Relations between electric fields, currents, and plasma in the polar magnetosphere-ionosphere system

P&net. Space Sci., Vol. 24, pp.

841

to 848

Perguoon

Press. 1976.

Printed in Northern

Ireland

RELATIONS BETWEEN ELECTRIC FIELDS, CURRENTS, AND PLASMA IN THE POLAR MAGNETOSPHERE-IONOSPHERE SYSTEM

A BAHNSEN and A. M. HANSEN Danish Space Research Institute, 2800 Lyngby, Denmark (Receiued in fimZ form 23 February1976) Ah&act--Some aspects of the interaction between the shocked solar wind and a magnetically closed magnetosphere are studied. At the high latitude magnetopause, plasma inflow is shown to be possible and to depend on the relative orientation of the magnetic fields on either side of the magnetopause. On this basis several observational characteristics of the plasma mantle and the polar cap electric fields are explained: the correlation between mantle and magnetosheath flow speed; the temperature anisotropy of the mantle plasma; the pressure gradient in the mantle transverse to the magnetic field; the correlation between the dawn-dusk asymmetry of the polar cap electric field and the Y-component of the interplanetary magnetic field; the average strength of the polar cap electric field. The between the polar ionosphere and -magnetosphere is emphasized through a de. . cotruling --

scnptron of the current circuits:

1. INTBODUWiON The large scale characteristics

of the interface

be-

tween the Earth’s magnetosphere and the solar wind are by now well established. Numerous satellite measurements have proven the existence of a bow shock, which modifies the solar wind plasma, and of the magnetopause, around which the modified solar wind, or magnetosheath plasma, flows. Theoret$al models of the magnetosphere account well for the shape and character of the ma~etopause facing towards the Sun, and have predicted the existence of neutral points or lines later identified with the polar cusp regions observed experimentally in recent years. Experimental studies in the polar magnetosphere and ionosphere and in the magneto&u1 have revealed several phenomena that are infhrenced by the solar wind, in particular the interplanetary magnetic field direction. Explanations of the observed correlations have been given in terms of magnetic field line reconnection, which results in a magnetically “open” magnetosphere at high latitudes (e.g. Dungey, 1963). A characteristic feature of an open model would be the existence of a magnetic field component normal to the magnetopause in the high latitude regions, in particular the cusp regions. Investigations of the distant cusp have failed to reveal such a field component, (Fairfield and Ness, 1972; Hansen et al., 1976), and in general, magnetopause studies attribute observed normal components to compres841

sional waves, whereas there is no measurable, normal component of a stationary nature (Aubrey et al., 1971; Ledley, 1971). This lends support to a magnetically closed model of the magnetosphere. It is the purpose of this paper to show that such a magnetosphere is not necessarily closed to solar wind plasma inflow and that many of the correlations observed follow from a few simple considerations. The next section gives a brief outline of the theory involved, and in the sections loflowing that we will discuss the observations of the magnetotail boundary layer or plasma mantle, the electric field in the polar ionosphere, and a polar current system. 2. ANALYSIS

Figure l(a) shows schematically the cross section of the magnetospheric magnetic field B, in the noon-midnight meridian, and Fig. l(b) shows a dawn-dusk view of the polar magnetosphere. The magnetosheath magnetic field for an away sector (BY> 0) with B, - 0 is indicated by I$,,. From this figure it is seen that there may exist a region where I3, is parallel to B.. Experiment~ly it has been found, moreover, that the magnitudes of B, and B, are often comparable at the polar magnetopause. It is interesting, therefore, to investigate some characteristics of a “magnetopause” with parallel B fields at which B, = i3,. In accordance with the remarks in the in~odu~on, we will assume B, = 0, and obtain for the electric field outside the

A. BAHHSENand A. M. HANSEN

842

which is satisfied either by V,,

= V,. = 0 or by B,

parallel to B,. This

shows that, if in a region

of

the mag-

netopause the magnetic fields are parallel on both sides

and

continuous

across

plasma flow is permitted such a plasma

the

surface,

then

across the surface, and

flow will be accompanied

by an

electric field tangential to the surface. In regions of the magnetopause where V, = 0, the electric field is perpendicular

to the surface, and

need not be the same on both sides. l(a). SCHEMATICCROSSSECTION OF THE EARTH‘S MAGNETOSPHERE INTHENOON-MIDNIGHT MERIDIAN. The lines connecting A,,, and A, symbolize the possible flow lines of an element of magnetosheathplasma.

