Plasmaspheric convection with non-closed streamlines

JournolofAtmospheric

and Erresrriai

Pergamon

Physics, Vol. 56, No. 12, pp. 1629-1633, 1994 Copyright 0 1994 Elsevier Science Ltd Pnnted inGreatBritain. All rights reserved

0021-9169194 37.00+ 0.00

0021-9169(93)E0004-5

Plasmaspheric convection with non-closed streamlines J. F.

LEMAIRE*

and R. W.

SCHUNK

Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322-4405, U.S.A. (Received infinalform

18 October 1993 ; accepted 1 November 1993)

Abstract-A mechanism is described to drive a continuous outflow of thermal plasma in the plasmasphere without violating Faraday’s law. It is based on time-dependent interchange motion.

I. INTRODUCHON

plasma

One of the most recent empirical electric field models for magnetospheric convection is shown in Fig. 1. It has been determined by MCILWAIN (1986) from dynamical energy spectra (< 10 keV) of electrons and ions observed along the geosynchronous orbit. The outer circle has a radius of 10 R,. The solid curves correspond to the equipotential lines of Mcllwain’s electrostatic field model when the level of geomagnetic activity is relatively low (Kp = 2). The last closed equipotential nasses through the point of singularity (6) where E =b. This point% also called the stagnation point because the convection velocity Y=

ExB/B’

density,

as well as the equatorial

density

n,,(L), is therefore expected to be rapidly in diffusive equilibrium within this closed shaded region. On the other hand, all plasma elements located outside the shaded area drift along open equipotential lines and do not have enough time to refill to high density levels. They contain almost no cold plasma when they drift down the magnetotail, and their time of residence before they reach the front side of the magnetopause is too short to accumulate an appreciable amount of ionospheric plasma. This is why NISHIDA (1966) and

DAWN

(1)

is equal to zero at this location. For Kp = 2 the stagnation point is at an equatorial distance of 8.1 RE in the dusk local time sector. For Kp = 0 it would be at a slightly larger radial distance (9 RE). The last closed equipotential (LCE) has often been identified with the plasmapause (see review by RYCROFT, 1974); it coincides with the outer boundary of the shaded region in Fig. I. All plasma elements inside this shaded region circulate along closed streamlines that are parallel to the equipotential lines confined inside the LCE. No plasma can drift out of this closed region. Since all plasma elements are trapped in this region, they should have ample time to refill and to saturate at density levels corresponding to diffusive equilibrium and near hydrostatic equilibrium. All flux tubes in this region are, therefore, expected to have the highest possible densities corresponding to isotropic Maxwellian velocity distributions which are in balante with the ionospheric plasma. The field aligned _ ..-.*On leave of absence from Institut d’Aeronomie Spatiale de Belgique, 3 Ave Circulaire, B-l 180 Brusselles, Belgium.

DUSK Fig. I. Magnetospheric convection. The solid curves correspond to electrostatic equipotentials obtained from the McIlwain electric field model for Kp = 2. The dotted circle is at a radius of 10 RE. The dashed curve passes through the dusk stagnation point. The shaded region corresponds to the closed field line region.

1629

1630

J. F. LEMAIREand R. W. SCHLJNK

BRICE (1967) expected that the last closed equipotential line should coincide with the position where GRINGAUZ (1961) and CARPENTER (1963) observed a sharp knee in the equatorial density distribution. According to this early scenario, the longer the Efield distribution remains in a steady state, the sharper the plasmapause density gradient should be. However, both whistler and satellite observations indicate that this is not the case. Indeed, it is not until after prolonged periods of quiet conditions that one observes well-defined plasmapause density gradients, but they occur immediately following substorm onsets associated with sudden changes in the magnetospheric electric field (GREBOWSKY, 1970). On the contrary, after 5-6 days of very quiet geomagnetic conditions, there is no evidence, up to L = 7-8, of a sharply defined plasmapause gradient. Furthermore, even after 5-6 days of quiet conditions, the equatorial density never reaches the expected saturation level corresponding to diffusive equilibrium ; its profile decreases with a characteristic slope ranging between L~-4 and L- 3 (CARPENTERand ANDERSON, 1992). Note that the equatorial density distribution corresponding to diffusive equilibrium is much flatter (ANGERAMI and THOMAS, 1964) and even increases with L beyond the geosynchronous radial distance. Finally, it has been shown from whistler observations that even after 8 days of very quiet conditions, corotating flux tubes at L - 3 are still in a state of refilling, with more ionization flowing up out of the dayside ionosphere than flowing down into the nightside ionosphere (PARK, 1970; TARCSAI, 1985). All these experimental observations have led LEMAIRE and SCHUNK (1992) to the conclusion that there should be a slow and continuous outflow of plasma from the plasmasphere, i.e. that there should be a net loss of plasma from the shaded region even during quiet conditions. This outward plasma drift has been called the ‘plasmaspheric wind’ by analogy with the corotation-expansion of the solar corona at low heliographic latitudes. Although it can be argued : (1) that under prolonged very quiet conditions the last closed equipotential may extend to the magnetopause, i.e. that the sharp plasma density gradient is located beyond L = 7-8, and, otherwise (2) that for L = 3 flux tubes, the hydrodynamic refilling models of RICHARDS and TORR (1985) and BAILEY et al. (1978) can match observed H+ densities for conditions close to diffusive equilibrium, there is, nevertheless, no obvious reason why a continuous plasmaspheric wind cannot exist. Indeed, this plasma flow pattern with open streamlines offers more general solutions of which the closed streamline model is a very singular one. It also offers

a relatively observations

simple, single explanation at once.

