refilling process in the plasmasphere and its relation to magnetic activity

11
Journrrl ofAtmospheric andTerrestrialPhysrcs, Vol.50,No. 3, pp. 185-195, 1988. OOZI-9169/B $3.00+.OO Printed inGreat Britain. Pergamon Press plc Refilling process in the plasmasphere and its relation to magnetic activity XIAO-TING SONG*, ROGER GENDRIN and GERARD CAUDAL Centre de Recherches en Physique de I’Environnement, Centre National d’Etudes des Telecommunications, 9213 1 Issy-les-Moulineaux, France (Received infinulform 21 October 1987) Abstract-When geomagnetic activity is moderate, the geosynchronous orbit crosses the plasmasphere bulge region in which the variations of plasma density from day to day can therefore be detected by geosynchronous satellites. The plasma density was measured by the Relaxation Sounder onboard ESA’s GEOS-2 satellite. Variations of plasma density reflect the combined effects of refilling of particles from the ionosphere and loss of plasma by convection. The saturation level of the electron density at the geo- synchronous orbit and the refilling rate under different conditions of geomagnetic activity have been obtained and are found to be 70.5cmm3 and 7-25cmm3daym’, respectively. In this paper the refilling morphology and the relationship between the refilling process and magnetic activity (Dst index) are analysed. The refilling rate or refilling time constant inferred from the data, either directly on fairly well- defined refilling events, or indirectly through a simple model, are found to compare reasonably well with the refilling time constant expected by theory. The observed correlation of refilling rate with Dst index is interpreted as resulting from the modification of the composition of the topside ionosphere occurring after intense storms 1. INTRODUCTION Since PARK (1970), using the whistler technique, com- puted the upward electron flux at an altitude of 1000 km, studies of the refilling of the plasmasphere by electrons from the ionosphere has made great pro- gress in both theoretical and experimental aspects (HORWITZ, 1982). The general features of the refilling phenomenon and the refilling rate have been derived from whistler observations and in situ measurements on spacecraft (PARK, 1970, 1974; CHAPPELL, 1972; CARPENTER and PARK, 1973). The mechanisms of refilling considering the evaporation of ionospheric particles to higher altitudes along magnetic flux tubes have been widely investigated with both kinetic and hydrodynamic models (BANKS and HOLZER, 1969 ; HOLZER et al., 1971; LEMAIRE and SCHERER, 1974; LEMAIRE, 1985; SINGH et al., 1986). In recent years plasma measurements performed by spacecraft cross- ing the equatorial plasmasphere or at the geo- synchronous orbit have greatly contributed to the study of the refilling process (CHAPPELL et al., 1970, 1971; GRINGAUZ, 1976 ; CHEN and GREBOWSKY, 1978 ; DBCRBAU et al., 1978, 1982; WRENN et al., 1984; HIGEL and Wu, 1984; SONG and CAUDAL, 1987). These measurements provided not only the dynamic * Present address : Geophysical Institute, Academia Sinica, P.O. Box 928, Beijing, People’s Republic of China. characteristics of plasma near the Equator but also their variations in relation to magnetic activity and to the convection electric field pattern. Though the convection field, combined with the corotation field, controls the boundary of the plasmapause, the refill- ing of particles from the ionosphere plays a crucial role in the actual formation of the plasmasphere inside the boundary. The particle coupling between iono- sphere and magnetosphere can also affect the for- mation of the plasmapause. Whereas there seems to be an agreement between the observed and theoretical values of the upward ionospheric electron flux (E 3 x 1 OS crn~‘s~ ‘) at plas- mapause latitudes (PARK, 1970 ; HOFFMAN et al., 1976 ; LEMAIRE, 1985) the equatorial values of the refilling parameters are not yet well evaluated. Refilling rates from 8cmm3dayy’ to 50cme3 day-’ have been reported by using GEOS-2 data (SOJKA and WRENN, 1985; DBCRBAU et al., 1986). Refilling time constants that vary between 2 and 15 days can be found in the literature (see references above), a situation which has not been clarified by more recent measurements (POULTER et al., 1981; WRENN and NORRIS, 1982; SOJKA and WRENN, 1985). The Relaxation Sounder (RS) on board ESA’s GEOS-2 satellite provided long term measurements of the cold plasma which yielded values of the electron density N, in the equatorial plane at 6.64 R,, from which the N, distribution with local time, the charac- 185

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Page 1: Refilling process in the plasmasphere and its relation to magnetic activity

Journrrl ofAtmospheric and TerrestrialPhysrcs, Vol. 50, No. 3, pp. 185-195, 1988. OOZI-9169/B $3.00+ .OO Printed in Great Britain. Pergamon Press plc

Refilling process in the plasmasphere and its relation to magnetic activity

XIAO-TING SONG*, ROGER GENDRIN and GERARD CAUDAL

Centre de Recherches en Physique de I’Environnement, Centre National d’Etudes des Telecommunications, 9213 1 Issy-les-Moulineaux, France

(Received infinulform 21 October 1987)

