- Email: [email protected]
The effect of local irregularities on large-scale ionospheric currents
Adv. Space Res. Vol. 22, No. 9, pp. 1353-1356. 1998 0 1998 COSPAR. Published by Elsevia Science Ltd. All rights reserved Printed in Great Britain 0273-l 177m $19.00 + 0.00 PII: SO273-1177(98)00186-O
Pergamon
The EFFECT of LOCAL IRREGULARITIES on LARGE-SCALE IONOSPHERIC CURRENTS L. S. Alperovich
Lkpartmentof Geophysicsand PkmetarySciencesof Tel-AvivUniversity,Tel-Aviv,69978, Israel
ABSTRACT Meewuements performed by the low-altitude satellites MAGSAT and TKIAD have discovered small-scale &L<80&m) magnetic fluctuationsat high latitudes. A relation between the fluctuation intensity, ionospheric conductivity and Birkeland currents was also ‘revealed. We assume that the magnetic perturbations are caused by small-scale ionospheric irregularities. We discuss here the influence of random ionospheric irre&a&es on the ei&ctive conductivity. Through analytical consideration, it is conchtded that the Pedersen ef&ctive conductivity may noticeably deviate from the average condud%y. The effect depends primarily on conditions of Hall current closing. Wherever the Hall currents flow is impossiile for any reason, the influence of weak irregularities is negligible. Zones of the equatorial and polar electrojets with electric field directed along electrojets are examples. Analytical consideration conducted for the regions exterior to these zones has shown that random weak ionospheric irregularities double the total Pedersen eRective integral conductivity increases. It is usually suggested in the description of the ionospheric conductivity that the ionosphere is either homogeneous or exhib&s local irregularity. The background sporadic irreg&%es in the ionosphere usually small scale is also well known. The research concentrated on two main items: the contribution of a random wind and conductivity field to the background and magnetospheric quasi-stationary electric and magnetic field, and the influence of small stochastic ionospheric irregularities on the e&ctive ionospheric COUdUCtiVity.
631998 COSPAR. Published by Elsevier Science Ltd.
CONTIUBUTION of a KANDOM WIND and CONDUCTMTY PIELD to the BACKGROUND and MAGNETOSPHEIUC QUASISTATIONAKY ELECTRIC and MAGNETIC PIELDS Let us write an equation describing quasi-stationary electric fields and currents in the ionosphere (Gurevich and Krylov, 1977) as follows: z.(-Gmdg++#@l)
=-GradF+Rot
G
(1)
Here Grad, Rot are twodimdonal operators of grti and rot reqebdy, p is a pot&al of the electricfield,Gisacurrentfbnction,Fisascalarc~thepote&lpartoftheionor@eric currem, 6 and U are respectively tensors of integral conductivity and the e%ctive wind velocity with Pedersen (mdex “p”) and Hall (index “h”) components. We define U as 1353
1354
L. S. Alpcrovich
where u is horizontal wind velocity, and u’Zis element of length along the geomagnetic field line. We suppose that the geomagnetic field is orthogonal to the ionosphere. To study a contribution of the stochastic field we proceed at follows. Let us present terms in Eq.( 1) in the form z=&+q;
F=F,
+F,,
G=GO+GI,
9=!& +px9
wl=re&, = @>, 4, = (F), p. = (g), Go = (G>, and Z,, g+, F, and G, are random fh~ctuations of the corresponding fields. Angle parenthesis denote average values. Let
((T(hpi)l )‘”/CO(h.p) <<1 Then, obviously, ((Grad q~r)*)“’/ Grudqo << 1. Neglecting squares of the small parameters terms we have C,E, = Rot GO- Grad F, for average values and ZO(-Gmd~l)+EBZ,
= -G&F1
+Rot Gl
for fluctuations . Here E, = -Grad q. + f [u,B]. We present two-dimensional field of the velocity U in the form U=-Gradf
+Rotg
Then the latter may be rewritten in the form (Alperovich, Gershenson, and Krylov ,1986) z;,,(Po + g) + 4<*,f + 4@* i 4@,(90 + g) - &Of
=6
+ ~~,,~I = Gl
Here g=g,Blc, f =f,j3l c . The system is completed in the same way for the corjugate ionosphere to define q+, F,, and G, .Omitting simple calculations, we have P+rJ,
G,),
and
* = {q*,,
&k+)? z;,p, 3 %-I]
P=L*T where vog- ;
f* LL-
z
-%:~ig+h
-
“ol,;f+i
%&%+g-);
rq:jf-
9
O(P)
L',+,(90+8+)+ here Z,,, = Coo,+)+ &.,+
‘O,,f+;
-
zO,p~(%+g,)
+
&h+,f+;
&(h+,(%+g-)
‘,h+,f+
I
subscripts “+‘I and “-” are related to values in two conjugate ionospheres.