for all these

2. CONVECTION VELOCITY MODELS WITH A DC RADIAL COMPONENT It is generally considered that a continuous outward plasma transport, like the plasmaspheric wind described above, requires an E-field with a non-zero DC eastward component in addition to the corotation component. This would imply that the streamlines inside the shaded area in Fig. 1 are not closed curves, but are open spirals as illustrated in Fig. 2(a) and 2(b). In these latter figures, an outward drift velocity of 100 m/s has been added to the convection velocities of McIlwain’s model. If the plasmaspheric velocity is smaller than 100 m/s, as suggested by LEMAIRE and SCHUNK (1992), the spirals would be tighter and plasma elements would have to circulate more times around the Earth before they escape the shaded region and reach the magnetopause in the afternoon local time sector. Furthermore, since the plasmaspheric wind is, in general, not azimuthally uniform, but is inversely proportional to the integrated Pedersen conductivity, the spirals would be less tight on the nightside than on the dayside. As a consequence, the late afternoon time sector where the plasma escapes should be less extended in local time than illustrated in Fig. 2(a) and (b). It follows that, according to this new magnetospheric convection model, a high-density plasma tail should always be present in the late afternoon local time sector. Note that this permanent plasma tail and its well-defined westward ‘shoulder’ are not formed as a result of a brief enhancement of the dawn-dusk electric field component, as in the MHD models of CHEN and WOLF (1972) and GREBOWSKY (1970). Furthermore, this plasma tail is a stationary feature of our model, i.e. it does not corotate to the east during the subsequent period when the intensity of the dawnAusk convection electric field decreases, which is in contrast to what occurs in the time-dependent MHD models by these authors. The tail-like area shaded horizontally in Fig. 2(b) may correspond to the ‘new plasma region’ identified by CARPENTER(1966) in the afternoon sector. The plasma density level in this non-corotating region is smaller than that in the main corotating plasmasphere [shaded obliquely in Fig. 2(b)], but it is higher than that in the plasma trough region (non-shaded zone). The existence of such a non-corotating plasma tail with intermediate densities has been confirmed and re-emphasized in a recent paper by CARPENTERet al.

1631

Plasmaspheric convection with non-closed streamlines DAWN

IlAwN

(b)

(4

Fig. 2. M&vain magnetospheric convection pattern with an outward drift velocity of 100 m/s superimposed. (a) Streamlines of the flow; (b) streamlines that extend from the low-latitude ionosphere to the magnetopause. The shaded region shows the connection of the plasmasphere to the magnetopause.

(1992). Therefore, the presence of this non-corotating plasma region beyond the plasmapause in the late afternoon sector with a well-defined westward edge supports the present model predictions (see also CARPENTERand ANDERSON,1992). There remains, however, one problem to be addressed : how to produce the eastward electric field component which drives the plasma outwards?

3. INDUCTIVE-ELECTRIC FIELD AND

MAGNETIC

FLUX

VARiATION

The convection electric field, E = -v x B, driving the outward cross-l plasma flow must be eastward. To determine the consequences of this, we consider a fixed, closed contour, C, that surrounds an open surface, S, in the equatorial plane of the magnetosphere, such as the dotted circle in Figs 1 and 2. The magnetic flux Q,(r) across the open surface is, Bfr, t) * n(r) dS,

(2)

where n is a unit vector normal to the open surface. Faraday’s law then indicates that E*dI = --$,(r).

If B is independent of time, then a’s is independent of time. Therefore, the line integral in equation (3) is zero. This indicates that the local time average of the azimuthal electric field component, E,, is zero, as is the case in the model of Fig. 1. This is the main reason why no previous magnetospheric electric field models have had a DC eastward component. However, the assumptions that the magnetic flux across any fixed surface is a constant and that aB/dt = 0 are violated all the time, not only due to a secular variation of the geomagnetic field, but more importantly due to the periodic and aperiodic variation of magnetospheric and ionospheric currents which produce inductive electric fields of the order of several mV/m in Canadian power lines. These AC, or short-term ~rturbations, are important for a number of magnetosphe~c effects, such as the acceleration of ring current particles, the ~netration of solar wind plasma into the ma~etosphere, and the plasmaspheric wind discussed in this article. In space plasma physics, it is generally considered that these AC inductive E-fields average out in a Iong-term limit, and that their effects, including power deposition in the magnetosphere, are small compared to the effects of DC electrostatic fields. Even though it has not yet been verified experimentally that in a long-term average, aB(r, l)/& is equal to zero and that B,(t) is

constant, this a priori assumption

is generally made

J. F. LBMAIRE and R. W. SCHUNK

1632

when steady-state magnetospheric convection (electrostatic) models are tailored. Of course, this simplifies considerably the mathematical descriptions, but it may not necessarily be a realistic assumption in modeling time-dependent magnetospheric effects. In the following paragraph, we describe a mechanism that leads to a plasmaspheric wind without violating Faraday’s law (3).