FIG.

This straightforward evaluation gives the result that plasma inflow to the magnetosphere possible

is only

at places where the magnetic fields are

exactly parallel on both sides. With a homogeneous (ideal)

magnetosheath

field this can at most

be

satisfied in two points of the magnetopause, and the consideration above would thus be of little consequence for the magnetosphere.

The usefulness of

the considerations and of equation (2) is, however, considerably

extended

by following

tions in some detail. With

particle mo-

a simple geometry

in

and B, are separated

which two magnetic fields B,

by a plane surface it is found (see appendix) that if B,,, has a component

parallel (antiparallel) to B.

then particles will gyrate in the same (opposite) FIG. l(b). SCHEMATIC DAWN-DUSKVIEW OF THE POLAR MAGNETOSPHERE. The directionto the Sun is out of the page.

sense and are transmitted (reflected) at the surface. Arguments

similar to these have been applied to

the equatorial magnetosphere Increasing

magnetopause: E,,,=-V,,,xB,;

EL=-V,,xB,;

E,,=-V,xB, (1)

deviation

The field E, perpendicular to the magnetopause

(reflection)

gyro-period.

per

calculations.

where B,

The paral-

rel field on the other hand must be equal on both

The

and V,,.

NV,ds I Surface = A, N, V,,

= 0

perpendicular

velocity and B,.

3. PLASMA

as a relation

Here N,,,, N, are the den-

fluid element. The expansion inside the magnetosphere is a result of the plasma runaway effect, when is limited

in extent.

Using

equation (1) we also have: -V,,xB,=-V,,xB,=E,,

show is

is in-

FLOW

that

“draped”

the

interplanetary

magnetic

field

around

netopause

by the flowing plasma-such

the

mag-

that the

condition B, = 0 is satisfied. On the sunward- or

sities and A,,,, A, are the cross sectional areas of a

the intrusion region

given in the

fluenced by the angle between B,

Measurements

ume indicated in Fig. la we get:

V,,

treatment

has a component parallel to B,, keeping

sides, since in the stationary case V x E = 0. Furth-

between

simple

that the

ermore V . (N V) = 0. Integrating this over the vol-

N,,, V,,

values

of equation (2) to any part of the magnetopause in mind

which gives: A,

Quantitative

can only be obtained by performing self consistent

may exist only outside, that is it can be shielded by

V.(NV)dT=

parallelism

causes a decreasing transmission

charges collected on the magnetopause.

“0,

strict

(antiparallelism)

appendix allows us, however, to extend the validity

assuming “frozen in” conditions.

I

by Cole (1974).

from

front-side of the magnetopause this means that the Y-component

of B,

(in a local coordinate system)

is positive during away-sectors and negative during toward-sectors. The z-component

takes on positive

and negative values in both cases, with an average value of zero. In the previous section it was found that a necessary condition for plasma flow into the magnetos-

