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Meridional ionospheric electric field caused by curvature current in the magnetosphere
00320633/83 $3.00 + 0.00 Pergamon Press Ltd.
Planer. Space Sci., Vol. 31, No. 10. pp. 1129-l 130, 1983 Printed in Great Britain.
MERIDIONAL IONOSPHERIC BY CURVATURE CURRENT
ELECTRIC FIELD CAUSED IN THE MAGNETOSPHERE
K. D. COLE’ Laboratory
for Planetary
Atmospheres,
NASA/Goddard
Space Flight Center, Greenbelt,
MD 20771, U.S.A.
(Received23 November 1982) Abstract-The bending of geomagnetic field lines towards the geotail produces a curvature drift of charged particles parallel to the geomagnetic axis. The divergence of the current so produced forms Birkeland current to the ionosphere where a meridional electric field is created. This field would drive ionospheric currents to
formanegativemagneticbayin thedawnsectoroftheauroralzoneandapositiveonein would cause a dawn-dusk field across the polar cap. expression
The geomagnetic field lines in the outer magnetosphere are curved in the direction of the geomagnetic tail (Fairfield, 1968; Sugiura, 1975). This curvature would cause the drift of charged particles parallel to the geomagnetic axis. The consequences of this for polar ionospheric current systems are investigated. The drift velocity of a charged particle in a magnetic field due to curvature of the field lines is given, in first order orbit theory (Chandrasekhar, 1960), by 2Cwll V cur” =-3-B @
x (B+
jz
2w3,)
BR,
emuy
(2)
where n is the number density of charged particles of average “parallel” energy (WI,) and R, the component of the radius of curvature parallel to the magnetic equatorial plane due to tail formation. Let us suppose the tail-shaped curvature exists over a range of N, Re (Earth radii) in radial extent and N, Re in longitude extent on (say) the dawn side. Then the total integrated current, of this origin, flowing North-South in the outer magnetosphere is
(1)
where W,, = $nVi, where VI, is the velocity of the particle parallel to the magnetic field Band m is the mass of the particle of charge q. When B is dipolar, this drift contributes to a ring current about the dipole, as is well known (Dessler and Parker, 1959). The geomagnetic field is far from dipolar in its outer reaches and its lines are swept downstream in the solar wind, giving a significant component ofthe “curvature” vector (B. V)B/B out of the meridian plane (see Fig. 1). Because of this, a component of current flows in the North-South direction across field lines in the entrapped plasma in the outer parts of the geomagnetic field, except in the region of the plane (near noon and midnight) where the field lines are in the plane of the meridian. Divergence of this North-South flow of current will create a North-South electric field and Birkeland currents to and from the ionosphere (see Fig. 1). Even the simplest mathematical analytical attempts to model the geomagnetic field produce horrendous expressions for V,,,,. Let us therefore estimate the magnitude of the curvature current here to demonstrate its geophysical significance, by the
thedusksector.Alsoit
jT
=
24 Yl )N,N, BN,
Re ’
(3)
where R, = N3 Re. Assuming N, = 3, N, = 10, N3 = 5, B = 10m3 and j x 10’ emu yields n(W,,) = 1.2 x loerg cme3 = 8.8 x lo3 eV cme3. Therefore a plasma of density 10 particles cm- 3 each of 1 keV would produce a
-
“NORMAL”
FIELD LINES
----
FIELD LINES “BENT”
TOWARDS TAIL
VIEW FROM NIGHT SIDE
* On leave from La Trobe University, Bundoora, Victoria, Australia, 3083.
FIG. 1. 1129
1130
geophysically say that
K. D. COLE
significant
jTQN,
current. Alternatively
pB*IN2Re
we can
emu,
where p = 8xn( FQ)/B’. Then j, 5 10’ emu implies /3 = 0.6. Such high -/3 plasma comes probably from the “neutral” sheet, being brought earthwards by dawn-dusk electric fields (Hare1 et al., 1981) to populate regions of field lines connected to the aurora1 oval. Notice, that, on the dawn side, the electric field produced by the charge separation due to V,,,, is equatorwards across the plasma region and polewards on the dusk side (see Fig. 1). This is the direction required to drive the Hall currents westwards in the dawn side and eastwards in the dusk side of the aurora1 ionosphere. Let us apply equation (2) in a different fashion to calculate the Birkeland current per cm of longitude (j, cm-‘) at the ionosphere for a range of values of the parameters. Thus, integrating j over a distance N, Re(= R,) j,
cm-’
=- 2fnWjl)AB qB2
’
or, j, cm-’
Pf
= GAB,
where f is the separation of two lines of force in the equatorial plane which are 1 cm of longitude apart in the ionosphere. For B 1: 0.5 and f = 5, AB = 10m3, j, cm-’ z 2 x 10m3 A cm-‘. Birkeland currents of such magnitude are observed (Potemra et al., 1979) at ionospheric heights.
