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The effect of an ionospheric inhomogeneity on magnetic pulsation polarization
Journal of Amospheric
Pergamon
and Solar-Terrestrial
PII: s1364-682q%)00182-4
Physics, Vol. 59, No. 12, pp. 1425-1434, 1997 0 1997 Elsevier Science Ltd All rights reserved. Printed III Great Britain 136&5826/97$17.00+0.00
The effect of an ionospheric inhomogeneity on magnetic pulsation polarization E. Belova, E. Pchelkina, Polar Geophysical
W. Lyatsky Institute,
Apatity,
and A. Pashin Russia
(Received in final form 28 May 1996; accepted 28 November 1996)
Abstract-The problem of magnetic disturbance polarization on the ground for a dipole source in the inhomogeneous ionosphere is solved for two kinds of an horizontal inhomogeneity. One is the case when the ionosphere is separated into two distinct parts with different conductivities and the other is a mesoscale strip in the ionosphere strip with enhanced conductivity which may be associated with an aurora1 arc. By using the ‘method of reflection’ an electric potential of the polarization field and a current function of the equivalent ionospheric currents are found for these cases. The distributions of the magnetic disturbance polarization ellipses on the ground have been obtained. It is found that under the certain ionospheric conditions the inhomogeneity can cause a significant (up to 40%) contribution to the magnetic disturbance amplitude on the ground and change essentially its polarization. For the first case the contribution of the inhomogeneity to magnetic variations on the ground is symmetric relative to the boundary. This boundary separates the regions with different rotation sense of the magnetic disturbance vector. For the case of the meso-scale strip, it is found that on the ground the magnetic polarization ellipse distribution becomes asymmetric and complicated. The line separating the regions with different rotation sense becomes curved. 0 1997 Elsevier Science Ltd
1. INTRODUCTION
It is evident that the spatial-distribution of ionospheric conductivity is able influence strongly the configuration of ionospheric current systems and as a consequence, the magnetic signature of these currents on the ground. The effect of horizontal non-uniformities in ionospheric conductivity has been theoretically investigate over the last 20 yr by a number of authors (Maltsev et al., 1974; Ellis and Southwood, 1983; Glassmeier, 1983, 1984). Ellis and Southwood (1983) studied the case of an Alfven wave incidence on the ionospheres which have various sharply discontinuous, horizontal distributions of conductivity. Glassmeier (1984) calculated the distribution of equivalent currents on the ground for an incident. Alfven wave on the ionosphere having an arbitrary non-uniform conductivity distribution. There are also interesting cases when the ground magnetic disturbances are generated not by an Alfven wave of magnetospheric origin but by an ionospheric source. When in the ionosphere a dipole source appears whose electric field changes in time with a frequency in the range of geomagnetic pulsations, polarized magnetic disturbances on the ground can be detected. This source may be a patch of the enhanced con-
ductivity in the ionosphere. It may be formed in a natural way, for example, caused by the electron precipitation [Maltsev et al., 1974; Oguti et al., 1984; Oguti and Hayashi, 19841 or artificially, for example, the results of ionospheric heating by a power modulated HF radio wave [Stubbe and Kopka, 1977; LotzIwen, 1983; Stubbe et al., 1985; Pashin et al., 19951. In the article of Maul et al., 1990 the polarization characteristics of artificial magnetic pulsations generated during the heating experiment in OctoberNovember, 1984 near Tromso, Norway, were studied. The observed polarization ellipses on the ground were presented and their characteristics were compared with those calculated using a stimulation model. In some cases the discrepancy between these results in the ellipticity and the inclination angle of the main ellipse axis was rather large. The authors did not propose a convincing explanation for this fact. However, in that article it was mentioned that during one of the experiments near the ionospheric heated region a quiet aurora1 arc was observed. Therefore the ionosphere was essentially inhomogeneous and that might influence the polarization characteristics of the magnetic pulsations. The aim of this work is to study the ground distribution of the polarization ellipses of the magnetic pulsations generated by an ionospheric dipole source
1425
E.
1426
Belova et al.
for the case of an inhomogeneous conductivity of the ionosphere. Two kinds of inhomogeneities are considered. In Section 2 we investigate the polarization on the ground from a dipole source in the homogeneous ionosphere. In Section 3 the ionosphere is assumed to be separated into two parts with different conductivities. In Section 4 the ionospheric inhomogeneity is considered to be in a form of a strip with enhanced conductivity. The latter case may be associated with an aurora1 arc.
