation of the first adiabatic invariant with a ratio

of the local magnetic field to equatorial magnetic field equal to 5. Increasing (decreasing) this ratio would lead to a shift of the above bell-shaped curve toward large (small) pitch angles.

In Plate 2 the logarithmic value of the flux is color- coded as in Plate 1. In Plates 2a-2c, the direction of the magnetic field is similar to that in the observations (Plate 1). In Plate 2a (L = 11) a beamlike distribu- tion is obtained with the electron population essentially along the magnetic field direction. At L = 9 (Plate 2b) a ringtype distribution can be seen with most of the electrons near 30 ø pitch angle. At L = 7 (Plate 2c) the bulk of the electron plasma is observed in the direction perpendicular to the magnetic field. These computed features closely resemble those presented in Plate 1. They directly follow from the magnetic field evolution along the Interball-Tail pass.

L • 7•

o

f

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PRE.. L - 1•- ....

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•%',•, ....... i ....... I Illill!

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(degree) (degree) (degree) Figure 6. Parallel (thin solid line), perpendicular (dotted line), and total (solid thick line) velocities before dipolarization as a function of pitch angle after dipolarization. These velocities are shown at selected L values (L - (a) 7, (b) 9, and (c) 11). The total velocity after dipolarization is constant and corresponds to an energy of 10 keV. The dashed lines indicate (top) parallel and (bottom) perpendicular velocities after the dipolarization.

3O

SMETS ET AL.: PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL 14,579

The origin of the PAD portrayed in Plate 2 must be looked for in the relative importance of betatron heating versus Fermi acceleration during the dipolarization pro- cess. Figure 6 presents the predipolarization velocity of electrons as a function of pitch angle (thick solid line) for a given postdipolarization velocity (corresponding to 10 keV energy). Solid and dotted lines present the par- allel and perpendicular velocities before dipolarization, respectively, and dashed lines present the (top) parallel and (bottom) perpendicular velocities after dipolariza- tion. Figures 6a-6c show the results obtained at L = 7, L = 9, and L = 11, respectively. In all cases one can note that the total velocity before dipolarization (solid thick line) is nearly equal to the parallel velocity (thin solid line), the perpendicular velocity (dotted line) be-

perpendicular velocity with pitch angle. Were this not the case, larger and larger equatorial pitch angles would be obtained; hence a gradual trapping of the electron at the equator. This enhancement of the parallel veloc- ity during dipolarization is directly linked to the taillike geometry of the magnetic field lines. This behavior ob- served at L = 11 is also obtained at L = 9 even though it is less pronounced. This region actually corresponds to the boundary between dipolelike magnetic field before the dipolarization, and taillike magnetic field after. The existence of a maximum in the parallel velocity which leads to the ring portrayed in Plate 2b at L = 9 is linked to the evolution of the magnetic field magnitude along a given magnetic field line.

At L ,,0 7, magnetic field lines are nearly dipMar be- ing much smaller. Most notably, it can be seen that the fore and after dipolarization. This magnetic field line direction of variation of the total velocity as a function of pitch angle significantly varies with L value.

At L = 7 the parallel velocity at the equator as well as the distance between equator and mirror point (mea- sured along the field line) decrease when the pitch angle increases. Hence the value of the second adiabatic in-

variant J also decreases when the pitch angle increases. In order to ensure conservation of J during dipMar- ization, the parallel velocity before dipolarization must also decrease, as is observed in Figure 6a. On the other hand, at L = 11 the value of the second adiabatic in- variant J also decreases when the pitch angle increases. However, before dipolarization, magnetic field lines are highly stretched. The electrons of interest in this study have relatively small equatorial pitch angles. They thus travel along the whole tail and exhibit low-Mtitude mir- ror points. The integral S - f0 •mi .... d._.q is thus much larger before dipolarization than after. As can be seen

geometry is at the origin of the perpendicularly peaked distributions as sketched in Figure 7. At L ,0 11, magnetic field lines remain significantly stretched af- ter dipolarization. The Fermi acceleration occurring in this regime leads to beamlike distributions. In be- tween, near L ,,0 9, magnetic field lines are taillike before dipolarization, and dipolelike after dipolarization, and the observation of ring-type distributions appears di- rectly linked to this very magnetic field topology. Thus, beamlike, ring-type, and perpendicularly peaked distri- butions correspond to distinct regions of space explored by InterbM1-TM1 in the near-Earth tail. It should be noted that similar variations were obtained using the long version of the Tsyganenko [1987] model. These variations thus are model independent and fairly insen- sitive to the Ifp levels considered. Of particular interest are the ring-type distributions which appear character- istic of the dipolelike-tMllike transition region and thus

in Figure 6, this large value of S implies small values of provide a remote sensing tool of this boundary. the parallel velocity before dipolarization at L = 11, as In the above modeling, no assumption was made on compared to that obtained at L = 7. the dipolarization timescale. We simply assumed dipo-

In Figure 6 it should also be noted that the parM- larization to occur on a timescale sufficiently large to lel velocity increases in response to the increase of the ensure conservation of the two first adiabatic invari-

PRE

perpendicularly peaked ringtype

POST beamlike

0 5 10 15 20 25 30 35

Figure 7. Schematic view of the three distinct domains in the near-Earth tail and their evolution during dipolarization with corresponding (3- (I) spectrograms.