The potential pJ defines those part of the ionospheric electric field E=-Grad pJ, that penetfates into the magnetosphere along force lines. The scalar field FJ is connected with field-aligned currents and therefore characterizes geomagnetic variations in the magnetosphere. Lastly, the current function GJ defines the solenoidal part of the ionospheric current generating ground perturbations. Fluctuations -(Pi&) contain of the integml ionosphere conductivities. Sormation on scale sizes and values of the random irqukties
Irregularities Effect on Ionospheric Currents
1355
(1981) have demo&rated the existence of such fhictuations by ident@@ oscihations of radio+@ inter&y with periods T=IO+5Osec tkomsatdlite ATS-6 with m geomagnetic pulsations in Z/3 of more than 100 cases. The same comparison of the radiosignal with magnetic pulsations on the-ground suke did not reveal such a strong correlation.
Okwawa
SMALL
and
D&es
STOCHASTIC IRREGULARITE S and the EFlXCTIVE CONDUCTMTY
Small local electron imgdadies and wind motions do not explain all the perturbations of the local current systems, however. Sign&ant progress in a disordered system studies has been achieved through a series of theoretical works and recent studies in the solid physics. It was proved, for example, that Bmall fluctuations of electron concentration in a partially ionized gas with a strong magnetic field may result in significant pemubstion of the etkctive conductivity.
Ifwe expand small fluctuations of conductivity in a Fourier series 4
with a spatial harmonics J&&&j and a wave number q, then one can obtain components of the etfective conductivitytensor&
Here Bk(q) is the sohnion of the equation
-c 4J,,,,(q -4’M”
4(q) = -q,,,wq,
(2,~,q”
4 W.
q’+O
Eq.(2)and(3)were! sohd for a magnetized electron plasma by Dreizin and Dichne.(1973). In a similar mamrer, one can find the total Pedersen conductivity for the electron-ion ionospheric plasma (Alperovich and Chaikovsky, 1996)
Here & is the fIuct&ion of electron concentmtion, aa is the electron cyclotron fkequency, v, represents the collision frequency of electron with neutrals, while &’ and 4’ are longitudinal electron conductivity and the Pedersen ion conductivity respectively. The relative value of the fluctuating part of the efktive
cWP
-= 4
(>
conductivity is of the form
(y2w, I vJZJ3 z;/q
We notice that the contribution of the fhrctuatmg part Z;,, becomes comparable with the background condu&@ 4 for y
-(CD, / v,)-y2((z;)/(z;))3’4
Ifwe substitute typical parameters of the lower ionosphere into this exprexkon, we find y- 0.9.