2. MAGNETIC SOURCE
PULSATIONS
GENERATED
IN THE HOMOGENEOUS
BY A DIPOLE
INONOSPHERE
In the ionosphere we consider that a region with the enhanced conductivity appears. By the presence of the ionospheric electric field, it is polarized. The polarization currents inside this region are closed by currents flowing outside it and the field-aligned currents. The resulting current system produces magnetic disturbances on the ground. 2.1. In the ionosphere
It is convenient to choose in the ionosphere a complex coordinate system w = x+iy according to Maltsev et al., 1974. Then the height-integrated ionospheric conductivity may be written in the complex form X = X,--E,, where C, is the Pedersen conductivity and X:His the Hall conductivity. Let us consider the polarization problem for an ambient horizontally homogeneous ionosphere with the height-integrated conductivity Co = CpO- Z,,, and with a circular region of disturbed conductivity, X1 = C,, -zZ~, having radius a. Outside the circle the polarization field caused by the presence of the ionospheric electric field E,, behaves as the field from the dipole source (Maltsev et al., 1974):
where
z$=-
~,-&l X:, +cg+2c,
x -6,
Here g is the polarization electric field inside the source region assumed to be homogeneous, C,. is an effective magnetosphere plasma conductivity (‘wave conductivity’) and symbol ‘*’ means the complex conjunction. In our case we took values of AX = X1 -X0 such that the source field has circular polarization rotating clockwise when viewed along the geomagnetic field. According to the article by Lyatsky and Maltsev,
1983 we take the electric potential cp and the current function IJ for the dipole source using a complex potential F and dipole moment q,, as follows: cp = ReF F=
40 w-w0
(3)
$ = Im(E*F) where w,, is the complex coordinate of the dipole source (the centre of the enhanced conductivity region) and dipole moment qO = - a2Ej; X is the conductivity in the region of interest. For this, the equivalent ionospheric current J is determined from the formula J =
k,,grWl
(4)
where the square brackets mean the vector product, eZ is the unit vector along the z-axis, assumed to be directed along the geomagnetic field. The lines of the equal current function values coincide with lines along which the currents flow and the line density is proportional to the ionospheric current value. Figure l(a) demonstrates the distribution of the polarization ellipses for the equivalent ionospheric current disturbances, calculated using expression (4), for a source with circular polarization. Calculations have been made for the case of CpO = Xc,,, = 5 S; in complex form this may be written as C,(S) = 5-5i; C,(s) = 0.05, for an ionospheric electric field of 50 mV/m assumed to be directed along the y-axis, for the amplitude of the conductivity disturbance AC of 0.1 S and for a = 10 km. The current disturbance magnitude at the source point is not shown because it is too large compared with the magnitudes at other points. The arrows demonstrate the polarization vector rotation sense. The polarization vector rotates in the opposite directions inside and outside the source region. The polarization in the ionosphere is circular everywhere except at the boundary of the source region where it is linear. 2.2. On the ground From the distribution of the equivalent current in the ionosphere using the Biot-Savart law, we can obtain the magnetic disturbance on the ground. The contribution to the magnetic disturbances at each point on the ground is given by the whole current system in the ionosphere. Thus the polarization distribution on the ground becomes more complicated than in the ionosphere but the central symmetry remains. Figure l(b) shows the distribution of the magnetic
Effect of ionospheric
inhomogeneity
on magnetic
Hodograms
of equivalent
ionospheric
1
l-
I
I
150
200
pulsation
1427
polarization
current disturbance
I
250
I
1
100
X distance, Hodograms 300
250
300
km
of magnetic disturbance
on the ground
2
/
250
/ E Y . g 5 200
.
t
t
5 5 > 150
%
100
,
/ t 1.1.10-2n
\ 50
100
/ 150
200
X distance,
250
300
3
km
Fig. 1. (a) Spatial distribution of the hodographs of equivalent ionospheric current disturbance (except the is assumed source point) in the ionosphere with conductivities X,, = ZH,, = 5 S. The source polarization to be circular. The source location is marked by a cross. The rotation sense of the ionospheric current vector is indicated by arrows, (b) Spatial distribution of the hodographs of the magnetic variation on the ground from the ionospheric currents shown at the top. The rotation sense of the magnetic disturbance vector is indicated by arrows.
1428
E. Belova et al.
disturbance vectors calculated for 8 instants of time during a period at each point on the ground. Using this graph it is easy to reconstruct the hodograph at any point; therefore we shall call such plots hodograms for convenience. On the ground the inner region with polarization as inside the source is extended as compared with that region in the ionosphere (Fig. 1(a)) and the radius of this region on the ground, r, is about the source height. Inside this region the vector AB shows the same rotation sense as in the source, and outside this region - the contrary sense of rotation. Besides that a wide region with the elliptical polarization appears on the ground. In the centre of the region the polarization is circular, but when we move away from the centre it becomes elliptical, and on the boundary it is linear with the vector AB directed along the boundary.
3. MAGNETIC SOURCE
PULSATIONS
GENERATED
IN THE INHOMOGENEOUS OF SEMI-INFINITE
CASE
PLANE
3.1. In the ionosphere Lyatsky and Maltsev (1983) solved this problem in the ionosphere and derives the potential and current function for this case. The ‘method of reflection’ was used. We consider a complex coordinate system in the ionosphere such that the line, separating the two regions with different conductivities coincides with the real axis and the source is at a distance w0 from the origin (Fig. 2). In the each region, we search the potential and current function as following:
* = Im(c*f)
(5) - ~ 4, w-w,*
= 4 w--w0
where qOis the dipole moment
82 I
II
0
+
Re w t
do
I Fig. 2. Diagram considering the ionosphenc region with a complex coordinate system. The real axis is the boundary between the two ionospheric parts with conductivities X0 and &. The source is the circle with radius a and conductivity C, situated at a distance of do from the centre.
are the moments of the ‘reflected’ dipoles. The values of qr and q’are determined from the continuity equations for cp and $ on the boundary of the regions (Eqs (5.100) and (5.101) in Lyatsky and Maltsev, 1983). So far as we are interested in the effect caused by the ionosphere inhomogeneity, for the analysis we shall use not the potentials and current function themselves but the difference between them and the potentials and current functions calculated for the homogeneous ionosphere described in Section 2.1. This difference defines the disturbance related to the inhomogeneity. We call these differences the disturbances. In Fig. 3 the distributions in the ionosphere of the disturbances of cp and $ are shown for the case: C,(S) = 5-5i; Z,(s) = 30-30i; Z,(s) = 5-5.li; C,,. = 0.05 S; the radius of the source a = 10 km and its distance from the boundary do = 50 km. As is seen the distributions of cp and IJ disturbances are symmetric relative to the boundary and have the form of two vortices with foci located on the boundary. The position of these vortices depends on the source polarization. The foci of the $ vortices are shifted relative to those of the UJvortices. 3.2. On the ground
q = ReF
F;(w)
0
BY A DIPOLE
IONOSPHERE:
At first we let the ionosphere be separated by a straight line into two parts with different conductivities X0 and X2. When in any part the dipole source appears, at the boundary supplementary polarization electric charges arise. A supplementary polarization electric field generating the additional currents inside and outside the source region arises as well. As a result the distribution and magnitude of the total ionospheric current disturbance changes and, hence, the magnetic effect on the ground changes too.