14,580 SMETS ET AL.: PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL

ants. It could thus be of interest to examine the case

of quasi-steady convection where magnetic field lines evolve from taillike to dipolelike configurations more slowly than during substorms. The modeling of such a process would require few changes in the calculations (take into account one and not two different I•'p levels but introduce the convection electric field value). Anal- ysis of Interball-Tail data would shed light on this point. We suspect that these calculations should provide some similar results.

Conclusion

In this paper we examined PAD of 10 keV electrons observed by Interball-Tail after the dipolarization phase of a substorm. Using model magnetospheric configura- tions before and after dipolarization, we calculated the energization rates resulting from betatron heating and Fermi acceleration. It was shown that the pitch angle distributions observed can be readily explained from the magnetic field evolution in the near-Earth tail. Three distinct domains can be distinguished. In the outermost domain (L --• 11), magnetic field lines remain substan- tially stretched after dipolarization. In this region of space, Fermi acceleration is quite efficient in produc- ing electron beams along the magnetic field directions. Close to Earth (L --• 7), magnetic field lines are not far from dipolaf both before and after dipolarization. In such a configuration the adiabatic transport of elec- trons leads to distributions peaked in the perpendicu- lar direction. Finally, there exists an intermediate re- gion (L --• 9) for which magnetic field lines are signif- icantly stretched before dipolarization and much more dipolaf after dipolarization. In this particular topology the adiabatic energization processes lead to the produc- tion of ring-type distributions. The good agreement between observations and computations clearly demon- strates that the evolution of the PAD is due to the spa- tial (and not temporal) displacement of Interball-Tail, and the occurrence of ring-type distributions appears as a characteristic signature of the dipolelike-taillike tran- sition region.

Acknowledgments. We gratefully acknowledge the use of magnetic data from the MIFM instrument provided by S. Klimov and S. Romanov.

Janet G. Luhmann thanks Lev Zelenyi and Tsugunobu Nagai for their assistance in evaluating this paper.

References

Baker, D. N., P. R. Higbie, E. W. Hones, Jr., and R. D. BellJan, High-resolution energetic particle measurements at 6.6 RE, 3., Low-energy electron anisotropies and short- term substorm predictions, J. Geophys. Res., 83, 4863, 1978.

Birmingham, T. J., and F. C. Jones, Identification of moving magnetic field lines, J. Geophys. Res., 73, 5505, 1968•

Bfichner, J., and L. M. Zelenyi, Regular and chaotic charged particle motion in magnetotaillike field reversals, 1, Basic

theory of trapped motion, J. Geophys. Res., 9•, 11,821, 1989.

Chen, J., and P. J. Palmadesso, Chaos and nonlinear dy- namics of single-particle orbits in magnetotaillike mag- netic field, J. Geophys. Res., 91, 1499, 1986.

Cowley, S. W. H., and M. Ashour-Abdalla, Adiabatic plasma convection in a dipole field: variation of plasma bulk pa- rameters with L, Planet. Space Sci., 23, 1527, 1975.

Delcourt, D.C., J. A. Sauvaud, and A. Pedersen, Dynamics of single-particle orbits during substorm expansion phase, J. Geophys. Res., 95, 20,853, 1990.

Delcourt, D.C., J. A. Sauvaud, R. F. Martin Jr., and T. E. Moore, On the nonadiabatic precipitation of ions from the near-Earth plasma sheet, J. Geophys. Res. 101, 17,409, 1996.

Hones, E. W., Jr., Transient phenomena in the magnetotail and their relation to substorms, Space Sci. Rev., 23, 393, 1979.

Johnstone, A.D., D. M. Walton, R. Liu, and D. A. Hardy, Pitch angle diffusion of low-energy electrons by whistler mode waves, J. Geophys. Res., 98, 5959, 1993.

Johnstone, A.D., S. Szita, N.J. Flowers, N. P. Mered- ith, Observations of particle injection from CRRES, Eur. Space Agency Spec. Pub., ESA SP-389, 1996.

Kan, J. R., L. Zhu, and S. I. Akasofu, A theory of substorms: Onset on subsidence, J. Geophys. Res., 93, 5624, 1988.

Kennel, C. F., and H. E. Petschek, Limit on stably trapped particle fluxes, J. Geophys. Res., 71, 1, 1966.

Klimov S., et al., ASPI experiment: Measurements of the fields and waves on board the INTERBALL-1 spacecraft, Ann. Geophys., 15, 514, 1997.

Lui, A. T., Extended consideration of a synthesis model for magnetospheric substorms, in Magnetospheric Substorms, Geophys. Monogr. Set., vol. 64, edited by J. R. Kan et al., pp. 43-60, AGU, Washington, D.C., 1991.