(2)

phere,

with the accompanying

tangential electric

Electric fields, currents and plasma in the polar region field, is that B,,, has a component parallel to B,. As can be seen from Fig. l(b) for the north polar magnetopause, this condition can be met over a large area for any orientation of B, except B, large positive. For the away sector field shown in Fig. 1 this area must be on the dawn (dusk) side of the north (south) polar magnetopause, whereas for toward sector fields the area of possible penetration must be on the dusk (dawn) side of the north (south) polar magnetopause. The extent of these areas and the magnitude of the plasma flow can only be found by performing self-consistent calculations based on precise plasma and magnetic field measurements. The simple calculations made in the appendix, together with Fig. 1, do show, however, that an average B, (B, = 0) allows plasma inflow over roughly one half of the polar magnetopause, and that the addition of a southward component to B, increases the “open areas” across the noon meridian. Figure 2 shows schematically the open areas for four main orientations of the interplanetary magnetic field: B, >O (away sector), O (northward) and (0 (southward). In order for plasma flow to occur in the “open” areas, the magnetosheath flow velocity must of course have a component V, perpendicular to the magnetopause. Precise measurements of V, are difficult to obtain, but there are indications (Hansen et al., 1976) that there exists a region in the magnetosheath in front of the polar magnetopause, where the flow is reduced from the free flow magnetosheath and has a direction not purely tangential to the polar magnetopause. We propose that the plasma flowing in across the By> 0

By<0

FIG. 2. ~CHE~T~CVIEWSOF~E~LARMAGNE~SPHERE ASSEENFROMTHESUN. The cross-hatching shows, for four main orientations

of the interplanetary magnetic field, the areas that are open to plasma flowing in from the magnetosheath.

843

open areas gives a main contribution to the plasma mantle observed by Hones et al. (1972), Akasofu et al. (1973), Rosenbauer et al. (1975) and Sckopke et al. (1976). These observations of the mantle, or magnetotail boundary layer, can be summarized as follows: 1. In the high latitude lobes of the tail a plasma layer or mantle has been observed in 25 out of 34 satellite passes (70%). A mantle may be found everywhere along the magnetopause except near the plasma sheet. 2. The thickness of the mantle varies greatly between passes, ranging from a fraction of an RE (earth radius) to 4R, (at X-O). A well developed mantle is found only when B, has a southward or a small northward component, and the thickness increases with increasing southward component. There is no clear correlation with Kp 3. The flow velocity V, is directed tailward, parallel to the magnetic field, and is correlated with, but always smaller than, V,,,. V, does not increase with increasing distance from the Earth. 4. Frequently a narrow (0.1 to 0.2 RB) gap in plasma density is observed just inside the magnetopause. 5. The ion temperature is normally lower along B than perpendicular to B, i.e. T,> I-r;,. 6. Density, temperature, and flow speed all tend to decrease with increasing distance inwards from the magnetopause. Point for point, these observational characteristics can be compared with the mechanism for plasma inflow proposed above: 1. If, as proposed, the mantle is due mainly to plasma flowing in across the open areas, we would expect the mantle to appear in the crosshatched areas shown schematically in Fig. 2. As the plasma flows tailward, it will expand somewhat due to curvature and gradient B drifts. Then a satellite crossing the high latitude lobes of the tail would detect mantle plasma in at least 50% of the passes-in reasonable agreement with the observed statistics. From the data it has been inferred (Rosenbauer et ai., 197.5) that the mantle, when present, extends almost completely around the magnetotail. It may, however, equally well be inferred that, in accordance with Fig. 2, a mantle is always present, but only over roughly half of the top and bottom magnetotail. 2. Modest changes in the direction of B, in the Y-Z plane can change significantly the size and position of the areas where plasma inflow is permitted, and such changes of B, are observed frequently. The correlation between thickness and B,

844

A.