F,(w) = 40 w-w0
T
Im w
of the source, qr and q’
From the symmetry of the current disturbance distribution relative to the boundary in the ionosphere, it is clear that this symmetry is kept on the ground. In Fig. 4 the hodograms of the magnetic effect on the ground calculated from the Ic/disturbance are presented. The polarization of the ionospheric source is assumed to be circular. These hodographs show the difference of the polarization ellipses for the case of
Effect of ionospheric
inhomogeneity
lsocontours
(a)
on magnetic
pulsation
polarization
1429
of electric potential
4oc)-
3X )-
3ocl-
E Y
25c I-
it 5 200 , z .0 >
150
100
50
n-
50
-0
100
150
200
X distance, @I 4oc
lsocontours
/
250
300
350
km
of current function
’
\
\
350
300
/
E 250 Y _
/
i? 5 200 5 .:
\ 150
\ 1
I
u
50
100
150
200
X distance,
250
300
350
km
Fig. 3. Distributions of the disturbances of electric potential in (a) Volts and (b) current Amperes, in the ionosphere separated into two parts with conductivities Z P0 = XHO= 5 S; XP2 = XH2 = 30 S. The separating line is located at y = 200 km. The conductivities in the source region are XP, = 2,,, = 4.9 S. The source location is marked by a cross.
1430
E. Belova et al. Hodograms of magnetic disturbance on the ground
300
250
100
50
150
100
200
250
300
350
X distance, km Fig. 4. Spatial distribution of the hodographs of the magnetic variation on the ground. The source polarization is assumed to be circular and the ionosphere conductivities are as in Fig. 3. The rotation sense of the magnetic disturbance vector is indicated by arrows.
the inhomogeneous
ionosphere
considered
from
the
l(b)). It is seen that on the ground far from the boundary the disturbance AB has the usual circular polarization; then the total magnetic vector is polarized as for the homogeneous ionosphere. This is because of the additional current sources associated with the inhomogeneity are situated on the boundary and, far from it, the influence of these sources is negligible. When we move to the boundary, the polarization becomes elliptical and then linear with the dominating direction of AB being along the boundary. Here the polarization vector changes rotation sense. Inside the source region on the ground the disturbance of AB has the same rotation sense as in the source in the ionosphere, but it has the contrary sense of rotation on the other side of the boundary. These results are valid for the case of a broad ionospheric region with enhanced conductivity. ellipses
for the homogeneous
4. MAGNETIC SOURCE
PULSATIONS
ionosphere
GENERATED
IN THE INHOMOGENEOUS
(Fig.
a strip. So far as this case has not studied earlier, we shall consider it in detail. 4.1. In the ionosphere Let the ionospheric inhomogeneity in form of a strip with d, width and CZ conductivity stretches parallel to the real axis of the complex coordinate system and be located on the distance of do from the source centre (Fig. 5). To determine the complex potentials in the each ionosphere region we also use the ‘method of reflection’. The potential in each region I, II and III we consider to be as a row of the potentials of dipoles obtained by successive ‘reflections’ of the initial dipole from each boundary of the strip:
FII
=
4
wfid,
(6)
Bll mw-i(2nd,+d,)
+ncI
C” +Z n- 1 w+i(2nd,+d,,)
BY A DIPOLE
IONOSPHERE:
A* cG w-id,, +~CI w-i(2nd,+d,,)
+-%+L wfid,,
(7)
CASE
D, FII, = q” f ? w+idO n= ’ w+i(2nd,+d,,)
OF A STRIP
When the region with the different conductivity not very wide, we can consider the inhomogeneity
is as
where
(8)
Effect of ionospheric inhomogeneity on magnetic pulsation polarization
c
%
We calculated these values numerically for the case: the undisturbed conductivity X0 = 5-5i; the wave conductivity C, = 0.05 S; the conductivity of the strip X2 = 30-30i; the disturbed conductivity in the circle C, = 5-5.li; a = 1Okm; do = 50km; d, = 40km. As in the previous case we calculate the disturbances of q and I) as the difference between this case and the case of the homogeneous ionosphere. In Fig. 6 the obtained disturbances of cp and $ in the ionosphere are shown. For this case the isopotential lines and currents are concentrated into the narrow strip. The spatial distributions of cp and tj became strongly asymmetric with respect to the strip boundary, unlike the previous large-scale case. Now the currents have four vortices, contrary to the two vortices for the of case of boundary.
I
do
c;i
20
a
Fig. 5. Diagram of the ionospheric region of interest with a complex coordinate system. The boundaries of the strip having width ds are indicated by straight lines. The complex conductivity in regions I and III is LX,,,and in region II X2. The source is the circle with radius a and conductivity Z, situated at a distance dOfrom the strip boundary.
4.2. On the ground The described distribution of currents produces a complicated picture of magnetic variations on the ground. In Fig. 7 the calculated hodographs of the magnetic disturbances on the ground for a dipole source with the circular polarization are shown. The distribution of the polarization ellipses becomes rather complicated indeed. The line separating the regions of different rotation senses does not now coincide with the strip border. The main axes of the polarization ellipses, near the separating line, are directed almost along it.
w%
a*(& -
q” = z,+c,*+2c,
(zl + XT+
, q =
2L)%
z:+Iz:o+2~,
PO-
wo*
qr = z* + x0*+ 22, q”
=
1431
@o$.v+ 2c,m, + z:+ 2C,)q, 1x2+ z:,*+ 2&f
The coefficients of this row, that are the dipole moment values, are constructed such as that on the strip boundaries the continuity conditions for electric potential and current function are fulfilled. The complex potentials and current functions for the regions I, II and III can be written in the form:
5. RESULTS
In this article the magnetic disturbance polarization in the ionosphere and on the ground from a dipole circularly polarized source in the inhomogeneous ionosphere has been considered for two cases.
