Out¯ow of cold dense plasma associated with variation ofconvection in the outer magnetosphere

Hiroshi Matsuia,*, Masato Nakamurab, Toshio Terasawab, Yuichi Izakib,Toshifumi Mukaic, Koichiro Tsurudac, Hajime Hayakawac,

Hiroshi Matsumotod

aSpace Science Center, University of New Hampshire, Morse Hall, Durham, NH 03824, USAbDepartment of Earth and Planetary Physics, University of Tokyo, Tokyo, Japan

cInstitute of Space and Astronautical Science, JapandRadio Atmospheric Science Center, Kyoto University, Kyoto, Japan

Received 30 July 1999; received in revised form 24 March 2000; accepted 3 April 2000

Abstract

Cold dense plasma with the ionospheric origin is often observed in the outer magnetosphere with L values as

large as 10. We have examined the electric ®eld data accompanied by the cold dense plasma. The electric ®eld dataare obtained by the direct measurement of the drift motion of electrons released from electron guns. We getwestward components of convection. In addition, there is an AC component of electric ®eld in the ULF range

larger than the DC component. If such a large variation of electric ®eld exists in the vicinity of the stagnation point,the plasmaspheric plasma is expected to ¯ow away to the outer magnetosphere. Then we have a test particlesimulation by adding a potential variable in time. There is a particle out¯ow accompanied by the AC variation of

electric ®eld in the ULF range. If there are more complicated variations of electric ®eld, it is possible that particles¯ow out frequently. 7 2000 Elsevier Science Ltd. All rights reserved.

1. Introduction

Cold dense plasma with the ionospheric origin is

often observed in the outer magnetosphere with L010

(Matsui et al., 1999). When they examine velocity

moment data, the plasma is often accompanied bywestward convection. It indicates that the plasma is

located outside the corotation region, in which the

convection is eastward. One possible source of the

plasma is direct supply from the ionosphere. The con-vection velocity passing through the region close to the

stagnation point is much smaller than the corotationvelocity so that a large quantity of plasma is supplied.Another possible source of the plasma is the plasma-sphere, from which particles ¯ow away because of the

quasi-continuous variation of the location of the stag-nation point. Such a variation of the location of thestagnation point is caused by the variation of the elec-

tric ®eld. As for magnetic variations ULF waves areoften observed at the geosynchronous orbit (Kokubunet al., 1989). It is expected that there is a large ¯uctu-

ation of the electric as well as the magnetic ®eld.Although the local time is di�erent, Equator-S

Journal of Atmospheric and Solar-Terrestrial Physics 62 (2000) 521±526

1364-6826/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved.

PII: S1364-6826(00 )00060-2

* Corresponding author. Tel.: +1-603-862-3693; fax: +1-

603-862-0311.

E-mail address: hiroshi.matsui@unh.edu (H. Matsui).

measurements by Quinn et al. (1999) reported large¯uctuation of the electric ®eld as compared to the DC

electric ®eld. Time scales of the ¯uctuations are severalseconds to minutes.In this paper, we investigate convections ac-

companied by the cold dense plasma obtained by thebeam instruments onboard Geotail. We try to see theAC component of electric ®eld. Based on the obser-

vations, there is possibility to have a large amplitudeof AC electric ®eld in the vicinity of the stagnationpoint. Thus we perform a test particle simulation. We

add AC component of electric ®eld in the ULF rangein order to see an out¯ow of the plasmaspheric plasmato the outer magnetosphere.

2. Observation of convection associated with the cold

dense plasma

Fig. 1 shows an example of the electron density ob-servation by Geotail in the outer magnetosphere with

MLT0 15. The data are obtained between 1030 and1100 UT on 11 April 1993. Each data point isobtained by visual inspection of the wave spectra from

the plasma wave instruments. Details of the instru-ments are discussed by Matsumoto et al. (1994). Thenumber of data points in Fig. 1 is not large because itis often hard to recognize the electron plasma fre-

quency. The average density is estimated to be 3.8cmÿ3. Although we cannot use the data from the par-ticle experiment. we infer that we have observed cold

dense plasma with low energy less than a few tens ofelectronvolts. One reason is that a typical density inthe outer magnetosphere observed by the particle