1356
L. S. Alperovich
Kvyatkovskiy (1983), for twodimensional media in the strong magnetic field show that the per&&&ion of the transverse conductivity may be defined 6om the relation The
estbtion,
after
‘12=
( 1o
z(UP - - Y -4 a, Jve 4,
where LA and L/l are scaksize of the ionospheric E-layer and the transverse scale-size inhomogeneities, respectively. We find after simple calculations that for small-scale inhomogeneities with L1 - LII the conductivity caused by irregularities becomes comparable with unperturbated background Pedersen conductivity for fl.2. Large-scale inhomogeneities, with Ll-lOOkm, increase the irregularity contribution roughly 3 times. Summa&@ the above, one can expect considerable changes of the relationship between the Pedersen and Hall conductivities in the ionospheric E-region even during weak perturbations and a marked increase in the intensity of the geomagnetic variations. This was also demonstrated in the series of model experiments on solid S&tihns with random irregularities in strong magnetic fields (Alperovich et al., 1997). The direct observations of small-scale (I < L1 c 35 km) magnetic fluctuations over the high-latitude ionosphere using the MAGSAT data and their comparison with large-scale Birkeland currents (Iyemori, Ike&, and Nakagawa, 1986) also demonstrates this relationship. The authors discovered variable correlation between the amplitude of small-scale and large-scale Birkeland currents for diierent high-latitude regions. A strong relationship between the intensity of small-scale perturbations and the ionospheric conductivity near the day-side poleward edge of the large-scale Birkeland current in the open “unbounded” region was also discovered. Although the key features of effect of random ionospheric irregularities on the efI&ctive Pedersen conductivity are realized now, attention should be paid to their contribution to the real global current systems, especiahy in the auroral and equatorial regions. These research problems are subject for future studies. REPERENCES Alperovich, L., N. I. Gershenson, and A. L. Krylov, The fluctuations of the quasistationary electric and magnetic fields as a result of the stochastic irregularities of the ionospheric conductivity, Geomagnetic andAeronomie, 26,928 (1986). Alperovich L., I. Chaikovsky, Gn the effective conductivity of the ionosphere with random irregularities, Ann&s Geoph., 13,339 (1995). Alperovich L., S. Grachev, Yu. Gtuvich, L. Litvak-Gorskaya, A. Melnikov, and I. Chaikovsky, An optical method for simulating of nonuniform systems, JEllD Leti., 65,224 (1997). Dreizin, Yu. A., and A M. Dichne, Anomalous conductivity of inhomogeneous media in strong magnetic field, Sav. Phys. .EZJ’, 36,127 (1973). Gurevich A. V., and A. L. Krylov, Electric fields and currents in the high-latitude ionosphere, Physics of the SoZid&rth, n.11, 100 (1977). Iyemori T., T. Ikeda, and A. Nakagawa, Characteristics of small-scale magnetic fluctuations over the high-latitude ionosphere. Proceedings of the Eighth S’posium on Coordinated Obsenations of the Ionosphere ami the Magnetoqhere in the Polar Regions, 1985. Memoirs of National Institute of Polar Research, Special issue, N.42,92 (1986). Kvyatkovskiy, 0. E., Effective conductivity of an inhomogeneous medium in a strong magnetic field, Sov. Phys. JZX?‘, 58 ,120 (1983). Okuzawa T., and K. Davies, Pulsations in total cohunnar electron content, J Geophys. Res., A86, 1355 (1981).
Pergamon
The EFFECT of LOCAL IRREGULARITIES on LARGE-SCALE IONOSPHERIC CURRENTS L. S. Alperovich
Lkpartmentof Geophysicsand PkmetarySciencesof Tel-AvivUniversity,Tel-Aviv,69978, Israel
ABSTRACT Meewuements performed by the low-altitude satellites MAGSAT and TKIAD have discovered small-scale &L<80&m) magnetic fluctuationsat high latitudes. A relation between the fluctuation intensity, ionospheric conductivity and Birkeland currents was also ‘revealed. We assume that the magnetic perturbations are caused by small-scale ionospheric irregularities. We discuss here the influence of random ionospheric irre&a&es on the ei&ctive conductivity. Through analytical consideration, it is conchtded that the Pedersen ef&ctive conductivity may noticeably deviate from the average condud%y. The effect depends primarily on conditions of Hall current closing. Wherever the Hall currents flow is impossiile for any reason, the influence of weak irregularities is negligible. Zones of the equatorial and polar electrojets with electric field directed along electrojets are examples. Analytical consideration conducted for the regions exterior to these zones has shown that random weak ionospheric irregularities double the total Pedersen eRective integral conductivity increases. It is usually suggested in the description of the ionospheric conductivity that the ionosphere is either homogeneous or exhib&s local irregularity. The background sporadic irreg&%es in the ionosphere usually small scale is also well known. The research concentrated on two main items: the contribution of a random wind and conductivity field to the background and magnetospheric quasi-stationary electric and magnetic field, and the influence of small stochastic ionospheric irregularities on the e&ctive ionospheric COUdUCtiVity.