BAHNSEN and

is a distinct feature of the proposed mechanism, as noted above. The lack of correlation with the three hour index Kp suggests that the mantle responds to near instantaneous changes in direction of the interplanetary field B,, as would be expected from the theory outlined in the previous section. 3. We first note that the measurements of the flow velocity are consistent with a smah perpendicular component; V, < 0.2 V,, is considered to be inside the experimental uncertainty (Rosenbauer et al., 1975). Secondly it is to be expected that the plasma in the mantle largely conserves the flow speed that it has at the point of entry, experiencing at most a weak acceleration along the magnetic field lines. The neighboring magnetosheath plasma on the other hand is accelerated to solar wind velocity while passing along the tail. The observation of a smaller but correlated mantle plasma velocity is thus well accounted for. In this connection we note that the plasma observations made in the “reduced flow” region in front of the polar magnetopause (Hansen et al., 1975) yield flow velocities inside the range of observed mantle flow velocities (Rosenbauer et al., 1975). 4. If the plasma entering the magnetosphere through a limited region has a small perpendicular velocity component, an observation of this plasma behind the point of entry is expected to show a small separation between the plasma and the magnetopause. In fact the measured gap, -0.2 RE at a position 2-5 RE behind the probable point of entry, gives a rough figure of V, -& to & of V,l. 5. If plasma inflow is assumed to proceed quasiadiabatically, the perpendicular temperature must be proportional to the magnetic field. Since normally B,
A. M. HANSEN Instead we postulate a basic electric field E,, on which is superposed the electric field Ei resulting from the (variable) plasma mantle in the distant polar magnetosphere. The basic electric field conl&uration is thought to be a result of the closure of the Chapman-Ferraro currents of the subsolar and the polar magnetopause through the ionosphere. The fieldaligned parts of the closure paths delineate the diffuse aurora1 oval and the ionospheric part of the circuit is formed by Pedersen currents, giving rise to an ionospheric electric field pattern Eo. If there is balance between the field aligned currents on the poleward and equatorward sides of the oval (Zmuda and Armstrong, 1974), the Pedersen currents will be concentrated in the oval, and only minor effects will be seen in the polar cap ionosphere. However, as pointed out by Yasuhara et al. (197.5) there is often an inbalance such that the poleward current pair is stronger than the equatorward pair. This will give rise to a polar cap Pedersen current and electric field. The plasma inflow discussed in the previous section entails an electric field in the polar magnetosphere, which causes a current and an electric field that is superposed on the basic configuration. In this section we discuss the mapping to the ionosphere, which results in the additional ionospheric field Ei, and in the next section the current loop associated with this electric field will be discussed. The direction of this current is such as to add to the “basic” current system over the polar cap. The electric field outside the magnetopause is given by equation (1). The strength of E, can be determined with good accuracy from the experimentat knowledge about V,, and B,. With respect to El we have upper estimates of V, from the previous section, and the qualitative information that V, is largest when B, is parallel to B,. The perpendicular component of E, can be shielded by surface charges on the magnetopause since even the “open” regions are connected to the ionosphere by magnetospheric field lines with good conductivity. We cannot estimate how effective this shielding will be, and for simplicity we wil1 &herefore assume that, in the stationary case, E, is shielded completely everywhere. During toward sectors El, is directed down (Ez negative) and will be transmitted through the dusk side of the northern magnetopause. From Fig. l(b) it is seen that this maps into a dawn-dusk directed electric field in the dusk ionosphere (curve C and Cl, Fig. lb). During away sectors El, is directed up,

Electric fields, currents and plasma in the polar region and the mapping in this case produces a dawn-dusk electric field in the dawn ionosphere. The electric field in the southern magnetosphere is obtained by simple symmetry considerations, and wilf also be in the dawn-dusk direction. The field strength Ei in the ionosphere is found by integrating VX E = 0 over the curve Cl, Fig. l(b). Assuming E = 0 along the field lines we get: Ei = EliF-