Lui, A. T., Current disruption in the Earth's magnetosphere: Observations and models, J. Geophys. Res., 101, 13,067, 1996.

Mauk, B. H., Quantitative modeling of the "convection surge" mechanism of ion acceleration, J. Geophys. Res., 91, 13,423, 1986.

Mauk, B. H., Generation of macroscopic magnetic-field- aligned electric fields by the convection surge ion accel- eration mechanism, J. Geophys. Res., 9•, 8911, 1989.

Nagai, T., and S. Machida, Magnetic reconnection in the near-Earth magnetotail, in New Perspectives on the Earth's Magnetotail, Geophys. Monogr. Set., vol. 105, edited by D. N. Baker, A. Nishida, and S. W. H. Cowley, pp. 211- 224, AGU, Washington, D.C., 1998.

Pulkkinen, T. I., D. N. Baker, R. J. Pellinen, J. B/ichner, H. E. J. Koskinen, R. E. Lopez, R. L. Dyson, and L. A. Franck, Particle scattering and current sheet stability in the geomagnetic tail during the substorm growth phase, J. Geophys. Res., 97, 19,283, 1992.

Roederer, J. G., Dynamics of Geomagnetically Trapped Ra- diation, Springer-Verlag, New York, 1970.

Sauvaud, J. A., and J. R. Winckler, Bynamics of plasma, energetic particles, and field near synchronous orbit in the nighttime sector during magnetospheric substorms, J. Geophys. Res., 85, 2043, 1980.

Sauvaud, J. A., P. Koperski, T. Beutier, H. Barthe, C. Aoustin, J. J. Thocaven, J. Rouzaud, E. Penou, O. Vais- berg, and N. Borodkova, The INTERBALL-TAIL ELEC- TRON experiment: initial results on the low-latitude boundary layer of the dawn magnetosphere, Ann. Geo- phys., 15, 587, 1997.

Schriver, D., M. Ashour-Abdalla, and R. L. Richard, On the origin of the ion-electron temperature difference in the plasma sheet, J. Geophys. Res., 103, 14,879, 1998.

SMETS ET AL.: PITCH ANGLE DISTRIBUTIONS OBSERVED BY INTERBALL-TAIL 14,581

Sergeev V. A., E. M. Sazhina, N. A. Tsyganenko, J. A. Lundblad, and F. Soras, Pitch angle scattering of en- ergetic protons in the magnetotail current sheet as the dominant source of their isotropic precipitation into the nightside ionosphere, Planet. Space Sci., 31, 1147, 1983.

Smets, R., D. Delcourt, and D. Fontaine, Ion and electron distribution functions in the distant magnetotail: Mod- eling of GEOTAIL observations, J. Geophys. Res., 103, 20,407, 1998.

Tsyganenko, N. A., Global quantitative models of the geo- magnetic field in the cislunar magnetosphere for different disturbance levels, Planet. Space Sci., 35, 1347, 1987.

Tsyganenko, N. A., A magnetospheric field model with a warped tail current sheet, Planet. Space Sci., 37, 5, 1989.

West, H. I., Jr., R. M. Bucks, and M. G. Kivelson, On the configuration of the magnetotail near midnight during quiet and weakly disturbed periods: State of the magne- tosphere, J. Geophys. Res., 83, 3805, 1978a.

West, H. I., Jr., R. M. Bucks, and M. G. Kivelson, On the configuration of the magnetotail near midnight dur- ing quiet and weakly disturbed periods: Magnetic field modeling, J. Geophys. Res., 83, 3819, 1978b.

West, H. I., Jr., The signature of the various regions of the outer magnetosphere in the pitch angle distributions of energetic particles, in Quantitative Modeling of Magneto-

spheric Processes, Geophys. Monogr. Ser., vol. 21, edited by W. P. Olson, pp. 150-179, AGU, Washington, D.C., 1979.

Zelenyi, L. M., A. Galeev, and C. F. Kennel, Ion precipita- tion from the inner plasma sheet due to stochastic diffu- sion, J. Geophys. Res., 95, 3871, 1990.

D. Delcourt, Centre d'4tude des Environnements Ter- restre et Plan4taires, Centre National de la Recherche Scien- tifique, 4 avenue de Neptune, 94107 Saint-Maur des Foss4s, France. (e-mail: dde@cetp.ipsl.fr)

P. Koperski, Space Research Center of Polish Academy of Sciences, ul. Bartycka 18 A, 00-716 Warszawa, Poland. (e-mail: piotrk@cbk.waw.pl)

J. A. Sauvaud, Gentre d'4tude Spatial des Rayonnements, Gentre National de la Recherche Scientifique, 9 Avenue du colonel Roche, 31029 Toulouse, France. (e-mail: sauvaud@cesr.fr)

R. Smets, Laboratory for Extraterrestrial Physics, NASA Goddard Space Flight Center, Code 692, Build- ing 2, Room W124, Greenbelt, MD 20771. (e-mail: roch @ xo mbul. gsfc. n as a. gov )

(Received September 16, 1998; revised November 30, 1998; accepted November 30, 1998.)