Abstract-When geomagnetic activity is moderate, the geosynchronous orbit crosses the plasmasphere bulge region in which the variations of plasma density from day to day can therefore be detected by geosynchronous satellites. The plasma density was measured by the Relaxation Sounder onboard ESA’s GEOS-2 satellite. Variations of plasma density reflect the combined effects of refilling of particles from the ionosphere and loss of plasma by convection. The saturation level of the electron density at the geo- synchronous orbit and the refilling rate under different conditions of geomagnetic activity have been obtained and are found to be 70.5cmm3 and 7-25cmm3daym’, respectively. In this paper the refilling morphology and the relationship between the refilling process and magnetic activity (Dst index) are analysed. The refilling rate or refilling time constant inferred from the data, either directly on fairly well- defined refilling events, or indirectly through a simple model, are found to compare reasonably well with the refilling time constant expected by theory. The observed correlation of refilling rate with Dst index is interpreted as resulting from the modification of the composition of the topside ionosphere occurring after intense storms

1. INTRODUCTION

Since PARK (1970), using the whistler technique, com- puted the upward electron flux at an altitude of 1000 km, studies of the refilling of the plasmasphere by electrons from the ionosphere has made great pro- gress in both theoretical and experimental aspects (HORWITZ, 1982). The general features of the refilling

phenomenon and the refilling rate have been derived from whistler observations and in situ measurements on spacecraft (PARK, 1970, 1974; CHAPPELL, 1972;

CARPENTER and PARK, 1973). The mechanisms of refilling considering the evaporation of ionospheric particles to higher altitudes along magnetic flux tubes have been widely investigated with both kinetic and hydrodynamic models (BANKS and HOLZER, 1969 ; HOLZER et al., 1971; LEMAIRE and SCHERER, 1974;

LEMAIRE, 1985; SINGH et al., 1986). In recent years plasma measurements performed by spacecraft cross- ing the equatorial plasmasphere or at the geo- synchronous orbit have greatly contributed to the study of the refilling process (CHAPPELL et al., 1970, 1971; GRINGAUZ, 1976 ; CHEN and GREBOWSKY, 1978 ; DBCRBAU et al., 1978, 1982; WRENN et al., 1984; HIGEL and Wu, 1984; SONG and CAUDAL, 1987).

These measurements provided not only the dynamic

* Present address : Geophysical Institute, Academia Sinica, P.O. Box 928, Beijing, People’s Republic of China.

characteristics of plasma near the Equator but also their variations in relation to magnetic activity and to the convection electric field pattern. Though the

convection field, combined with the corotation field, controls the boundary of the plasmapause, the refill- ing of particles from the ionosphere plays a crucial role in the actual formation of the plasmasphere inside the boundary. The particle coupling between iono- sphere and magnetosphere can also affect the for- mation of the plasmapause.

Whereas there seems to be an agreement between the observed and theoretical values of the upward ionospheric electron flux (E 3 x 1 OS crn~‘s~ ‘) at plas- mapause latitudes (PARK, 1970 ; HOFFMAN et al., 1976 ; LEMAIRE, 1985) the equatorial values of the refilling parameters are not yet well evaluated. Refilling rates from 8cmm3dayy’ to 50cme3 day-’ have been reported by using GEOS-2 data (SOJKA and WRENN,

1985; DBCRBAU et al., 1986). Refilling time constants that vary between 2 and 15 days can be found in the literature (see references above), a situation which

has not been clarified by more recent measurements (POULTER et al., 1981; WRENN and NORRIS, 1982;

SOJKA and WRENN, 1985). The Relaxation Sounder (RS) on board ESA’s

GEOS-2 satellite provided long term measurements of the cold plasma which yielded values of the electron density N, in the equatorial plane at 6.64 R,, from which the N, distribution with local time, the charac-

185

Page 2: Refilling process in the plasmasphere and its relation to magnetic activity

186 X.-T. SONG, R. GENDRIN and G. CAUDAL

teristics of the plasmaspheric bulge and N, variations with magnetic activity can be obtained (HIGEL and Wu, 1984; SONG and CAUDAL, 1987). The relaxation sounder (ETCHETO et al., 1978) is particularly suited for studying the refilling process since, contrary to most particle detectors, it can yield reliable data in low temperature plasmas (kT<c 1 eV) the temperature of plasmaspheric electrons in the bulge region being usually of the order of 0.5 eV km’ (DPCRRAU et al.,

1982). This paper supplies the study of refilling with new complementary data The purpose here is to study the relation between the refilling process and magnetic activity (Section Z), and to interpret the results in the light of the theory of LEMAIRE (1985) with simple modelling (Section 3).

2. THE MORPHOLOGY OF THE REFILLING PROCESS AT THE GEOSYNCHRONOUS ORBIT

The refilling process is a phenomenon by which particles are transported along the field lines from the ionosphere to the magnetic equator. Generally, during the daytime, particles evaporate upward from the ionosphere into the plasmasphere, whereas during the night-time particles are transported downward. Ordi- narily the flux upward is greater than that downward (PARK, 1970), so that above the altitude of 1000 km an accumulation of particles must exist, which con- stitutes the stable distribution of plasma inside the magnetosphere. However the erosion which is associ- ated with the large scale convection electric field and with its fluctuations (i.e. CHAPPELL, 1970, 1972) counteracts this permanent refilling and the daily average value of N, at the geostationary orbit may present large variations (HIGEL and Wu, 1984).