EII(BJB,~“,

(3)

where Bi is the magnetic field strength in the ionosphere. The measurements of the polar cap electric field by low altitude satellites (Heppner, 1972, 1973) and by balloons Mozer and Gonzalez, 1973; Mozer et al., 1974; Gonzalez and Mozer, 1974) can be summarized in the following points: 1. The polar cap electric field (Ei) is dominantly in the dawn-dusk direction, and has an average magnitude of 30 mV/m. 2. The electric field over the polar cap measured along the dawn-dusk meridian correlates well with the azimuth of the interplanetary B,, field in the way that fast convection (strong E-field) occurs on the side (dawn or dusk) where magnetospheric field lines have a component parallel to the direction of I?,,. Note that this implies that in general the divergence of E, is not everywhere zero. 3. The area where an appreciable electric field is observed is larger, and the peak magnitude of Ei is larger, when Bi, has a southward component. This correlation appears to be instantaneous on a time scale of -15 min. 4. On the average, E, increases linearly with increasing southward Bi, with a slope of 3 mV/m for each 1y in B,. For northward I$,, the average E is smaller, and independent of the size of the northward component. There is, however, a large scatter around these average values. Comparing these observations theory outlined above we obtain:

with the simple

The dawn-dusk direction of E,(pt. 1) is predicted for both main orientations of the interplanetary magnetic field. The magnitude of E, depends on two parameters B, and V,. If we use B, =50-y as a typical value from the measurements, then Ei = 30 mV/m corresponds to V, - 20 km/set, which is roughly l/10 of the mantle flow velocity. The second observational point directly supports the discussion on plasma inflow in Section 3 provided that the anafysis in Section 2 is used to obtain the electric field.

845

Point 3 in the list of observations is in qualitative agreement with the discussion on plasma inflow where it was noted that a southward ~mponent of B, would facilitate the inflow of plasma by increasing the component of parallel magnetic field. We further note that since an electric field parallel to the magnetopause does not entail any charge accumulation-as is the case with a perpendicular field-the time constant for mapping to the ionosphere can be much shorter than the -i hr time constants involved in the charge accumulation process (Garrett et al., 1974). The quantitative relationship between B, and Ei described in point 4 is in agreement with Equation (1) if we insert V, - 20 km/see. The hypothesis for plasma infIow of Section 3 (Fig. 2) predicts limited plasma inflow for a northward component of B, and thus a weaker electric field. 5. IONOSPHERIC CURRENTS

From the previous sections we extract three points to use in this section: (i) Given favourable conditions, some of the magnetosheath plasma flows into the high latitude magnetosphere. (ii) The component of tIow velocity perpendicular to the magnetic field is ac~mpanied by an electric field, which is mapped to the ionosphere according to equation (3). (iii) The electric field measured in the polar cap is generally not divergence free in the cap itself. The most complete data on the mantle plasma are found in the paper by Rosenbauer et al. (1975). From their Figs. 2 and 3 we may obtain rough values for the kinetic energy’ per particle in the mantle and in the magnetosheath just outside the magnetopause. These numbers are given in Table 1. It is seen that in all cases the mantle particles are less energetic, by about 3 x lo-r7 J. If we make the reasonabte assumption that the particles do not lose energy when Sowing in across the magnetopause, and that this process furthermore is independent of particle energy (no filtering) then the mantle plasma appears to have lost kinetic energy from the time of injection to the time of detection. During TABLE 1. SINGLE PARTICLE ENERGIES (J)

ORBIT In mantle In magnetosheath

20

21

2 x 10-l’ 6 x 10-l’

25

48

2 x 10-I’

5 x 10-l’

5 x 10-l’

5 x10-"

8x10-"

8x10-17

A. BAHNSEN and A. M. HANSEN

846

this time interval the plasma is in contact with the polar cap ionosphere, where dissipative Pedersen currents flow, driven by the electric field E,. We propose that the kinetic energy lost by the mantle plasma is delivered mainly to the ionosphere as ohmic heating. The total energy lost by the mantle may be estimated from the data of Rosenbauer et al. (1975). Taking as an example orbit 21 we find a flow velocity V, - 120 kmlsec and a density profile N--4x lo6 exp (-r/lR,)m-‘. Here r is the perpendicular distance from the magnetopause. There is appreciable mantle in this case to about 2R, in from the magnetopause. The flux through a plane sheet perpendicular to B,, of dimensions 2R, perpendicular to the magnetopause and 1 m along it is then: F=

I

V,Nxda=1.2x105x

lxR,

2

x

4 x lo6 e-“dx = 2.7 x lo’* m-*/sec.