DISCUSSION
The high -b plasma invoked in this discussion may be energized plasma from the geomagnetic tail driven earthward by the cross-tail dawndusk electric field. Upon encountering the region of “bent” geomagnetic field the plasma would be subject to a component curvature different due to this bending of the lines towards the tail. This sets in train the production of Birkeland current and meridional electric fields at the ionosphere. The most poleward Birkeland currents would reinforce the pre-existing Birkeland currents, the so-called Region I currents of Potemra et al. (1979). The equatorward return Birkeland currents would form part of the so-called Region II currents. If there were a large change in direction of the solar wind and a corresponding change in direction of the geomagnetic tail the pattern of curvature of magnetospheric field lineswouldrotateandchange thesiteinlocal timeofthe corresponding ionospheric currents. These processes would appear to produce geophysically significant electric current and provide an explanation of some “Region II” Birkeland currents. Acknowledgement-The author is indebted to the National Academy of Sciences, U.S.A., for the award of a Research Associateship and Goddard Space Flight Center for hospitality. REFERENCES Chandrasekhar,S.(1960)PlasmaPhysics. PhoenixBooks,The University of Chicago Press. Dessler, A. J. and Parker, E. N. (1959) J. qeophys. Res. 64,389. Fairfield, D. H. (1968) J..geophys. Res. 73, 7359. Hare]. M.. Wolf. R. A.. Rieff. P. H.. Sniro. R. W.. Burke. W. J.. Rich, F: J. and Smiddy, G. (198i) >. g&phys.‘Res. 86,2217: Potemra, T. A., Iijima, T. and Saflekos, N. A. (1979) Dynamics of the Magnetosphere (Edited by Akasofu, S.-I.), p. 3. D. Reidel, Dordrecht. Sugiura, M. (1975) J. geophys. Rex 80,2057.
Planer. Space Sci., Vol. 31, No. 10. pp. 1129-l 130, 1983 Printed in Great Britain.
MERIDIONAL IONOSPHERIC BY CURVATURE CURRENT
ELECTRIC FIELD CAUSED IN THE MAGNETOSPHERE
K. D. COLE’ Laboratory
for Planetary
Atmospheres,
NASA/Goddard
Space Flight Center, Greenbelt,
MD 20771, U.S.A.
(Received23 November 1982) Abstract-The bending of geomagnetic field lines towards the geotail produces a curvature drift of charged particles parallel to the geomagnetic axis. The divergence of the current so produced forms Birkeland current to the ionosphere where a meridional electric field is created. This field would drive ionospheric currents to
formanegativemagneticbayin thedawnsectoroftheauroralzoneandapositiveonein would cause a dawn-dusk field across the polar cap. expression
The geomagnetic field lines in the outer magnetosphere are curved in the direction of the geomagnetic tail (Fairfield, 1968; Sugiura, 1975). This curvature would cause the drift of charged particles parallel to the geomagnetic axis. The consequences of this for polar ionospheric current systems are investigated. The drift velocity of a charged particle in a magnetic field due to curvature of the field lines is given, in first order orbit theory (Chandrasekhar, 1960), by 2Cwll V cur” =-3-B @
x (B+
jz
2w3,)
BR,
emuy
(2)
where n is the number density of charged particles of average “parallel” energy (WI,) and R, the component of the radius of curvature parallel to the magnetic equatorial plane due to tail formation. Let us suppose the tail-shaped curvature exists over a range of N, Re (Earth radii) in radial extent and N, Re in longitude extent on (say) the dawn side. Then the total integrated current, of this origin, flowing North-South in the outer magnetosphere is
(1)
where W,, = $nVi, where VI, is the velocity of the particle parallel to the magnetic field Band m is the mass of the particle of charge q. When B is dipolar, this drift contributes to a ring current about the dipole, as is well known (Dessler and Parker, 1959). The geomagnetic field is far from dipolar in its outer reaches and its lines are swept downstream in the solar wind, giving a significant component ofthe “curvature” vector (B. V)B/B out of the meridian plane (see Fig. 1). Because of this, a component of current flows in the North-South direction across field lines in the entrapped plasma in the outer parts of the geomagnetic field, except in the region of the plane (near noon and midnight) where the field lines are in the plane of the meridian. Divergence of this North-South flow of current will create a North-South electric field and Birkeland currents to and from the ionosphere (see Fig. 1). Even the simplest mathematical analytical attempts to model the geomagnetic field produce horrendous expressions for V,,,,. Let us therefore estimate the magnitude of the curvature current here to demonstrate its geophysical significance, by the
thedusksector.Alsoit
jT
=
24 Yl )N,N, BN,
Re ’
(3)
where R, = N3 Re. Assuming N, = 3, N, = 10, N3 = 5, B = 10m3 and j x 10’ emu yields n(W,,) = 1.2 x loerg cme3 = 8.8 x lo3 eV cme3. Therefore a plasma of density 10 particles cm- 3 each of 1 keV would produce a
-
“NORMAL”
FIELD LINES
----
FIELD LINES “BENT”
TOWARDS TAIL
VIEW FROM NIGHT SIDE
* On leave from La Trobe University, Bundoora, Victoria, Australia, 3083.