Figure 1 displays a sample of the RS data (bottom panel) illustrating the refilling process occurring after an intense storm, whose strength is evidenced by the curves giving the variations of L)st and elsewhere Kp

(upper panels). On the dayside of the storm day a region having a high value of cold plasma density can appear, which may correspond to the phenomenon of detached plasma (CHAPPELL et af., 1970, 1972), or to the movement of the quiet day plasma bulge towards the dayside before the storm (HIGEL and WV, 1984). If we define N,,,, as being the maximum value of N, (averaged over 12min) for a given day, we see that N,,,, decreases rapidly to a minimum value of the order of 10cme3 (the continuous line drawn on the

1 i

Page 3: Refilling process in the plasmasphere and its relation to magnetic activity

Refilling in the plasmasphere 187

bottom panel of Fig. 1) and that the plasma bulge

disappears at the geostationary orbit (periods labelled

ES and PM on Fig. 1). Thereafter, during the devel-

opment of the recovery phase when the magnetic activity decreases, the plasma bulge gradually reappears. During this period the electron density con- tinually increases until it reaches its saturation level, if it is not interrupted by subsequent substorms. Here we define the saturation level as the maximum value of N,,,, at the geosynchronous orbit. Usually it is limited to z 70 cme3.

One may be surprised to observe that the minimum of N,,,, does not occur immediately at the time of the storm main phase, but occurs one or two days later. A possible explanation is the following: when the storm starts, the large scale convection electric field suddenly enhances, displacing the last closed equi-

potential line quickly toward the Earth, and thus leav- ing the region of observation on open equipotential lines. The particles left on open equipotential lines

now take part in the convection and are transported to the magnetopause. This is the process which makes

the electron density decrease. Because the convection velocity is limited, the decrease of electron density may take one or two days after the main phase of the storm. At the beginning of the recovery phase, the closed equipotential lines return to their original location, the particles are no longer swept away by the convection and the electron density stops decreasing.

Therefore, the day on which N,,,, reaches a minimum is a critical day, indicating the end of the particle convection and the return of the last closed equi- potential line to its original position. After that time particles are no longer removed by large scale con- vection, and the variation of N, from thereon reflects the characteristics of transport along field lines. If the electron density increases day by day, this means that the particles originating from the ionosphere accumu- late in the equatorial region. This is the so-called refilling process.

Here we define the phase of minimum (PM) as the time at which N,,,, reaches its minimum value. Before this time the depletion of electrons dominates the situation; after that time the refilling process dom- inates. The resolution with which the time of mini- mum is determined by this technique is one day, with a possible error of the order of one half day. Our analysis of a large number of events shows that after nearly every storm the minimum appears. This means that this phenomenon is a permanent pheno- menon, and provides evidence for the occurrence of the refilling process. It is also a signature indicat- ing that the last closed equipotential line has returned to its original position.

Table 1. The saturation electron density and corresponding Dst index for the data set from 20 November 1978 to 2

March 1980

Date

12.12.78 13.01.79 14.01.79 11.02.79 18.03.79 09.06.79 16.06.79 03.07.79 04.07.79 05.07.79 06.07.79 11.09.79 24.09.79 25.10.79 28.10.79 30.11.79 02.12.79 04.12.79 15.12.79

70.20 71.06 70.02 71.37 71.13 71.19 69.64 69.16 70.28 69.40 71.37 71.11 70.42 70.44 70.93 70.99 70.62 69.12 71.11

Average 70.5

Saturation N,(cme3)

D%,,(nV Dst(nT) (for the (18.0%

previous day) 18.00 UT)

-11 +1 -8 -4 -9 -5

-16 -4 -22 -7 - 17 -6

-3 -7 + 10 +34

+2 -3 -16 +2

-2 f9 -30 -23 -27 -11 -26 -25 -18 -12 + 10 f21 -11 -3 -30 -16

fl +4

- 12 -3

2.2. The saturation level of electron density at geo-

synchronous orbit

From Fig. 1 it can be seen that the storm which

starts on 25 November 1978 and continues to 26 November is very intense. During that time Dst

reaches - 183 nT, K, reaches the value 7,. Two days

later, on 28 November 1978, the electron density decreases to its minimum value. This is the phase of

minimum. Then the electron density begins to increase. Near 12 December it reaches its saturation value of 70 cm-‘.

Generally, the saturation value of electron density is reached in the plasma bulge region in the dusk sector. According to the statistical results obtained by

using the CEOS-2 RS data set of 20 November 1978 to 2 March 1980, the saturation value is 70.5 cm 3 on average with a standard deviation of 0.7cm-’ (see

Table 1). The reasons that this value can be thought as the saturation value in the plasmasphere at 6.64 R,

are as follows. Firstly, it can be reached only after a long time of refilling. This can be seen from a com- parison between the day to day variation of the elec- tron density and the corresponding magnetic activity. Secondly, in all the high density value intervals in the data set used here there was no case in which the Relaxation Sounder failed to measure due’ to lack of the equipment frequency range (HEEL and Wu, 1984).