The energy lost per second between the place of entry and the place of observation is then P c =Fx3xlO-“=81W. This may be compared to the dissipation in a strip of the ionosphere of area Ai = 1 x 2R,Mm2, where M is the mapping factor, -30. If cp, the height integrated Pedersen conductivity, is set equal to 3 R-’ we have: Pi = E&A,

= ET x 3 x 2R, x 1O-3 = P,,

This gives Ei = 40 mV/m. This very crude estimate thus gives a value for the ionospheric field only slightly higher than the measured average of 30 mV/m. The Pedersen current connects to field aligned currents originating in the mantle. The circuit must be closed by a transverse current in the mantle, which must run from dusk to dawn since the Pedersen current (like the E-field) is oriented dawn to dusk. In Section 3 the last observational point mentioned was that in the mantle density, tempera; ture, and flow velocity all tend to decrease inwards. This corresponds to a pressure gradient directed outwards, which produces a transverse current density J = (B xVp)/B2. The direction of J is the proper one, namely from dusk to dawn.

According to Section 2, plasma inflow is controlled by the local magnetic field orientations. This should give rise to pressure gradients in the mantle directed parallel to the magnetopause, i.e. in the direction of curvature and gradient currents and would be a source of field aligned currents (Vasyliunas, 1970) closing in the ionosphere. Thus in general the dayside polar cap ionosphere should be penetrated by distributed field aligned currents originating in the outer magnetosphere. The following considerations show that this is not inconsistent with the observed ionospheric electric field pattern. The height-integrated ionospheric current is given as J=xp xE-z,(ExBJBi) (cp and CH are the height-integrated Pedersen and Hall conductivities). The horizontal divergence of this current is given as Vh.J=~~VI.E+E.VhCP-(ExBi/Bi)X V&f, where V XE is assumed zero on the time scales of interest. We disregard the effect of ipnospheric inhomogeneities and get Vh - J = CpVh . E. Seen from the ionosphere this must be equal to the field aligned current density (positive for downward currents). So we have that in a region of the polar cap ionosphere where the divergence of the electric field is different from zero, field aligned currents must flow. Using the electric field profiles given by Heppner (1973), we find that typical current densities are of the order of lo-'A/m’, which is almost an order of magnitude lower than field aligned current densities measured in the aurora1 oval (Zmuda and Armstrong, 1974). 6.

SUMMARY

AND DISCUSSION

A simple theory has been developed to describe plasma flow in the region of the polar magnetopause. This theory has enabled us to explain some important features of the polar ionosphere and magnetosphere: 1. The mechanism by which magnetosheath plasma is transported across the magnetopause to form the mantle. 2. The relation between mantle formation and the direction of the interplanetary magnetic field Bi, 3. The source of at least one component of the ionospheric electric field, Ei. 4. The variation of Ei with Bi, 5. The energy source needed to maintain the dissipative current corresponding to Ei. We have shown that existing data on the mantle and the polar cap electric field are in reasonable agreement with the theory proposed.

Electric fields, currents and I plasma in the polar region

We now discuss in a more speculative way some further consequences of this theory. Consider the situation where the mantle suddenly increases in density, cross section, and perpendicular tlow velocity. This would be the result of a southward turning of Bip, and would have the following magnetospheric effects: The diamagnetic effect of the plasma will cause an increase in the flaring angle of the high latitude magnetopause, since the plasma will “push” magnetic flux out of the volume it occupies. The increased flaring angle necessitates an increase in the Chapman-Ferraro current. Near the Earth, at X%--l0 RE, this current closes, through field aligned currents in the polar ionosphere, adding current to the loop: Mantle, dawn field lines, ionosphere-dusk field lines. As shown by Maltsev and Lyatsky (1975) the effects of a current in this circuit is to shift the polar cusp equatorward and to move the subsolar point of the magnetopause earthward. Further tailward, for X2 -10 Rar the Chapman-Ferr~o current closes through the neutral sheet. This results in an increase in total magnetic flux in the tail. The equatorward motion of the cusp and the increase in tail flux both wntribute to enlarging the polar cap. In this way, the size of the polar cap is directly related to properties of the plasma mantle. The effects listed here are considered important in the study of magnetosphere dynamics, in particular substorm studies. Thus it may be useful to include the temporal variations of the mantle in such studies.