FIG. 1. 1129
1130
geophysically say that
K. D. COLE
significant
jTQN,
current. Alternatively
pB*IN2Re
we can
emu,
where p = 8xn( FQ)/B’. Then j, 5 10’ emu implies /3 = 0.6. Such high -/3 plasma comes probably from the “neutral” sheet, being brought earthwards by dawn-dusk electric fields (Hare1 et al., 1981) to populate regions of field lines connected to the aurora1 oval. Notice, that, on the dawn side, the electric field produced by the charge separation due to V,,,, is equatorwards across the plasma region and polewards on the dusk side (see Fig. 1). This is the direction required to drive the Hall currents westwards in the dawn side and eastwards in the dusk side of the aurora1 ionosphere. Let us apply equation (2) in a different fashion to calculate the Birkeland current per cm of longitude (j, cm-‘) at the ionosphere for a range of values of the parameters. Thus, integrating j over a distance N, Re(= R,) j,
cm-’
=- 2fnWjl)AB qB2
’
or, j, cm-’
Pf
= GAB,
where f is the separation of two lines of force in the equatorial plane which are 1 cm of longitude apart in the ionosphere. For B 1: 0.5 and f = 5, AB = 10m3, j, cm-’ z 2 x 10m3 A cm-‘. Birkeland currents of such magnitude are observed (Potemra et al., 1979) at ionospheric heights.
DISCUSSION
The high -b plasma invoked in this discussion may be energized plasma from the geomagnetic tail driven earthward by the cross-tail dawndusk electric field. Upon encountering the region of “bent” geomagnetic field the plasma would be subject to a component curvature different due to this bending of the lines towards the tail. This sets in train the production of Birkeland current and meridional electric fields at the ionosphere. The most poleward Birkeland currents would reinforce the pre-existing Birkeland currents, the so-called Region I currents of Potemra et al. (1979). The equatorward return Birkeland currents would form part of the so-called Region II currents. If there were a large change in direction of the solar wind and a corresponding change in direction of the geomagnetic tail the pattern of curvature of magnetospheric field lineswouldrotateandchange thesiteinlocal timeofthe corresponding ionospheric currents. These processes would appear to produce geophysically significant electric current and provide an explanation of some “Region II” Birkeland currents. Acknowledgement-The author is indebted to the National Academy of Sciences, U.S.A., for the award of a Research Associateship and Goddard Space Flight Center for hospitality. REFERENCES Chandrasekhar,S.(1960)PlasmaPhysics. PhoenixBooks,The University of Chicago Press. Dessler, A. J. and Parker, E. N. (1959) J. qeophys. Res. 64,389. Fairfield, D. H. (1968) J..geophys. Res. 73, 7359. Hare]. M.. Wolf. R. A.. Rieff. P. H.. Sniro. R. W.. Burke. W. J.. Rich, F: J. and Smiddy, G. (198i) >. g&phys.‘Res. 86,2217: Potemra, T. A., Iijima, T. and Saflekos, N. A. (1979) Dynamics of the Magnetosphere (Edited by Akasofu, S.-I.), p. 3. D. Reidel, Dordrecht. Sugiura, M. (1975) J. geophys. Rex 80,2057.