Page 4: Refilling process in the plasmasphere and its relation to magnetic activity

188 X.-T. SONG, R. GEN~RIN and G. CAUDAL

The saturation value should be reached in the case of quiescent conditions. In the analysis performed, as explained in the next section, we have taken the minimum Dst index on the preceding day, Dstme as a parameter to sort out the observations. We ob- tained that the saturation level is reached for Dstmi, = - 12 nT on the average, with a standard devi- ation of 12 nT. Note that the statistical deviation is of the same order as the average value, so that the result should be understood as indicating a significant variability of the level of Dst at which the saturation level is reached, indicating however that saturation is reached at low levels of magnetic activity. If, instead of taking Dst,,, for the preceding day, we choose the average value of Dst between 18.00 the previous day and 18.00 the same day (last column of Table l), we find an average value of - 3 nT, which is really representative of quiet periods.

2.3. The relationship between electron density and magn~t~c acfiuity

The refilling process, by which the electron density gradually reaches its saturation situation, should nat- urally be controlled by the large-scale dynamical pro- cesses occurring in the magnetosphere. In other words, it is likely to be affected by the magnetic activity. We have thus attempted here to compare the behaviour of electron density and magnetic activity. For this purpose, the maximum value of the electron density (N,,,,,,) in the bulge region for each day is used. If there is no bulge appearing on some day (22% of cases during the studied period) the maximum value of rzp on that day is used.

During a long quiet period following an intense storm, the flux tubes at geostationary orbit, which have been emptied by the storm, are gradually replen- ished (refilling process). Meanwhile the ring current particles, which have been injected from the tail by the storm, are gradually eroded. Also, both phenomena (refilling of the plasmasphere and erosion of the ring current) will be interrupted by the next occurrence of an active period. Since the ring current intensity is indicated by the Dst index, one thus expects some similarity between the behaviour of N,,,, and the Dst index. For every day there are 24 values of Dst. We have chosen the minimum value of Dst over the day (Dst,,,) to represent a given day (using the maximum or average value would not change the qualitative conclusions of our study). We have tried to compare Ds&,,i, and N,,,,, and have found that a time delay of 1 day should be introduced in the plasmapause response (rljem_) to get the best correlation. This could probably be related to the fact that the injection of

\

\

Fig. 2. Comparison between the variations of measured N,,,, (solid line), modelled N,,, (dashed line) and Dst,,,, for the

period 28 November-13 December 1978.

ring current particles occurs much more rapidly than the removal of plasmapause particles under sudden enhancements of magnetospheric convection. For this reason the values of Dst,, indicated below (Fig. 2) for a given day will be taken from the preceding day.

Figure 2 shows the variation of N,,,, and z)st,,,,, for the event occurring on 15 consecutive days from 28 November to 12 December 1978. On the figure are also plotted the results of a model which will be dis- cussed in Section 3. From this figure we can see the following features.

{a) The behaviour of N,,,, and Dst,;, are very similar. During the 15 days Dstmin has a tendency to increase progressively and so does N,,,. When Dst,in reaches - 13 nT, N,,,, approaches the saturation level (70.2cm-‘). This good relation between N,,, and Ds~,,,~,, indicates the controlling effects of the magnetic activity on the electron density distribution and the reasonable selection of a time delay of 1 day between the values of Dst and those of N,,,,.

(b) The periods of increase of N,,,, seen on Fig. 2 are of two kinds. The first one, that we shall ascribe to normal refilling process, is observed from 28 November to 1 December 1978. During this period, the electron density increases from 11 cmm3 to 43 cme3, giving an average refilling rate of N 10cm-3day-‘. According to this rate, the electron density will reach the saturation level after 6 days. But on 2 December the increase of the magnetic activity with respect to 1 December (the Dstmin decreased by 18 nT) interrupted the

Page 5: Refilling process in the plasmasphere and its relation to magnetic activity

Refilling in the plasmasphere 189

Fig.

(c)

3. As Fig. 2, but for the periods 28 June-13 July 1979 and 22-31 October 1979.

refilling process and caused a drop in the electron density to 8 cmm3. The particles which have been

supplemented by the refilling process are de- pleted by the enhanced magnetic activity. After 2 December the electron density increases again and reaches 60cme3 on 4 December. The rate of increase in this time interval is 26cme3 day-’ which is larger than the value for 28 November

to 1 December by nearly a factor of 3 (see also the extremely rapid increase for 7-8 December or lo-11 December). Such increases are not related to direct refilling by ionospheric electrons at a stationary position. It is more probable that

the plasmaspheric bulge was not encountered by GEOS-2 at the dates for which rather low den- sities are observed (2, 6-7, 10 December), which makes the subsequent refilling rates appear rather high. We shall call this process by which large

densities are recovered ‘recovery process’. Also, when magnetospheric convection is strong, the geosynchronous orbit may be entirely located in the region of open equipotentials. The tra- jectories of particles there are thus open and the plasma is being convected away toward the mag- netopause. Convection thus constitutes an important loss process for the plasma during moderately active to active periods. The super- position of the refilling process with all these dynamical processes makes the behaviour of

N PmaX very complicated, except during quiet days just following an intense storm, where pure nor- mal refilling process can be isolated.