instruments above the energy is less than 1 cmÿ3 (Mat-sui et al., 1999).Fig. 2 shows three components of convections

obtained by the beam instruments with the same inter-

val as Fig. 1. Details of the instruments are given inTsuruda et al. (1994) and Tsuruda et al. (1998). The

calculated electric ®eld is estimated by using the drift-step method (Paschmann et al., 1998). Radial com-ponent ER, azimuthal component EA, and upward

component EZ are shown in the SM coordinate systemand in the frame moving with the satellite. Positivedirection is outward for ER and eastward for EA. The

instrument measures the drift motion of electrons byreleasing them in the perpendicular direction to theambient magnetic ®eld. The dominant component of

the drift motion is the E� B drift. In Fig. 2 we canrecognize a westward component of convection, whichis inferred from positive values of ER. We should notethat the direction of the electric ®eld is perpendicular

to that of the convection. The average value of ER, is0.91 m V/m. If we take into account the e�ect of the

Fig. 2. Electric ®eld pro®le between 1030 and 1100 UT on 11

April, 1993. Radial component ER, azimuthal component EA,

and upward component EZ are shown in the SM coordinate

system and in the frame moving with the satellite.

Fig. 1. Density pro®le between 1030 and 1100 UT on 11

April 1993.

H. Matsui et al. / Journal of Atmospheric and Solar-Terrestrial Physics 62 (2000) 521±526522

motion of the satellite, the azimuthal velocity in theinertia frame is ÿ11.9 km/s. The obtained value is

close to the average value of the observations by theparticle instruments (Matsui et al., 1999). We shouldalso note that there is a large ¯uctuation of electric

®eld with an approximate period of several minutes.The ¯uctuation is larger than the DC component. Thestandard deviation of the azimuthal component of

electric ®eld is 1.50 mV/m. Such a situation with ACcomponent larger than DC component is also reportedby Quinn et al. (1999) in the dawnside magnetosphere,

although the location is not often categorized as theplasmasphere. When we discuss drift motion of par-ticles, we usually assume that the convection electric®eld only consists of the DC component. However,

orbits of particles are modulated by the AC com-ponent of electric ®eld with a size larger than the DCcomponent. If such a large component of AC electric

®eld actually exists in the vicinity of the stagnationpoint, the behavior of particle out¯ow from the plas-masphere could be more complicated. Thus, we set a

model AC electric ®eld in the ULF range and traceorbits of test particles in order to see the possibility oflarge occurrence frequency of cold dense plasma in the

outer magnetosphere.

3. Calculation

For the above purpose, we have calculated orbits ofparticles by using a model electric ®eld. First, we

assume a Volland±Stern-type convection model. Thepotential F is given as

F � C1

Lÿ C2Lsin f, �1�

where C1 and C2 are parameters, L is the L-value, and

f is the magnetic local time. The ®rst term in the rightside of the equation represents the corotation electric

®eld, while the second term is the convection electric®eld. The parameter C1 is constant, because particlescorotate with the Earth once a day. On the other

hand, C2 is a variable depending on the condition ofthe solar wind. Fig. 3 shows an orbit of a particle inthe vicinity of the stagnation point with the above po-

tential. We calculated the E� B drift at the geomag-netic equator by using the Runge-Kutta method. Thetime step is 0.5 s. The location of the stagnation point

is set at 6RE from the Earth. We assumed the geomag-netic ®eld as a dipole. The particle orbit at 18 MLT islocated at 5.99RE from the Earth. The location is justinside the stagnation point. The particle mostly spends

time at a region close to the stagnation point. Theorbit is not variable in time with a period of 3355 min,although it is much longer than 1 day. There is no

possibility that the particle ¯ows away to the outermagnetosphere, if the potential is constant. However,

Fig. 4. Particle orbits with a Volland±Stern-type and a vari-

able potential in time with amplitudes of (a) 0.35 kV and (b)

0.45 kV. The region in the vicinity of the stagnation point is

shown.

Fig. 3. Particle orbit with a Volland±Stern-type convection

model. The region in the vicinity of the stagnation point is

shown.