847

Chandrasekhar, S. (1962). PJasma Physics. The University of Chicago Press. Cole, K. D. (1974). Outline of a theory of solar wind interaction with the magnetosphere. Planet. Space Sci. 22, 1075. Dungey, J. W. (1963). The structure of the exosphere or adventures in velocity space, in Geophysics, 7’he Earth’s Enuironmenr, (Eds.. d. de Witt, -J.‘ Hieblot and L. LeBau). on. . . 503-550, Gordon & Breach, NY. Fairfield, D. H. and Ness, N. F. (1972). Imp 5 magneticfield measurement in the high latitude outer magnetosphere near the noon meridian. J; geophys. Res. 77, 611. Garrett, H. B. Dessler, A. J. and Hill, T. W. (1974). Influence of solar wind variability on geomagnetic activity. .I. geophys. Res. 79, 4603. Gonzalez, W. D. and Mozer, F. S. (1974). A quantitative model for the potential resulting from re~nn~ion with an arbitrary inte~laneta~ magnetic fieid. J. geophys. Res. 79, 4186. Hansen, A. M., Bahnsen A. and D’Angelo, N. (1976). The cusp-magnetosheath interface. J. geophys. Res. 81, 556. Heppner, J. P. (1972). Polar-cap electric field distributions related to the interplanetary magnetic field direction. .l. geophys. Res. 77, 4877. Heppner, J. P. (1973). High latitude electric fields and the modulations related to interplanetary magnetic field parameters. Radio Sci. 8, 933. Hones, E. W., Jr., Asbridge, J. R., Bame, S. J., Montgomery, M. D., Singer, S. and Akasofu, S. -J. (1972). Measurements of magnetotail plasma flow made with Vela 4B. J. aeovhys. Res. 77, 5503. Ledley, B. G- (i971}. Magn~topause attitudes during OGO-5 crossings. J. geophys. Rex 76, 6736. Maltsev, Y. U. P. and Lyatsky, W. B. (1975). Fieldaligned currents and erosion of the dayside magnetosohere Planet. Space Sci. 23, 1257. Mozer, F. S. and-Gonzalez, W. D. (1973). Response of polar cap convection to the interplanetary magnetic field. 1. geovhys. Res. 78, 6784. Mozer, F. S., G&zalez, W. D., Bogott, F., Kelley, M. C. Acknowledgements-One of us (A. Mencke Wansen) was and Schutz. S. (1974). High latitude electric fields and supported by the Danish National Research Council the three dimensional interaction between the interpunder grant 511-5181. lanetary and terrestrial magnetic fields. .I. geophys. Res. 79, 56. Paschmann, G., Sckopke, N. and Griinwaldt, H. (1976). Note added in proof--After completing the manuscript it Plasma in the polar cusp and plasma mantIe. ,Magnetohas been pointed out to us that the HEOS-2 observations spheric Particles and Fields (Ed. B. M. McCormac). of the mantle have been further analyzed (Paschmann et To be published. at. 1976, and private communi~tion). This analysis supRosenbauer, H., Griinwaldt, H., Montgomery, M. D., ports (a) our hypothesis that a component of B, parallel Paschmann, G. and Scopke, N. (197.5). HEOS-2 plasma with B, favors formation of the mantle, and (b) our observations in the distant polar magnetosphere-the conjecture of a velocity component V, of the mantle plasma mantle J. geophys. Res. 80, 2723. plasma inwards. The measured average of V, is smaller Sckopke, N., Paschmann, G., Rosenbauer, H. and than our estimate in Section 4. Fairfield. D. H. (1976). Influence of the interplanetarv magnetid field on the’occurrence and thickness of the olasma mantle. S. neoohvs. Res. 81. To be PubIished. REFERENCES Vasyliunas, V. M. (¶97i)).‘Mathematical models of magAkasofu, S. -I., Hones, Jr., E. W., Bame, S. J., Asbridge, netospheric convection and its coupling to the ionosJ. R. and Lui, A. T. Y. (1973). Magnetotail and phere. Particles and fields in the Magnetosphere (Ed. boundary layer at a geocentric distance of 18&: Vela B. M. McCormac), pp. 60, Reidel, Dordrecht, Hol5 and 6 observations. J. geophys. Res. 78, 7257. land. Aubrey, M. P., Kivelson, M. G. and Russell, C. T. (1971). Yasuhara, F., Kamide, Y. and Akasofu, S. -1. (1975). Motion and structure of the magnetopause. .I. geop~ys. Field aligned and ionospheric currents. Planer. Space Res. 76, 1673. Sci. 23, 1355.