Having reached the saturation level, the electron density may still fluctuate. These fluctuations are clearly associated to the fluctuations of Dst,,, as shown in the two events presented on Fig. 3. An increase of the magnetic activity, as reflected by the decrease of Dst,,,, is always accompanied by a decrease of N,,,,. A large number of similar events have been observed during the period of

-10

-20 i

50

@5-

mE 40 ' 0

%llax *I'

is 30

5

z

P

20 /' I'

-_I 10 _-*-

OU 19 20 21 22 23 24 25

December.1978. days

Fig. 4. As Fig. 2, but for the period 19-26 December 1978 (note the large negative average value of Dst).

9 10 1, 12 13 14 15 I6 17 18 19 20

January,1979, day5

Fig. 5. As Fig. 2, but for the period 9-20 January 1979 (note the low negative average value of Dst).

analysis. They have not been presented here for the sake of brevity.

A few exceptions to this statement however exist, as in the cases for instance of 16 or 19 January 1979 (Fig. 5) for which the continuous decrease of Dst,,,

is not associated with a low value of N,,,,, or in the case of 24 December 1978 (Fig. 4) for which a decrease

in N,,, is observed whereas Dst,,, does not decrease. But in general the variation of N,,, is well correlated with the variation of Dst,i, either during the refilling or after reaching the saturation level. This fact sug- gests that the refilling process is mainly controlled by the magnetic activity and the use of Dst index one day in advance as a parameter to sort out the N,,,, variation due to the refilling or to the expansion of

Page 6: Refilling process in the plasmasphere and its relation to magnetic activity

190 X.-T. SONG, R. GENDRIN and G. CAUDAL

the plasmaspheric bulge to geostationary altitudes is rational.

It is interesting to compare this 24 h delay with the 20 h delay which DBCU&AU et al. (1982) have found for maximum antico~elation between the electron density measured at dusk for L > 6 and the A, index (their figure 13). Since a high value of A, is associated with a low value of Dst,,,, and‘since N, reaches its maximum value near the dusk hours, the two results are consistent: the electron density at the geo- stationary orbit and near the dusk hours is minimum 2@-24 h after the world wide magnetic activity has been maximum.

2.4. The tzjilling rate Rr and its relation to the Dst index

In studying the refilling rate, the normal refilling and the recovery process must be considered separ- ately. Here, we are interested in normal refilling and should eliminate recovery events from our analysis. This is done by considering only the two to three day periods which immediately follow an intense storm (x;l> 5 or Dst,,,,, -C -5OnT). After such storms the plasmaspheric plasma at the geostationary orbit has been considerably evacuated (typically N,,,, ,< 10 crn3) and the main plasmaspheric bulge lies well inside the L = 6.6 shell, so that increases of N PInaX can be attributed to normal refilling with good confidence. The refilling rates for these fairly defined refilling events are determined by the simple formula

R, = N,,&nal) - LAnitial) (number of days of refilling)’ (1)

In Fig. 2, the refilling rate, calculated from the interval 28 November-l December, which can be clearly ascribed to normal refilling, is x 10 cme3 day- ‘. Dur- ing this period when refilling is observed, the average of Dst,,, is Dst,,, = -44.7nT. Other examples of refilling events are displayed in Figs. 4 and 5. The refilling rate in Fig. 4 (calculated for the interval 19- 25 December) is 6.5 cm-I day-‘, for Dst,,, = - 59 nT. In Fig. 5, the refilling rate (calculated for the interval 9-12 January) is 20 cmm3 day-‘, for D.J~,,,~, = - 22 nT. Examination of a number of such fairly defined refill- ing events (see Table 2) shows a tendency for smaller refilhng rate Rf when the absolute value of L)stmi, is larger. A scatter plot of the refilling rate vs. G,, is shown in Fig. 6. Its best-fit regression line is given by

_.-._ R, = 25.8+0.33Dst,i,cm-3 day-‘,

with a correlation coefficient of 0.83. Thus the average value of Rf is of the order of

10cm-3dayy’ for Dst,,, z - 50 nT, and of the order

of 25 cm-‘day-’ for G,,,,, z OnT. The reason for this dependence of Rf on Dst,,,i, will be discussed in Section 3. These values of the refilling rate give refilling time constants ranging from z 3 days to more than 7 days. Note that a saturation value of t00em-3 and refilling rates of 30-50crn3day~ have been given by SOJKA and WRENN (1985) by using the GEOS-2 SPA (Suprathermal Plasma Analyser) data. These results give a refilling time constant of two or three days which is the lower limit of our values. D&RJ?AU et al. (1986) used a refilling rate of 8cm-‘day--’ to fit their data, which corresponds to a refilling time constant of 7 days. This value and the more than g-day time constant given by POULTER et af. (198 1) or the &day time constant obtained theoretically by CHEN and WOLF (1972) are essentially within the range of our values. The results which are presented here confirm all these values but the more refined analysis which we have made helps us to understand their variability : the refilling rate and the refilling time constant depend upon the magnetic activity level, as measured by Dst.

3. INTERPRETATlON AND MODELLING

With the aid of LEMAIRE’S (1985) theory, we try to interpret theoretically some of the observed phenom- ena. This will permit us to compare theoretically deduced quantities with values determined from the measured parameters. A simple model, based on qualitative arguments will help us to go a little further in the interpretation, and allow us to describe reason- ably the variation of N,,,, during several days after an intense magnetic storm.