H. Matsui et al. / Journal of Atmospheric and Solar-Terrestrial Physics 62 (2000) 521±526 523

the electric ®eld is quite weak around the stagnationpoint, at which the magnitude of corotation electric

®eld is comparable to that of convection electric ®eld.It indicates that the particle orbit can change dramati-cally, if we add a potential DF around the stagnation

point.Although the actual con®guration of the variable

potential is complicated, we assume the following po-

tential DF with a simple form. It is mostly limitedaround the stagnation point and is variable with aperiod T,

DF � a � exp� ÿ br 2 � � sin

�2ptT

�, �2�

where r is the distance from the stagnation point and aand b are parameters relevant to the size of the poten-

tial. We neglect a variable component of magnetic®eld.As for DF, there are three parameters. T is set as 5

min, because we are interested in potential variable intime in the ULF range. The parameter a relevant tothe amplitude of the potential is set as a free parameterin this case. It is chosen between 0.00 and 1.00 kV

with a step of 0.05 kV. The parameter b relevant tothe spatial extent is taken as 1:0� 104 Rÿ2E : It indicatesthat the scale length of the potential is 0.01RE, which

is the same as the minimum value of the distancebetween the stagnation point and the particle orbitwithout any variable potential. We expect that the par-

ticle orbit is modulated by the variable potential DF:Fig. 4 shows two orbits of particle drift with di�er-

ent amplitudes of potential. The orbits in the ®gure are

con®ned within a region around the stagnation point.Fig. 4a is a simulation for a case with a � 0:35 kV,while Fig. 4b is that with a � 0:45 kV. An initial lo-cation of the particles is located at 15MLT. There are

few e�ects of the perturbation, when the locations ofthe particles are far away from the stagnation point.As the distance between the location of the particles

and the stagnation point becomes as small as 0.02RE

with increasing magnetic local time, the particle orbitsbegin to oscillate around the stagnation point. The

particle orbit with a � 0:35 kV is not so di�erent fromthat with a � 0:45 kV, when the particle approaches tothe vicinity of the stagnation point. Then the particleorbit with a � 0:35 kV is connected to the location

with later magnetic local time so that the orbit is con-®ned within the corotation region. On the other hand,the magnetic local time of the particle orbit with a �0:45 kV becomes earlier so that it is connected withthe outer magnetosphere. As for other values value ofa, the particle orbits with aR0:35 kV are con®ned

within the corotation region, while the particle orbitswith ar0:40 kV are connected with the outer magne-tosphere. A potential with a larger perturbation leads

to out¯ow of plasma. One reason is that the particle

orbit with a larger perturbation is largely shifted fromthe original orbit without any variable potential.We set a parameter a as 0.45 kV for one of the

simulations. The minimum distance between the stag-nation point and the particle orbit is about 0.02RE

which is shown in Fig. 4b. The amplitude of variableelectric ®eld is as large as 0.52 mV/m at a location,0.02RE from the stagnation point. Such a magnitude

of electric ®eld variation could exist, if we refer to theobservations at other regions by Geotail and Equator-S. The ambient electric ®eld at 0.02RE from the stagna-

tion point and at Y � 6 RE is about 1:3� 10ÿ3 mV/m,so that the particle drift in the ambient ®eld is much

slower than the motion caused by the variable poten-tial. It indicates that the particle motion is sensitive tothe AC variation of the electric ®eld.

In this simulation we have calculated orbits of theE� B drift of particles. However, there are other typesof drifts. If magnitudes of such drifts are not negli-

gible, the motion of ions is di�erent from that of elec-trons, which generates the current. In that case the

situation simulated in this study is not realistic. Thus,we estimate e�ects of the curvature drift, the gradientB drift, the polarization drift, and the drift caused by

non-uniform electric ®eld. The magnitudes of the cur-vature drift and the gradient B drift are mostly con-stant in the vicinity of the stagnation point. They are

smaller than 1/10 of the magnitude of the E� B driftby the ambient electric ®eld at the closest location

between particle orbits and the stagnation point. In thecalculation the energy of particles for both perpendicu-lar and parallel components is set as 1 eV, which is a

typical value for ionospheric plasma. The latter twodrifts, the polarization drift and the drift caused bynon-uniform electric ®eld, are important at locations

with a large amplitude of AC electric ®eld comparedto the magnitude of the ambient electric ®eld. The

amplitude ratios of the drifts to the E� B drift for theAC components are smaller than 1/100 with the abovecondition. The results from the calculations indicate

that the ratios of the four drifts to the E� B drifts aresmall, so that we have neglected the e�ects of the driftsother than the E� B drift. Nevertheless, it would be a

future work to calculate orbits a�ected by the otherdrifts to see the di�erence from the particle orbits only

with the E� B drift.We do not assume magnetic components of vari-

ation to simplify the calculation. One reason is that

the AC component of the magnetic ®eld is muchweaker than the DC component in the magnetosphere

near the Earth. It indicates that the magnetic variationis categorized as a higher term of components, so thatwe can neglect it. It is not true for the electric ®eld.