IL - z312’“- “(C, - &)(&i + g+
ICf+&+
+% J’m =
2&J@,
+ xc:+ 2Z,)q,*
22,j2”(Z2+Z,*+ 2Z,)(w - i(2nd,+ 4))
IX*- &/*(n-‘)(X2-T&p, JZf+&+2P’~*“(w
AND DISCUSSION
+ z,*+ 2E”)qo*
- i(2nd,+ do))
1x2- w2”(c0-- x,*+ 2Z,)q, I~:+c,+2C,12”(Z:~,+2~~)(w-i(2nd,+d,)) - zg + 2&p* + XT+ 2&)q, IX:+ CO+ 2Z.,f2”+ ‘)(w - i(2nd,+ do))
1x2 - &I*“(&
(9)
E. Belova et al.
1432
(4
lsocontours of electric potential
300 -
E 250Y _ L? 5 200Iii z >
150-
01 0
50
100
150
200
250
300
350
300
350
X distance, km lsocontours of current function
@I
350
300
E Y
250
i? 5 200 z E >
150
100
50
0
1
50
100
150
200
250
X distance, km Fig. 6. Distributions of the disturbances of electric potential in (a) volts and (b) current function in Amperes are XP2 = XH2 = 30 S. The in the ionosphere with conductivities XPO = CHD = 5 S. The strip conductivities ionospheric geometry is as in Fig. 5. The boundaries of the strip are located at y = 200 km and y = 240 km. The conductivities in the source region are C,, = E,,, = 4.9 S. The source location is marked by a cross.
Effect of ionospheric
inhomogeneity
Hodoarams
on magnetic
pulsation
of magnetic disturbance
1433
polarization
on the ground
150
100 L
50
100
150
200
250
300
3
X distance, km Fig. 7. Spatial distribution of the hodographs of the magnetic variation on ground. The source polarization is assumed to be circular and the ionospheric conductivities are as in Fig. 6. The rotation sense of the magnetic disturbance vector is indicated by arrows.
In the magnetic between and the the same
case of a semi-infinite plane, the current and disturbances obtained as the difference the values for the inhomogeneous ionosphere values for the homogeneous ionosphere for source have the following features:
The polarization ellipse distribution in the ionosphere and on the ground is symmetric relative to the boundary. On the ground this boundary is a line separating regions with different vector polarization rotation sense. Outside the boundary the polarization vector rotates as inside the source; inside the boundary this vector rotates in the opposite direction. The polarization on this line is linear and the polarization vector AB is directed along the line. Away from the separation line, the polarization becomes elliptical and then circular. For the values of the ambient conductivities Z:w = ZHO = 5 S; XP2 = CNZ = 30 S, the maximum magnetic effect on the ground caused by the ionospheric inhomogeneity reaches up to 40% of the magnetic disturbance generated by the same source in the homogeneous ionosphere with conductivities ZPO and
L/cl.
For the strip, the difference magnetic disturbance on the ground has the following characteristics: 1. The magnetic polarization ellipse distribution on the ground becomes essentially asymmetric relative to the strip. 2. The line separating the regions with different rotation senses of the polarization vector becomes curved with respect to the strip projection on the ground. For a strip of 40 km width with conductivities CPZ = ZHZ = 30s in the ionosphere, with conductivities ZPO = C,, = 5 S outside, the maximum magnetic effect caused by the inhomogeneity reaches 30%. Expressions for the potentials of the polarization electric fields and current functions of ionospheric disturbed currents are obtained for the ionosphere with strip inhomogeneity. The results may be important both for the interpretation of data of natural magnetic pulsation polarization and for the study of artificial magnetic pulsations generated by ionosphere heating. The ‘method of reflection’ used here and, consequently, the obtained results are valid for the case when the dimensions of the source (strip) are sufficiently small.
E. Belova et al.
1434
REFERENCES Ellis P. and Southwood
D. J.
1983
Glassmeier
K.-H.
1983
Glassmeier
K.-H.
1984
Lyatsky
W. B. and Maltsev
Malsev Yu. P., Leontyev
Maul A.-A.,
Rietveld
Yu. P.
S. V. and Lyatsky
1974
H.
K.
1990
1984
K.
Pashin A. B., Belova E. G. and Lyatsky
Stubbe P. and Kopka
W. B.
M. T., Stubbe P. and Kopka
Oguti T., Meek J. H. and Hayashi Oguti T. and Hayashi
1983
1984
W. B.
1995
1977
H.
Stubbe P., Kopka H., Rietveld M. T., Frey A., Hoeg P., Kohl H., Nielsen E., Rose G.,LaHoz Barr R.. Derblom H., Hedbera A., Tide B.. Jones T: B., Robinson T., Brekke A., Hansen and Holt 0. Lotz-Iwen H. J.
1995 C.,
Reflection of Alfven waves bv non-uniform ionospheres. Planet. Space Sci. 31;107-117. Reflection of MHD-waves in the Pc4-5 Deriod range at ionospheres with non-uniform conductivity Idistributions. Geophys. Res. Left. 10, 678-681. On the influence of ionospheres with non-uniform conductivity distribution on hydromagnetic waves. J. Geophys. 54, 125-137. Magnetosphere-ionosphere interaction, Nauka, Moscow. Pi2 pulsations as a result of evolution of an Alfven impulse originating in the ionosphere during a brightening of aurora. Planet. Space Sci. 22, 15 19-1533. Excitation of periodic magnetic field oscillations in the ULF range by amplitude modulated HF waves. Ann. Geophys. 8,765-780. Multiple correlation between aurora1 and magnetic pulsations. J. geophys. Res. 89,2295-2303. Multiple Correlation hetween aurora1 and magnetic pulsations. 2. Determination of electric currents and electric fields around pulsating aurora1 patch. J. geophys. Res. 89,7467-748 1. Magnetic pulsation generation by a powerful groundbased modulated HF radio transmitter. J. atmos. terr. Phys. 51,245-252. Modulation of the polar electrojet by powerful HF waves. J. geophys. Res. 82,2319-2325. Ionospheric modification experiments with the Tromso heating facility. J. atmos. terr. Phys. 47, 1151.