A.

848

BAHNSEN

andA.M.

HANSEN

Zmuda, A. J., and Armstrong, J. C. (1974). The diurnal flow pattern of field-aligned currents. J. geophys. Res. 79, 4611. APPENDIX

Motion of Charged Particles at a Magnetic Field Discontinuity Consider a magnetopause, idealized to a tangential discontinuity. Figure 3 shows the magnetospheric field B, pointing out of the page, separated from the magnetosheath field B, by a plane perpendicular to the page. B, has an arbitrary direction, parallel to the discontinuity plane. The magnetospheric part of a proton orbit is shown. The particle is assumed to have an inward drift velocity V,, bringing the guiding centre from C-D during the time the particle is influenced by B,. If the angle between B, and B,,, is less than 90”, i.e. B, has a component parallel to B,, then the particle will gyrate always in the same sense (clockwise) and the guiding centres corresponding to the maguetosheath field are A and B before entry to, and after exit from the magnetosphere respectively. If on the other hand B, has a component antipar~lel to B., then the gyration will be in the opposite sense in B,, and the corresponding guiding centres are A’ and B’. From Fig. 3 it is seen that the motion A-B is inwards, whereas the motion from A’ to B’ is outwards. A negatively charged particle will move in the same direction ~~ndic~ar to, but opposite from the positive particle -along the discontinuity. -For the case shown in Fig. 3, B,
FIG. 3.

THE PATH

OF A POSITIVE CHARGE MAONETOSPHERE.

INSIDE THE

See appendix for further details. From Fig. 3 we now find the displacements perpendicular to the discontinuity, d, and along the discontinuity, I and I’: d=p’(cosx-case)

I = (p’ - 0,) (sin x +sin e) i’=(p’+p.)(sinx-tsine), where p’ is the projection of the gyroradius in the field II,. For small drift velocities, i.e. V,/(o,p,)<< 1, we can obtain approximate expressions for d, 1, and 1’ by using the equation for the exit angle. We get: d-ZfZw-2e)mse &I’-(p’*p,)[asine-2(27r-2e)cosel. Since the projected gyroradius p’ decreases as the angle between 3, and B, goes to 90”, we see that both d and I, I’ decrease in this case. These results may be summarized as follows: Plasma particles moving in the magnetic fields B, and B, with an initial drift velocity from B, to I3, will continue moving inwards, when B,,, has a component parallel to B,, but will be reflected when B, has a component antiparallel to B,. In addition, currents will flow, which in the parallel case tend to minimize the difference between B, and B,, and in the antiparallel case tend to increase this difference. Both the pe~endicular motion and the currents are maximum when the fields are exactly parallcl or antiparallel.