Another reason is that if both the electric and mag-netic ®elds are variable, the variation often corre-

H. Matsui et al. / Journal of Atmospheric and Solar-Terrestrial Physics 62 (2000) 521±526524

sponds to the Alfve n waves with magnetic as well aselectric components. However, some of the waves with

a period as long as 5 min are categorized as standingwaves which are con®ned within a geomagnetic ®eldline between ionospheres of both hemispheres. There

are no magnetic components at the geomagneticequator in the fundamental mode of the standingwaves (Kivelson, 1995). It indicates that the relation

between magnetic and electric components could becomplicated so we have only tried a simulation withoutany magnetic components of variation.

4. Discussion and conclusion

We have examined electric ®eld data obtained by thebeam experiment by Geotail. Cold dense plasma is ac-

companied by the westward convection. Moreoverlarge amplitude of AC electric ®eld with a period ofseveral minutes is observed. The Equator-S obser-

vation by Quinn et al. (1999) also shows a large ampli-tude of the AC electric ®eld compared to the DCelectric ®eld. If such a variation could exist in thevicinity of the stagnation point, particles possibly ¯ow

away to the outer magnetosphere. In that case, itmight be possible to explain the frequent out¯ow ofthe plasma in the outer magnetosphere.

So far the AC electric ®eld in the ULF range is notemphasized as a source to generate out¯ow of the plas-maspheric plasma. Thus we have a test particle simu-

lation with the Volland±Stern-type potential and thepotential variable in time in the ULF range in thevicinity of the stagnation point. Although Chen and

Wolf (1972) investigated e�ects of the convection vari-able in time, the time scale adopted by them is 8 h. Itis much longer than that of the present study. More-over, they tried to explain out¯ow of plasmaspheric

plasma related to substorms. Such a point is di�erentfrom our point to explain frequent out¯ow of theplasma. The spatial extent of the AC electric ®eld they

chose is large, while that in our study is con®ned inthe region near the stagnation point. In our simulation,an out¯ow of particles could exist, if there is a large

amplitude of AC electric ®eld in the ULF range. Fur-thermore, the situation has changed, if we set a par-ameter with a variable amplitude in time. After wetrace particle orbits with the parameter for one period

to corotate with the Earth without any perturbations,some particles ¯ow away to the outer magnetosphere.Some other particles are con®ned within the corotation

region. The ®nal location of the particles depends onthe initial phase of the variable potential. The actualcon®guration of the electric ®eld is expected to be

complicated compared to the above situation. Theamplitude is variable in time with multiple frequencyranges. The spatial variation of the potential could be

irregular. It is not so strange to have continuous out-¯ow from the vicinity of the stagnation point. More-

over protons and electrons could have di�erentbehaviors by the drifts other than the E� B drift. Forexample, it is true for the case with steep variations of

potential in time and/or in space compared to the vari-ation discussed in this study. A current could be gener-ated by a charge separation. There is a possibility that

plasma waves are destabilized by micro-instabilities.The next step is to construct a more realistic modelbased on the observations of the electric ®eld in the

vicinity of the stagnation point.So far we have discussed the e�ect of AC electric

®eld to the plasma out¯ow from the plasmasphere. Onthe other hand, the plasma out¯ow is often related to

the large geomagnetic activity. If there is a large vari-ation of convections, the plasmaspheric particles arerelocated in the open convection line. They are con-

vected toward the outer magnetosphere. We assumethat such an e�ect is also important as well as thee�ect of AC electric ®eld. It is a future work to investi-

gate the relative importance of the above two mechan-isms.

Acknowledgements

We are grateful to Tsugunobu Nagai and MasakiFujimoto for their valuable suggestions.

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