3.1. Expression of the rate of wfilling process for a quiet period

We use the simple formula (3.33) of LEMAIRE (1985), corrected by a factor of 2 for considering the refilling from two ends of the magnetic tube

dn/dt = -(n/v)(dV/dt)+2l;i,s,/v, (2)

where n is the equatorial electron density, F;, is the flux of ionospheric refilling ions passing through the exobase to the plasmasphere, S, and V are the surface (at the altitude tzO) and the volume of the unit flux tube as given by

S,(L) = 4.8

x 10s[4-3(R,+h0)/LR,]~‘iz(cm2 I%-‘), (3)

V(L) = 1.89 x 10”L4(cm3 IV&‘), (41

where R, c 6400 km and h, x 1000 km are respec- tively the radius of the Earth and the altitude of the

Page 7: Refilling process in the plasmasphere and its relation to magnetic activity

Refilling in the plasmasphere

Table 2. Refilling events and corresponding magnetic activity

IYI

Time 01 commcnccmcnt of Minimum Time of Refilling rate Average

magnetic storms KP D.sr(nT) refilling events (cm ‘day ‘) Ds/(nT)

25 Nov. lY7X 70 - IX3 2X Nov.--I Dec. 1978 IO -44.7 IX Dec. 1978 6 -07 IY-25 Dec. 1978 6.5 .. 59 7 X Jan. 1979 5 -94 Y 12Jan. l97Y 20 _ 22 24 25 Jan. 1979 6 -79 27 30 Jan. 1979 12.3 29.5 II I2 Feb. lY7Y 4,) -58 13 15 Feb. 1979 18.5 - 12.3 6 Mar. I979 5 -71 7-9 Mar. l97Y 18.5 -2X.6 IO II Mar. l97Y 7,, -129 13-17 Mar. I979 25 - 10.4 6 June 1979 70 -85 34-26 June lY7Y 21.8 -29

26 June I979 5 -45 28 30 June 1979 23.5 IO 2Y Aug. I979 x - I50 l-5 Sept. 1979 12.5 _ ‘2.8 IX scp. I Y79 70 - I56 3 60ct. 1979 ix.0 -- 24.5

Fig. 6. The distribution of R, with DsI,,,, and the regression line.

exobasc. The variations of S,, and V with L are given by Fig. 9 of LEMAIRE (1985). For L = 6.6. h,, =

1000 km, one obtains

S,, = 2.6 x IO” cm’ W/I ‘. (5)

V= 3.6 x lO”‘cm’ W/J ‘. (6)

The Hux F, can be approximated by equation (3.22) Of LEMAIRF: ( 1985)

with

F = F”(l -n!n,,) (7)

F, = n,C,,,:‘4. (8)

Here, no is the exobasc density and C,,, the average thermal ion speed at the altitude of the exobase. n,>, is the value of equatorial electron density cor- responding to diffusive equilibrium. Equation (7) expresses the fact that thcrc is no net upward Hux of ionospheric electrons when the equatorial density has reached its saturation value which is the one cor- responding to diffusive equilibrium.

The first term of the right-hand side of equation (2) corresponds to the variation of the density associated with the contraction or the expansion of the tube of force considering its movements of corotation and

convection. Figure 14 of LEMAIRE (1985) shows that

the daily variation ofn,,, associated with this term may be very important for a ‘tear drop’ plasmapause. But in our case, WC neglect this term since WC arc only

intcrcstcd in the variations of N,,,,,,,, in the period of 24 h. After 24 h the tube of force returns to its original

position again. at least if the radial expansion of the plasmasphere has not yet been too important. So we can write simply

dn 2f-,.S,,

dr = .- v--

or. according to equation (7)

dn 2F,,S,,

dt = (n

Vn,,: I)’ -12). (10)

We rewrite this in the form

dn n,,,--n

dt= .r ’

where

(11)

Vn,,

’ = 2F,S,, (I’)

r rcprcscnts the characteristic time for II to reach the saturation value nUL.

Equation (7) indicates that the Hux from the iono-

sphere to the plasmasphere should vanish when the equatorial electron density reaches the saturation value n,,,, which is achieved when the diffusive cqui- librium (DK) is established. WC USC the saturation value of the electron density obtained earlier as the value of nDF. So. we have

t1 . ..=7lcm ‘.

Equation (8) gives the expression of F,,, where

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192 X.-T. SONG, R. GENDRIN and G. CAUVAL

C,, = (8kT/rrm)“’ (13)

Following LEMAIRE (1985), we take the parameters at the altitude of exobase as follows

n, = 103cmm3,

TH+ z 3000K,

which gives

C th = 8 x 105cmss’,

F0 = 2 x lo* cm-* ss’.

Taking the values of F,, S,,, V given above, and choosing the value of nDE = 71 cmP3, one finds from equation (12)

T = 2.5 x lo5 s % 2.8days. (14)

As we shall see later, this value is comparable to the value determined from empirical modelling obtained from several storms (see Section 3.3).

The solution of equation (11) is

n = nDE + (n, - nDE) exp ( - t/z). (1%

Here n, is the initial value of density at the time of beginning of the refilling process. Since n, ,< 10cmP3 one has nDE >> n, and one can approximate equation (15) at least at the beginning of the event, by

Hence

%so v ’ (17)

and with the value that we have chosen one finds

R/ z 24cmm3 day-‘.