631998 COSPAR. Published by Elsevier Science Ltd.
CONTIUBUTION of a KANDOM WIND and CONDUCTMTY PIELD to the BACKGROUND and MAGNETOSPHEIUC QUASISTATIONAKY ELECTRIC and MAGNETIC PIELDS Let us write an equation describing quasi-stationary electric fields and currents in the ionosphere (Gurevich and Krylov, 1977) as follows: z.(-Gmdg++#@l)
=-GradF+Rot
G
(1)
Here Grad, Rot are twodimdonal operators of grti and rot reqebdy, p is a pot&al of the electricfield,Gisacurrentfbnction,Fisascalarc~thepote&lpartoftheionor@eric currem, 6 and U are respectively tensors of integral conductivity and the e%ctive wind velocity with Pedersen (mdex “p”) and Hall (index “h”) components. We define U as 1353
1354
L. S. Alpcrovich
where u is horizontal wind velocity, and u’Zis element of length along the geomagnetic field line. We suppose that the geomagnetic field is orthogonal to the ionosphere. To study a contribution of the stochastic field we proceed at follows. Let us present terms in Eq.( 1) in the form z=&+q;
F=F,
+F,,
G=GO+GI,
9=!& +px9
wl=re&, = @>, 4, = (F), p. = (g), Go = (G>, and Z,, g+, F, and G, are random fh~ctuations of the corresponding fields. Angle parenthesis denote average values. Let
((T(hpi)l )‘”/CO(h.p) <<1 Then, obviously, ((Grad q~r)*)“’/ Grudqo << 1. Neglecting squares of the small parameters terms we have C,E, = Rot GO- Grad F, for average values and ZO(-Gmd~l)+EBZ,
= -G&F1
+Rot Gl
for fluctuations . Here E, = -Grad q. + f [u,B]. We present two-dimensional field of the velocity U in the form U=-Gradf
+Rotg
Then the latter may be rewritten in the form (Alperovich, Gershenson, and Krylov ,1986) z;,,(Po + g) + 4<*,f + 4@* i 4@,(90 + g) - &Of
=6
+ ~~,,~I = Gl
Here g=g,Blc, f =f,j3l c . The system is completed in the same way for the corjugate ionosphere to define q+, F,, and G, .Omitting simple calculations, we have P+rJ,
G,),
and
* = {q*,,
&k+)? z;,p, 3 %-I]
P=L*T where vog- ;
f* LL-
z
-%:~ig+h
-
“ol,;f+i
%&%+g-);
rq:jf-
9
O(P)
L',+,(90+8+)+ here Z,,, = Coo,+)+ &.,+
‘O,,f+;
-
zO,p~(%+g,)
+
&h+,f+;
&(h+,(%+g-)
‘,h+,f+
I
subscripts “+‘I and “-” are related to values in two conjugate ionospheres.
The potential pJ defines those part of the ionospheric electric field E=-Grad pJ, that penetfates into the magnetosphere along force lines. The scalar field FJ is connected with field-aligned currents and therefore characterizes geomagnetic variations in the magnetosphere. Lastly, the current function GJ defines the solenoidal part of the ionospheric current generating ground perturbations. Fluctuations -(Pi&) contain of the integml ionosphere conductivities. Sormation on scale sizes and values of the random irqukties
Irregularities Effect on Ionospheric Currents
1355
(1981) have demo&rated the existence of such fhictuations by ident@@ oscihations of radio+@ inter&y with periods T=IO+5Osec tkomsatdlite ATS-6 with m geomagnetic pulsations in Z/3 of more than 100 cases. The same comparison of the radiosignal with magnetic pulsations on the-ground suke did not reveal such a strong correlation.
Okwawa
SMALL
and
D&es
STOCHASTIC IRREGULARITE S and the EFlXCTIVE CONDUCTMTY
Small local electron imgdadies and wind motions do not explain all the perturbations of the local current systems, however. Sign&ant progress in a disordered system studies has been achieved through a series of theoretical works and recent studies in the solid physics. It was proved, for example, that Bmall fluctuations of electron concentration in a partially ionized gas with a strong magnetic field may result in significant pemubstion of the etkctive conductivity.