T. 1983
Doctoral
Thesis, Universitat
Gottingen.
Pergamon
and Solar-Terrestrial
PII: s1364-682q%)00182-4
Physics, Vol. 59, No. 12, pp. 1425-1434, 1997 0 1997 Elsevier Science Ltd All rights reserved. Printed III Great Britain 136&5826/97$17.00+0.00
The effect of an ionospheric inhomogeneity on magnetic pulsation polarization E. Belova, E. Pchelkina, Polar Geophysical
W. Lyatsky Institute,
Apatity,
and A. Pashin Russia
(Received in final form 28 May 1996; accepted 28 November 1996)
Abstract-The problem of magnetic disturbance polarization on the ground for a dipole source in the inhomogeneous ionosphere is solved for two kinds of an horizontal inhomogeneity. One is the case when the ionosphere is separated into two distinct parts with different conductivities and the other is a mesoscale strip in the ionosphere strip with enhanced conductivity which may be associated with an aurora1 arc. By using the ‘method of reflection’ an electric potential of the polarization field and a current function of the equivalent ionospheric currents are found for these cases. The distributions of the magnetic disturbance polarization ellipses on the ground have been obtained. It is found that under the certain ionospheric conditions the inhomogeneity can cause a significant (up to 40%) contribution to the magnetic disturbance amplitude on the ground and change essentially its polarization. For the first case the contribution of the inhomogeneity to magnetic variations on the ground is symmetric relative to the boundary. This boundary separates the regions with different rotation sense of the magnetic disturbance vector. For the case of the meso-scale strip, it is found that on the ground the magnetic polarization ellipse distribution becomes asymmetric and complicated. The line separating the regions with different rotation sense becomes curved. 0 1997 Elsevier Science Ltd
1. INTRODUCTION
It is evident that the spatial-distribution of ionospheric conductivity is able influence strongly the configuration of ionospheric current systems and as a consequence, the magnetic signature of these currents on the ground. The effect of horizontal non-uniformities in ionospheric conductivity has been theoretically investigate over the last 20 yr by a number of authors (Maltsev et al., 1974; Ellis and Southwood, 1983; Glassmeier, 1983, 1984). Ellis and Southwood (1983) studied the case of an Alfven wave incidence on the ionospheres which have various sharply discontinuous, horizontal distributions of conductivity. Glassmeier (1984) calculated the distribution of equivalent currents on the ground for an incident. Alfven wave on the ionosphere having an arbitrary non-uniform conductivity distribution. There are also interesting cases when the ground magnetic disturbances are generated not by an Alfven wave of magnetospheric origin but by an ionospheric source. When in the ionosphere a dipole source appears whose electric field changes in time with a frequency in the range of geomagnetic pulsations, polarized magnetic disturbances on the ground can be detected. This source may be a patch of the enhanced con-
ductivity in the ionosphere. It may be formed in a natural way, for example, caused by the electron precipitation [Maltsev et al., 1974; Oguti et al., 1984; Oguti and Hayashi, 19841 or artificially, for example, the results of ionospheric heating by a power modulated HF radio wave [Stubbe and Kopka, 1977; LotzIwen, 1983; Stubbe et al., 1985; Pashin et al., 19951. In the article of Maul et al., 1990 the polarization characteristics of artificial magnetic pulsations generated during the heating experiment in OctoberNovember, 1984 near Tromso, Norway, were studied. The observed polarization ellipses on the ground were presented and their characteristics were compared with those calculated using a stimulation model. In some cases the discrepancy between these results in the ellipticity and the inclination angle of the main ellipse axis was rather large. The authors did not propose a convincing explanation for this fact. However, in that article it was mentioned that during one of the experiments near the ionospheric heated region a quiet aurora1 arc was observed. Therefore the ionosphere was essentially inhomogeneous and that might influence the polarization characteristics of the magnetic pulsations. The aim of this work is to study the ground distribution of the polarization ellipses of the magnetic pulsations generated by an ionospheric dipole source
1425
E.
1426
Belova et al.
for the case of an inhomogeneous conductivity of the ionosphere. Two kinds of inhomogeneities are considered. In Section 2 we investigate the polarization on the ground from a dipole source in the homogeneous ionosphere. In Section 3 the ionosphere is assumed to be separated into two parts with different conductivities. In Section 4 the ionospheric inhomogeneity is considered to be in a form of a strip with enhanced conductivity. The latter case may be associated with an aurora1 arc.