This is in very good agreement with the observations (see Section 2) at least for the case of weak Dst indices.

3.2. The rate of rejlling under disturbed conditions

From equation (17), together with equations (8) and (13), one sees that the refilling rate Rr is pro- portional to in’/*, where m is the ionic mass. For a given temperature and density at the exobase, one thus expects the refilling rate Rf to decrease when the average mass of ions is increased. In other words, the light ions can be removed upwards more easily than the heavy oxygen ions from the topside ionosphere. TAYLOR (1972) reported evidence for a transition region, related to the location of the plasmapause, poleward of which the concentration of light ions (H+, He+) decreases sharply, and referred to as the

light ion trough. Taylor has shown that the light ion trough minimum moves equatorward, and deepens, in response to magnetic storms. After an intense storm (a situation corresponding to strongly negative

Dst index) one then expects the topside ionosphere to be depleted of light ions. In this picture, periods when the average Dst index is the most strongly negative would tend to correspond to smaller concentrations of light ions, and thus to smaller values of the refilling rate R,. This process might explain the anticorrelation which has been found in Fig. 6 between R, and the absolute value of Dst, though more experimental data on ionospheric composition at exospheric altitudes are needed to confirm the validity of this interpret- ation.

3.3. Modelling

We have seen above that it is somewhat difficult to

isolate pure refilling events from variations of N,,, related to other causes because the processes of trans- port along field lines and across field lines (under magnetospheric convection) are intermixed. For this reason, we have tried to construct a simple model in

which both sources and losses of plasma are included. Also, the notion of refilling rate (RJ is not very

adequate in this context where electron density is expected to increase towards saturation with an exponential (rather than linear) law [equation (15)]. In Section 2, refilling rates RJ have been determined assuming implicitly a linear increase of N,,,, with

time [equation (l)]. It is probably more accurate to determine a time constant (r), rather than a refilling rate (R,) from the data set. Therefore we propose a model in which the variation of the (maximum) den- sity n at geosynchronous orbit is given by

dn/dt = (nDE- n)/z, -max(K,,(t-At)

--&,Cr)(n-nmin)/r2. (18)

The first term on the right-hand side corresponds to the refilling process as discussed in Section 3.1 [equa- tion (1 l)]. The second term is a loss term introduced to account for the effect of convection. For modelling this effect, the Kp index is used, since it allows for a better time resolution than Dst,,, does, the loss processes being efficient on time scales much smaller than 24 h. The size of the plasmasphere is controlled by the strength of the convection which is itself related to the K,, index (see for instance, Wu et al., 1981; ZI et al., 1982 ; HIGEL and Wu, 1984). Here we assume that, as long as the K, index remains smaller than a threshold value K,, the geosynchronous orbit crosses the plasmapause, so that the spacecraft encounters the tubes drifting along closed orbits for which no

Page 9: Refilling process in the plasmasphere and its relation to magnetic activity

Refilling in the plasmasphere

Table 3. Results of the model

193

Standard

($ 2) rr, iz Number of deviation

Dates Figure days used error (cm-‘) -_

1978: 28 Nov.--13 Dec. 2 72 3 2 15 16 13.3 1978 : 19-26 Dec. 4 93 6 3 6 7 3.9 1979 : 9-20 Jan. 5 27 18 2 24 12 Il.1 1979 : 28 June-13 July 3 69 24 3 21 16 14.2 1979 : 22-31 Oct. 3 21 3 2 15 10 16.2

Average d:;) II 2.4 16 (= 2.3

The standard deviation error is given by [(Z,“_ , e~)/N]“‘, where e, is the difference between the measured value of Nmax and the value given by the model for a given day, and N is the number of days used in the computation of the model parameters.

plasma is lost by convection. In that case, since K,, < KF;,, max (KP - Kpo, 0) = 0 and equation (I 8) does not contain any loss term. On the contrary when KP > K, the geosynchronous orbit lies entirely outside the plasmasphere and plasma loss through convection starts to be efficient, its efficiency being larger and larger as K, increases above Kpo. Since the process of the plasmasphere contraction is not immediate, a time delay At has been introduced in equation (18). The time t which intervenes in the second member of this equation is the time at which the maximum value of N, was observed for a par- ticular day.

Two other parameters have been introduced to model this convection loss. One is the time constant z2 which expresses the rapidity with which the plasma is convected. The other one is nmin, which is the mini- mum value of N,,,. Over the 4 month period over which this study has been performed, IV,,,, was never observed to drop below li,in = 7cmm3. The loss pro- cess can never bring n below nmin. This fact can be interpreted in the following manner. During the after- noon, even when the GEOS orbit does not cross the plasmasphere, it encounters open convection tra- jectories which have been convected to the daylight ionosphere for almost half a day. The electron pro- duction of the daylight ionosphere is always sufficient to bring the equatorial density to a value equal to or larger than 7 cm -3.

Thus. the two imposed parameters in equation (I 8) are nDE = 71 cmM3 and nmin = 7cme3, as determined from the observations. The other parameters (z,, r2, I$,,, At) are free parameters, which have been adjusted to the data by the least square method. We have applied this method to the 5 magnetic storms dis- played in Figs. 2-5. The results are reported in Table 3.