4.

TRANSPORT

BY PLASMA

INTERCHANGE

MOTION

Let us first consider the time-dependent case when Ep(t) is eastward along some parts of the contours C and westward along other parts of this contour, such that the local time average of E, and $c E - dl = Z(t) are equal to zero, or that the value of Z(f) fluctuates in time around a zero mean value (I, = 0). In this time-dependent situation, a net flow of plasma can be transported from the inner to the outer plasmasphere across the fixed contour C, despite the fact that the universal time average of magnetic flux Qs(t) is a constant. This occurs when the plasma density is denser at all, or at most, places where Eti is eastward, while it is less dense where E, < 0. Indeed, the E, x B/B2 drift is then outwardly directed where the plasma density is enhanced and inward where it is depressed relative to the background density. We assume for simplification that /I is small and that B is the same along the contour C, i.e. that this contour corresponds to an iso-intensity contour of B. As a result of the non-uniform distribution of plasma, there is a net outward mass flow of plasma, despite the fact that O,,(t) is constant or is so in a long-term average. This occurs in a plasmasphere wherein the density distribution is highly structured and non-uniform in the azimuthal and radial directions (e.g. an inhomogeneous plasma with small-scale density enhancements and depressions like those that scatter or guide whistler waves along geomagnetic field lines). As a consequence of the eastward gravitational drift of the positively charged ions and of the oppositely directed drift motion of cold electrons, an azimuthal polarization electric field is set up inside all plasma density enhancements, while outside and within density depressions oppositely directed electric fields are set up, as described by LEMAIRE(1976). The result is that dense cold plasma elements fall down in the gravitational potential well, while the less dense material bubbles upwards. In this situation, there is a net downward plasma flow due to gravitationally induced plasma interchange motions. For ions with energies greater than 0.5 eV, the gradient-B and curvature drifts dominate the gravitational drift. This

happens to be the case in the middle and outer plasmasphere. In this case, the directions of the azimuthal electric fields are reversed ; eastward polarization Efields are present inside plasma density enhancements, while westward fields occur in density depressions. The net result is that for suprathermal plasma (T > 5000 K) there is a continuous outflow of mass due to plasma interchange motion driven by gradientB and curvature drifts. A detailed mathematical formulation of plasma interchange motion can be found in SOUTHWOOD and KIVELSON(1989). MORFILL et al. (1993) have proposed that radial plasma transport is driven in dusty planetary magnetospheres, like that of Saturn, by an interchange mechanism similar to that we have proposed for the Earth’s plasmasphere. A net outward transport of plasma by interchange motion is the mechanism that we propose for driving the plasmaspheric wind. With this mechanism, fc E - dl and dQ,/dt remain equal to zero, at least in a long-term average sense.

4. CONCLUSIONS

A cross-l outward flow of plasma has been suggested by LEMAIREand SCHUNK(1992) based on a set of whistler and satellite observations which have been recalled in the Introduction. Such a net outflow of plasma, which we called a plasmaspheric wind, is, however, inconsistent with most of the convection electric field models available. It requires a DC eastward electric field which is not present in models like that illustrated in Fig. 1. Indeed, it is generally considered that a radial expansion of the plasmasphere would violate Faraday’s law (equation 3). In this paper, we have described a physical mechanism which can account for such a plasmaspheric wind expansion without violating Faraday’s law. The mechanism that drives a plasma flow from the inner to the outer plasmasphere and through the plasmapause is plasma interchange motion induced by gradient-B and curvature drifts of the ions and electrons with energies larger than 0.5 eV. Indeed, these drifts induce eastward electric fields in small-scale plasma density enhancements and westward electric fields in density depressions. Such density features are always present in the middle and outer plasmasphere. On average, the eastward E-fields may be balanced by the westward fields so that the line integral $c E *dl is equal to zero or fluctuates around an almost zero mean value. Nevertheless, the eastward electric field drives a larger mass of plasma outwards, then the

Plasmaspheric convection with non-closed streamlines

1633

fietd drives toward the Earth. The net flow of plasma is, therefore, outwards, despite the fact that the magnetic fiux inside any fixed closed contour C

during substorm events, when large pieces of the nightside plasmasphere are peeled off.

remains constant, at least in a long-time average. This continuous transport of plasma adds to that occurring

grant NAGS-1484 and NSF grant ATM-93-08163 to Utah State University.

westward

~c~no~~edge~enf-This research was supported by NASA

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