2. MAGNETIC SOURCE
PULSATIONS
GENERATED
IN THE HOMOGENEOUS
BY A DIPOLE
INONOSPHERE
In the ionosphere we consider that a region with the enhanced conductivity appears. By the presence of the ionospheric electric field, it is polarized. The polarization currents inside this region are closed by currents flowing outside it and the field-aligned currents. The resulting current system produces magnetic disturbances on the ground. 2.1. In the ionosphere
It is convenient to choose in the ionosphere a complex coordinate system w = x+iy according to Maltsev et al., 1974. Then the height-integrated ionospheric conductivity may be written in the complex form X = X,--E,, where C, is the Pedersen conductivity and X:His the Hall conductivity. Let us consider the polarization problem for an ambient horizontally homogeneous ionosphere with the height-integrated conductivity Co = CpO- Z,,, and with a circular region of disturbed conductivity, X1 = C,, -zZ~, having radius a. Outside the circle the polarization field caused by the presence of the ionospheric electric field E,, behaves as the field from the dipole source (Maltsev et al., 1974):
where
z$=-
~,-&l X:, +cg+2c,
x -6,
Here g is the polarization electric field inside the source region assumed to be homogeneous, C,. is an effective magnetosphere plasma conductivity (‘wave conductivity’) and symbol ‘*’ means the complex conjunction. In our case we took values of AX = X1 -X0 such that the source field has circular polarization rotating clockwise when viewed along the geomagnetic field. According to the article by Lyatsky and Maltsev,
1983 we take the electric potential cp and the current function IJ for the dipole source using a complex potential F and dipole moment q,, as follows: cp = ReF F=
40 w-w0
(3)
$ = Im(E*F) where w,, is the complex coordinate of the dipole source (the centre of the enhanced conductivity region) and dipole moment qO = - a2Ej; X is the conductivity in the region of interest. For this, the equivalent ionospheric current J is determined from the formula J =
k,,grWl
(4)
where the square brackets mean the vector product, eZ is the unit vector along the z-axis, assumed to be directed along the geomagnetic field. The lines of the equal current function values coincide with lines along which the currents flow and the line density is proportional to the ionospheric current value. Figure l(a) demonstrates the distribution of the polarization ellipses for the equivalent ionospheric current disturbances, calculated using expression (4), for a source with circular polarization. Calculations have been made for the case of CpO = Xc,,, = 5 S; in complex form this may be written as C,(S) = 5-5i; C,(s) = 0.05, for an ionospheric electric field of 50 mV/m assumed to be directed along the y-axis, for the amplitude of the conductivity disturbance AC of 0.1 S and for a = 10 km. The current disturbance magnitude at the source point is not shown because it is too large compared with the magnitudes at other points. The arrows demonstrate the polarization vector rotation sense. The polarization vector rotates in the opposite directions inside and outside the source region. The polarization in the ionosphere is circular everywhere except at the boundary of the source region where it is linear. 2.2. On the ground From the distribution of the equivalent current in the ionosphere using the Biot-Savart law, we can obtain the magnetic disturbance on the ground. The contribution to the magnetic disturbances at each point on the ground is given by the whole current system in the ionosphere. Thus the polarization distribution on the ground becomes more complicated than in the ionosphere but the central symmetry remains. Figure l(b) shows the distribution of the magnetic
Effect of ionospheric
inhomogeneity
on magnetic
Hodograms
of equivalent
ionospheric
1
l-
I
I
150
200
pulsation
1427
polarization
current disturbance
I
250
I
1
100
X distance, Hodograms 300
250
300
km
of magnetic disturbance
on the ground
2
/
250
/ E Y . g 5 200
.
t
t
5 5 > 150
%
100
,
/ t 1.1.10-2n
\ 50
100
/ 150
200
X distance,
250
300
3
km
Fig. 1. (a) Spatial distribution of the hodographs of equivalent ionospheric current disturbance (except the is assumed source point) in the ionosphere with conductivities X,, = ZH,, = 5 S. The source polarization to be circular. The source location is marked by a cross. The rotation sense of the ionospheric current vector is indicated by arrows, (b) Spatial distribution of the hodographs of the magnetic variation on the ground from the ionospheric currents shown at the top. The rotation sense of the magnetic disturbance vector is indicated by arrows.
1428
E. Belova et al.
disturbance vectors calculated for 8 instants of time during a period at each point on the ground. Using this graph it is easy to reconstruct the hodograph at any point; therefore we shall call such plots hodograms for convenience. On the ground the inner region with polarization as inside the source is extended as compared with that region in the ionosphere (Fig. 1(a)) and the radius of this region on the ground, r, is about the source height. Inside this region the vector AB shows the same rotation sense as in the source, and outside this region - the contrary sense of rotation. Besides that a wide region with the elliptical polarization appears on the ground. In the centre of the region the polarization is circular, but when we move away from the centre it becomes elliptical, and on the boundary it is linear with the vector AB directed along the boundary.
3. MAGNETIC SOURCE
PULSATIONS
GENERATED
IN THE INHOMOGENEOUS OF SEMI-INFINITE
CASE
PLANE
3.1. In the ionosphere Lyatsky and Maltsev (1983) solved this problem in the ionosphere and derives the potential and current function for this case. The ‘method of reflection’ was used. We consider a complex coordinate system in the ionosphere such that the line, separating the two regions with different conductivities coincides with the real axis and the source is at a distance w0 from the origin (Fig. 2). In the each region, we search the potential and current function as following:
* = Im(c*f)
(5) - ~ 4, w-w,*
= 4 w--w0
where qOis the dipole moment
82 I
II
0
+
Re w t
do
I Fig. 2. Diagram considering the ionosphenc region with a complex coordinate system. The real axis is the boundary between the two ionospheric parts with conductivities X0 and &. The source is the circle with radius a and conductivity C, situated at a distance of do from the centre.
are the moments of the ‘reflected’ dipoles. The values of qr and q’are determined from the continuity equations for cp and $ on the boundary of the regions (Eqs (5.100) and (5.101) in Lyatsky and Maltsev, 1983). So far as we are interested in the effect caused by the ionosphere inhomogeneity, for the analysis we shall use not the potentials and current function themselves but the difference between them and the potentials and current functions calculated for the homogeneous ionosphere described in Section 2.1. This difference defines the disturbance related to the inhomogeneity. We call these differences the disturbances. In Fig. 3 the distributions in the ionosphere of the disturbances of cp and $ are shown for the case: C,(S) = 5-5i; Z,(s) = 30-30i; Z,(s) = 5-5.li; C,,. = 0.05 S; the radius of the source a = 10 km and its distance from the boundary do = 50 km. As is seen the distributions of cp and IJ disturbances are symmetric relative to the boundary and have the form of two vortices with foci located on the boundary. The position of these vortices depends on the source polarization. The foci of the $ vortices are shifted relative to those of the UJvortices. 3.2. On the ground
q = ReF
F;(w)
0
BY A DIPOLE
IONOSPHERE:
At first we let the ionosphere be separated by a straight line into two parts with different conductivities X0 and X2. When in any part the dipole source appears, at the boundary supplementary polarization electric charges arise. A supplementary polarization electric field generating the additional currents inside and outside the source region arises as well. As a result the distribution and magnitude of the total ionospheric current disturbance changes and, hence, the magnetic effect on the ground changes too.