From the figures, one sees that the model (dashed line) reproduces rather well the observations (con- tinuous line), though some discrepancies can be noticed. One may note in particular that the trend in the vacation of N,,, at the beginning of the refilling process is correctly reproduced, whether this variation is fast (Fig. 5) or slow (Fig. 4). The decreases of N,,,, associated with small decrease of Dstmi, occurring dur- ing the recovery phase are also reproduced, at least in a qualitative sense (2 and 6 December, Fig. 2 ; 8 July and 30 October, Fig. 3 ; 17 January, Fig. 5).

Examination of Table 3 shows that 3 of the unknown parameters fzt, t2, At) have values which depend on the storm under study, but that their aver- age values are realistic. For instance the average value of T, (2.3 days) is at least comparable with the theor- etical value (2.8 days) calculated in Section 3.1. The average values of the time constant r2 and the time delay At are also of the same orders of magnitude as the ones found for the erosion of the plasmasphere (CHAPPELL et at., 1970, 1972) or for the displa~ment of the eastward boundary of the plasmaspheric bulge (HIGEL and Wu, 1984).

The fourth unknown parameter I$ is on the con- trary very stable (between 2 and 3) whatever the characteristics of the storm. This gives us confidence that there is a rather well defined value of K,, of the order or 2,) 3 _ below which the plasmaspheric bulge always crosses the geostationary orbit. In such cases there is no loss of plasmasphe~c plasma on equi- potentials which cross this orbit and the daily maximum of the plasma density is just the result of the refilling process.

It is clear that our model suffers from some incon- sistencies. For instance cases for which zz is small whereas At is large are difficult to interpret (first and last cases of Table 3). This is due to the fact that we

Page 10: Refilling process in the plasmasphere and its relation to magnetic activity

194 X.-T. SONG, R. GENDRIN and G. CAUVAL

have used an index of geomagnetic activity which is defined by its instantaneous 3 h value. For processes which in fact depend on the history of geomagnetic activity it would be better to use an index which reflects this history by integrating and smoothing the past and recent activity.

Such an index has been recently introduced by WRENN (1987) and its interest for classifying the daily variations of foF2 at ionospheric stations or of N, at geostationary altitude has been demonstrated (WRE:NN et al., 1987). Further studies which would make use of such an index should be undertaken and some of the inconsistencies of our model would prob- ably disappear (WRENN, private communication).

The following points summarize the analyses of the GEOS-2 RS data concerning the characteristics of the

(1)

refilling process.

(2)

There are good relationships between the vari- ations from day to day of the maximum electron density in the plasmaspheric bulge region and the variations of the minimum Dst index taken on the preceding day. This probably refIects the fact that erosion of ring current particles and refilling of the plasmasphere are two processes occurring under comparable conditions (both processes occur under quiet periods and are inter~pted by enhancements of magnetosphere activity). The delay of 1 day is probably due to the injection of ring current particles being more rapid than the removal of plasmaspheric particles by sudden enhancements of magnetospheric convection. The refilling rate increases with the decrease of absolute value of list index. With the aid of exist- ing data it is found to range from N 10 to 25 cmP3 day-‘. The corresponding refilling time constant ranges from x 3 days to more than 7 days, depending on Dst index. This dependence

4. CONCLUSION

is interpreted as being due to the change of com- position in the topside ionosphere occurring under disturbed conditions.

(3) With the simple equation of LEMAIRE (1983, reproduced here in equation (Z), after correction by a factor of 2 to include the refilling from both ends of the magnetic tube, we can compute the refilling time and the corresponding refilling rate expected by theory. This last quantity com- pares well with the average refilling rate (Z 25 cmm3 day-‘) that has been experimentally deduced for small absolute value of Dst.

(4) A simple model has been developed, which gives the variation of electron density under the com- bined effect of refilling from the ionosphere and loss by convection. It generally provides reason- able accord with the observations. There is some scatter in the parameters determined by the model from one event to the other, due to the complexity of the factors governing the variation of the distribution of electron density at the geo- synchronous orbit or at ionospheric levels. How- ever the study shows that the value of Kp that statistically separates situations in which GEOS crosses the plasmapause (and therefore measures plasma for which there is no loss by convection over a 24 h period) from situations in which it does not, can be determined very accurately (& = 2 _ ,3 +) . On average, the refilling time con- stant inferred by the model (2.3 days) is com- parable, although somewhat smaller than the value inferred from theory (2.8 days).

Further improvement in the theory could be made only by having better information on the ionospheric temperature and composition at the exobase and on their variation with magnetic activity. These par- ameters are fundamental for evaluating the upward flux of electrons which governs the refilling of the plasmasphere.

AckHow/edget~lentr----We thank the two referees for their con- structive remarks.

BANKS P. M., and HOLZER T. E. CARPENTER D. L. and PARK C. G. CHAPPELL C. R., HARRIS K. K. and SHARP G. W. CHAPPELL C. R., HARRIS K. K. and SHARP G. W. CHAPPELL C. R. CHEN A. J. and WOLF R. A. CHEN A. J. and GREBOWSKV J. M. D~~CX&AU P. M. E., ETCH~TO J., KNOTT K.,

PEDERSEN A., WRENN G. L. and YOUNG D. T. D~CRBAU P. M. E., B~GHIN C. and PARROT M.

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