Ifwe expand small fluctuations of conductivity in a Fourier series 4
with a spatial harmonics J&&&j and a wave number q, then one can obtain components of the etfective conductivitytensor&
Here Bk(q) is the sohnion of the equation
-c 4J,,,,(q -4’M”
4(q) = -q,,,wq,
(2,~,q”
4 W.
q’+O
Eq.(2)and(3)were! sohd for a magnetized electron plasma by Dreizin and Dichne.(1973). In a similar mamrer, one can find the total Pedersen conductivity for the electron-ion ionospheric plasma (Alperovich and Chaikovsky, 1996)
Here & is the fIuct&ion of electron concentmtion, aa is the electron cyclotron fkequency, v, represents the collision frequency of electron with neutrals, while &’ and 4’ are longitudinal electron conductivity and the Pedersen ion conductivity respectively. The relative value of the fluctuating part of the efktive
cWP
-= 4
(>
conductivity is of the form
(y2w, I vJZJ3 z;/q
We notice that the contribution of the fhrctuatmg part Z;,, becomes comparable with the background condu&@ 4 for y
-(CD, / v,)-y2((z;)/(z;))3’4
Ifwe substitute typical parameters of the lower ionosphere into this exprexkon, we find y- 0.9.
1356
L. S. Alperovich
Kvyatkovskiy (1983), for twodimensional media in the strong magnetic field show that the per&&&ion of the transverse conductivity may be defined 6om the relation The
estbtion,
after
‘12=
( 1o
z(UP - - Y -4 a, Jve 4,
where LA and L/l are scaksize of the ionospheric E-layer and the transverse scale-size inhomogeneities, respectively. We find after simple calculations that for small-scale inhomogeneities with L1 - LII the conductivity caused by irregularities becomes comparable with unperturbated background Pedersen conductivity for fl.2. Large-scale inhomogeneities, with Ll-lOOkm, increase the irregularity contribution roughly 3 times. Summa&@ the above, one can expect considerable changes of the relationship between the Pedersen and Hall conductivities in the ionospheric E-region even during weak perturbations and a marked increase in the intensity of the geomagnetic variations. This was also demonstrated in the series of model experiments on solid S&tihns with random irregularities in strong magnetic fields (Alperovich et al., 1997). The direct observations of small-scale (I < L1 c 35 km) magnetic fluctuations over the high-latitude ionosphere using the MAGSAT data and their comparison with large-scale Birkeland currents (Iyemori, Ike&, and Nakagawa, 1986) also demonstrates this relationship. The authors discovered variable correlation between the amplitude of small-scale and large-scale Birkeland currents for diierent high-latitude regions. A strong relationship between the intensity of small-scale perturbations and the ionospheric conductivity near the day-side poleward edge of the large-scale Birkeland current in the open “unbounded” region was also discovered. Although the key features of effect of random ionospheric irregularities on the efI&ctive Pedersen conductivity are realized now, attention should be paid to their contribution to the real global current systems, especiahy in the auroral and equatorial regions. These research problems are subject for future studies. REPERENCES Alperovich, L., N. I. Gershenson, and A. L. Krylov, The fluctuations of the quasistationary electric and magnetic fields as a result of the stochastic irregularities of the ionospheric conductivity, Geomagnetic andAeronomie, 26,928 (1986). Alperovich L., I. Chaikovsky, Gn the effective conductivity of the ionosphere with random irregularities, Ann&s Geoph., 13,339 (1995). Alperovich L., S. Grachev, Yu. Gtuvich, L. Litvak-Gorskaya, A. Melnikov, and I. Chaikovsky, An optical method for simulating of nonuniform systems, JEllD Leti., 65,224 (1997). Dreizin, Yu. A., and A M. Dichne, Anomalous conductivity of inhomogeneous media in strong magnetic field, Sav. Phys. .EZJ’, 36,127 (1973). Gurevich A. V., and A. L. Krylov, Electric fields and currents in the high-latitude ionosphere, Physics of the SoZid&rth, n.11, 100 (1977). Iyemori T., T. Ikeda, and A. Nakagawa, Characteristics of small-scale magnetic fluctuations over the high-latitude ionosphere. Proceedings of the Eighth S’posium on Coordinated Obsenations of the Ionosphere ami the Magnetoqhere in the Polar Regions, 1985. Memoirs of National Institute of Polar Research, Special issue, N.42,92 (1986). Kvyatkovskiy, 0. E., Effective conductivity of an inhomogeneous medium in a strong magnetic field, Sov. Phys. JZX?‘, 58 ,120 (1983). Okuzawa T., and K. Davies, Pulsations in total cohunnar electron content, J Geophys. Res., A86, 1355 (1981).