F,(w) = 40 w-w0
T
Im w
of the source, qr and q’
From the symmetry of the current disturbance distribution relative to the boundary in the ionosphere, it is clear that this symmetry is kept on the ground. In Fig. 4 the hodograms of the magnetic effect on the ground calculated from the Ic/disturbance are presented. The polarization of the ionospheric source is assumed to be circular. These hodographs show the difference of the polarization ellipses for the case of
Effect of ionospheric
inhomogeneity
lsocontours
(a)
on magnetic
pulsation
polarization
1429
of electric potential
4oc)-
3X )-
3ocl-
E Y
25c I-
it 5 200 , z .0 >
150
100
50
n-
50
-0
100
150
200
X distance, @I 4oc
lsocontours
/
250
300
350
km
of current function
’
\
\
350
300
/
E 250 Y _
/
i? 5 200 5 .:
\ 150
\ 1
I
u
50
100
150
200
X distance,
250
300
350
km
Fig. 3. Distributions of the disturbances of electric potential in (a) Volts and (b) current Amperes, in the ionosphere separated into two parts with conductivities Z P0 = XHO= 5 S; XP2 = XH2 = 30 S. The separating line is located at y = 200 km. The conductivities in the source region are XP, = 2,,, = 4.9 S. The source location is marked by a cross.
1430
E. Belova et al. Hodograms of magnetic disturbance on the ground
300
250
100
50
150
100
200
250
300
350
X distance, km Fig. 4. Spatial distribution of the hodographs of the magnetic variation on the ground. The source polarization is assumed to be circular and the ionosphere conductivities are as in Fig. 3. The rotation sense of the magnetic disturbance vector is indicated by arrows.
the inhomogeneous
ionosphere
considered
from
the
l(b)). It is seen that on the ground far from the boundary the disturbance AB has the usual circular polarization; then the total magnetic vector is polarized as for the homogeneous ionosphere. This is because of the additional current sources associated with the inhomogeneity are situated on the boundary and, far from it, the influence of these sources is negligible. When we move to the boundary, the polarization becomes elliptical and then linear with the dominating direction of AB being along the boundary. Here the polarization vector changes rotation sense. Inside the source region on the ground the disturbance of AB has the same rotation sense as in the source in the ionosphere, but it has the contrary sense of rotation on the other side of the boundary. These results are valid for the case of a broad ionospheric region with enhanced conductivity. ellipses
for the homogeneous
4. MAGNETIC SOURCE
PULSATIONS
ionosphere
GENERATED
IN THE INHOMOGENEOUS
(Fig.
a strip. So far as this case has not studied earlier, we shall consider it in detail. 4.1. In the ionosphere Let the ionospheric inhomogeneity in form of a strip with d, width and CZ conductivity stretches parallel to the real axis of the complex coordinate system and be located on the distance of do from the source centre (Fig. 5). To determine the complex potentials in the each ionosphere region we also use the ‘method of reflection’. The potential in each region I, II and III we consider to be as a row of the potentials of dipoles obtained by successive ‘reflections’ of the initial dipole from each boundary of the strip:
FII
=
4
wfid,
(6)
Bll mw-i(2nd,+d,)
+ncI
C” +Z n- 1 w+i(2nd,+d,,)
BY A DIPOLE
IONOSPHERE:
A* cG w-id,, +~CI w-i(2nd,+d,,)
+-%+L wfid,,
(7)
CASE
D, FII, = q” f ? w+idO n= ’ w+i(2nd,+d,,)
OF A STRIP
When the region with the different conductivity not very wide, we can consider the inhomogeneity
is as
where
(8)
Effect of ionospheric inhomogeneity on magnetic pulsation polarization
c
%
We calculated these values numerically for the case: the undisturbed conductivity X0 = 5-5i; the wave conductivity C, = 0.05 S; the conductivity of the strip X2 = 30-30i; the disturbed conductivity in the circle C, = 5-5.li; a = 1Okm; do = 50km; d, = 40km. As in the previous case we calculate the disturbances of q and I) as the difference between this case and the case of the homogeneous ionosphere. In Fig. 6 the obtained disturbances of cp and $ in the ionosphere are shown. For this case the isopotential lines and currents are concentrated into the narrow strip. The spatial distributions of cp and tj became strongly asymmetric with respect to the strip boundary, unlike the previous large-scale case. Now the currents have four vortices, contrary to the two vortices for the of case of boundary.
I
do
c;i
20
a
Fig. 5. Diagram of the ionospheric region of interest with a complex coordinate system. The boundaries of the strip having width ds are indicated by straight lines. The complex conductivity in regions I and III is LX,,,and in region II X2. The source is the circle with radius a and conductivity Z, situated at a distance dOfrom the strip boundary.
4.2. On the ground The described distribution of currents produces a complicated picture of magnetic variations on the ground. In Fig. 7 the calculated hodographs of the magnetic disturbances on the ground for a dipole source with the circular polarization are shown. The distribution of the polarization ellipses becomes rather complicated indeed. The line separating the regions of different rotation senses does not now coincide with the strip border. The main axes of the polarization ellipses, near the separating line, are directed almost along it.
w%
a*(& -
q” = z,+c,*+2c,
(zl + XT+
, q =
2L)%
z:+Iz:o+2~,
PO-
wo*
qr = z* + x0*+ 22, q”
=
1431
@o$.v+ 2c,m, + z:+ 2C,)q, 1x2+ z:,*+ 2&f
The coefficients of this row, that are the dipole moment values, are constructed such as that on the strip boundaries the continuity conditions for electric potential and current function are fulfilled. The complex potentials and current functions for the regions I, II and III can be written in the form:
5. RESULTS
In this article the magnetic disturbance polarization in the ionosphere and on the ground from a dipole circularly polarized source in the inhomogeneous ionosphere has been considered for two cases.
IL - z312’“- “(C, - &)(&i + g+
ICf+&+
+% J’m =
2&J@,
+ xc:+ 2Z,)q,*
22,j2”(Z2+Z,*+ 2Z,)(w - i(2nd,+ 4))
IX*- &/*(n-‘)(X2-T&p, JZf+&+2P’~*“(w
AND DISCUSSION
+ z,*+ 2E”)qo*
- i(2nd,+ do))
1x2- w2”(c0-- x,*+ 2Z,)q, I~:+c,+2C,12”(Z:~,+2~~)(w-i(2nd,+d,)) - zg + 2&p* + XT+ 2&)q, IX:+ CO+ 2Z.,f2”+ ‘)(w - i(2nd,+ do))
1x2 - &I*“(&
(9)
E. Belova et al.
1432
(4
lsocontours of electric potential
300 -
E 250Y _ L? 5 200Iii z >
150-
01 0
50
100
150
200
250
300
350
300
350
X distance, km lsocontours of current function
@I
350
300
E Y
250
i? 5 200 z E >
150
100
50
0
1
50
100
150
200
250
X distance, km Fig. 6. Distributions of the disturbances of electric potential in (a) volts and (b) current function in Amperes are XP2 = XH2 = 30 S. The in the ionosphere with conductivities XPO = CHD = 5 S. The strip conductivities ionospheric geometry is as in Fig. 5. The boundaries of the strip are located at y = 200 km and y = 240 km. The conductivities in the source region are C,, = E,,, = 4.9 S. The source location is marked by a cross.
Effect of ionospheric
inhomogeneity
Hodoarams
on magnetic
pulsation
of magnetic disturbance
1433
polarization
on the ground
150
100 L
50
100
150
200
250
300
3
X distance, km Fig. 7. Spatial distribution of the hodographs of the magnetic variation on ground. The source polarization is assumed to be circular and the ionospheric conductivities are as in Fig. 6. The rotation sense of the magnetic disturbance vector is indicated by arrows.
In the magnetic between and the the same
case of a semi-infinite plane, the current and disturbances obtained as the difference the values for the inhomogeneous ionosphere values for the homogeneous ionosphere for source have the following features:
The polarization ellipse distribution in the ionosphere and on the ground is symmetric relative to the boundary. On the ground this boundary is a line separating regions with different vector polarization rotation sense. Outside the boundary the polarization vector rotates as inside the source; inside the boundary this vector rotates in the opposite direction. The polarization on this line is linear and the polarization vector AB is directed along the line. Away from the separation line, the polarization becomes elliptical and then circular. For the values of the ambient conductivities Z:w = ZHO = 5 S; XP2 = CNZ = 30 S, the maximum magnetic effect on the ground caused by the ionospheric inhomogeneity reaches up to 40% of the magnetic disturbance generated by the same source in the homogeneous ionosphere with conductivities ZPO and
L/cl.
For the strip, the difference magnetic disturbance on the ground has the following characteristics: 1. The magnetic polarization ellipse distribution on the ground becomes essentially asymmetric relative to the strip. 2. The line separating the regions with different rotation senses of the polarization vector becomes curved with respect to the strip projection on the ground. For a strip of 40 km width with conductivities CPZ = ZHZ = 30s in the ionosphere, with conductivities ZPO = C,, = 5 S outside, the maximum magnetic effect caused by the inhomogeneity reaches 30%. Expressions for the potentials of the polarization electric fields and current functions of ionospheric disturbed currents are obtained for the ionosphere with strip inhomogeneity. The results may be important both for the interpretation of data of natural magnetic pulsation polarization and for the study of artificial magnetic pulsations generated by ionosphere heating. The ‘method of reflection’ used here and, consequently, the obtained results are valid for the case when the dimensions of the source (strip) are sufficiently small.
E. Belova et al.
1434
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D. J.
1983
Glassmeier
K.-H.
1983
Glassmeier
K.-H.
1984
Lyatsky
W. B. and Maltsev
Malsev Yu. P., Leontyev
Maul A.-A.,
Rietveld
Yu. P.
S. V. and Lyatsky
1974
H.
K.
1990
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K.
Pashin A. B., Belova E. G. and Lyatsky
Stubbe P. and Kopka
W. B.
M. T., Stubbe P. and Kopka
Oguti T., Meek J. H. and Hayashi Oguti T. and Hayashi
1983
1984
W. B.
1995
1977
H.
Stubbe P., Kopka H., Rietveld M. T., Frey A., Hoeg P., Kohl H., Nielsen E., Rose G.,LaHoz Barr R.. Derblom H., Hedbera A., Tide B.. Jones T: B., Robinson T., Brekke A., Hansen and Holt 0. Lotz-Iwen H. J.
1995 C.,
Reflection of Alfven waves bv non-uniform ionospheres. Planet. Space Sci. 31;107-117. Reflection of MHD-waves in the Pc4-5 Deriod range at ionospheres with non-uniform conductivity Idistributions. Geophys. Res. Left. 10, 678-681. On the influence of ionospheres with non-uniform conductivity distribution on hydromagnetic waves. J. Geophys. 54, 125-137. Magnetosphere-ionosphere interaction, Nauka, Moscow. Pi2 pulsations as a result of evolution of an Alfven impulse originating in the ionosphere during a brightening of aurora. Planet. Space Sci. 22, 15 19-1533. Excitation of periodic magnetic field oscillations in the ULF range by amplitude modulated HF waves. Ann. Geophys. 8,765-780. Multiple correlation between aurora1 and magnetic pulsations. J. geophys. Res. 89,2295-2303. Multiple Correlation hetween aurora1 and magnetic pulsations. 2. Determination of electric currents and electric fields around pulsating aurora1 patch. J. geophys. Res. 89,7467-748 1. Magnetic pulsation generation by a powerful groundbased modulated HF radio transmitter. J. atmos. terr. Phys. 51,245-252. Modulation of the polar electrojet by powerful HF waves. J. geophys. Res. 82,2319-2325. Ionospheric modification experiments with the Tromso heating facility. J. atmos. terr. Phys. 47, 1151.
T. 1983
Doctoral
Thesis, Universitat
Gottingen.