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\
PERGAMON
Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

A generation model of small!scale geomagnetic _eld!aligned plasma inhomogeneities in the ionosphere
V[M[ Sorokin\ V[M[ Chmyrev \ N[V[ Isaev
Institute of Terrestrial Magnetism\ Ionosphere and Radiowave Propagation\ Russian Academy of Sciences\ Troitsk\ Moscow Region\ 031981\ Russia Received 14 April 0885^ received in revised form 6 July 0887^ accepted 02 July 0887

Abstract The dissipative instability of acoustic!gravity waves in the ionosphere is investigated[ This instability results in formatting the horizontal periodic structure of conductivity disturbances which move with the velocities considerably less than the sound velocity[ In the presence of an external DC electric _eld the conductivity variations in the E!layer lead to an appearance of polarization electric _elds propagating into the upper ionosphere and generating the plasma density variations at these altitudes[ Estimates of the space!time and amplitude characteristics of the excited ionospheric disturbances and their comparison with the experimental data show that the developed mechanism can be applied to generation model of the earthquake!related small!scale plasma inhomogeneities in the upper ionosphere[ ÷ 0887 Elsevier Science Ltd[ All rights reserved[

0[ Introduction Experimental studies of the ionospheric structure by means of both ground!based radio sounding technique and of direct measurements of the ionospheric par! ameters onboard satellites and rockets performed during the last decades have revealed that the ionosphere dis! plays strongly irregular structure with the spatial scales of irregularities in the range from several cms to hundreds of kms[ Many papers are devoted to experimental studies of the irregular ionospheric structure as well as to gen! eration mechanisms of ionospheric irregularities[ The results of these investigations are most comprehensively systemized in the review papers by Fejer and Kelley "0879#\ Ossakow "0868# and Kelley "0878#[ The irregular structure of the ionosphere is pro! nounced most of all in the high!latitude and near!equa! torial regions[ This fact is argued by numerous results of radar observations "Evans\ 0864^ Greenwald et al[\ 0867# and by in situ satellite and rocket measurements "Clark and Raitt\ 0865^ Dyson\ 0858^ Dyson et al[\ 0863#[ To account for the generation mechanisms of the iono!

Corresponding author[ Tel[] 996 84 223 9019^ fax] 996 84 223 9013^ e!mail] chmyrevùizmiran[rssi[ru

spheric plasma density irregularities\ various types of plasma instabilities are considered[ Formation of small! scale irregularities in the ionospheric current jets "equa! torial and polar electrojets# are explained by a devel! opment of the FarleyïBuneman two!stream instability "Farley\ 0852^ Buneman\ 0852^ Fejer and Providakes\ 0876# or by gradientïdrift "EâB# instability "Farley and Balsley\ 0862^ Knox\ 0853^ Fejer and Providakes\ 0876#[ The gradientïdrift instability was considered also to account for the midlatitude sporadic E!layer "Tsuda et al[\ 0855#\ equatorial spread Es!layer "Martyn\ 0848^ Simon\ 0852# and the irregular structure of the high! latitude F!layer "Unwin and Knox\ 0860#[ The other types of instabilities playing an important role in the formation of the irregular structure of the ionosphere are the Postï Rosenbluth instability "Ott and Farley\ 0864^ Reid\ 0857# and electrostatic ion!cyclotron instability "Kindel and Kennel\ 0860^ Ungstrup et al[\ 0868#[ According to COSMOS!0798 satellite data "Chmyrev et al[\ 0886# inhomogenites of electron density with the spatial scale ¾ 09 km arise in the upper ionosphere before an earthquake[ They are localized in the geomagnetic force tube with the root on the projection of an epicentral zone onto the ionosphere E!layer[ The characteristic hori! zontal scale of the disturbed region occupied by these inhomogenites is 299ï349 km[ We note in this connection that such irregularities with magnitude dNe:Ne â 4) are

S0253ï5715:87:,*see front matter ÷ 0887 Published by Elsevier Science Ltd[ All rights reserved PII] S 0 2 5 3 ï 5 7 1 5 " 8 7 # 9 9 9 6 7 ï 8


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V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

Fig[ 0[ An example of seismic related plasma density variations dNe "upper panel# over the Spitak earthquake zone ½ 2[2 h before the shock on 19 January 0878[ Lower panels present plasma density Ne and intensities B of ELF magnetic _eld oscillations at the frequencies ½ 039 and 349 Hz[

not typical for the midlatitude ionosphere under normal conditions "Clark and Raitt\ 0865#[ Figure 0 presents an example of experimental data by Chmyrev et al[ "0886# on the distributions of plasma density Ne and its variations dNe together with ELF radi! ation intensity at the frequencies f ½ 039 and 349 Hz over the zone of seismic activity 2[3 h before an aftershock of the Spitak earthquake on 19 January 0878[ The time instant 99[93[95 UT when the satellite crossed the geo! graphic latitude of the earthquake focus is marked with the vertical arrow[ The measurements were carried out in the night!time sector during the recovery phase of geomagnetic storm[ As seen from Fig[ 0 the small!scale ~uctuations of plasma density dNe "upper panel in Fig[ 0# with characteristic spatial scales l ¼ 7 km and the magnitude dNe:Ne up to 7) were observed in the region where intense burst of electromagnetic emission at the frequencies f ½ 039 Hz "bottom panel# with the ampli! tude up to 09 pT was observed in the longitude range 30[5 ¨ l ¨ 31[9> i[e[ approximately 1> to the west from the earthquake focus and in the latitude range 29 ¨ f ¨ 22[0>[ A weaker increase of electromagnetic noise "up to 2 pT# in the same region was observed also at the frequencies f ½ 349 Hz[ At higher frequencies no emissions were registered[ The zone of increased values of the radiation intensity and the plasma density vari! ations is marked by vertical dotted lines in Fig[ 0[ The dimension of this zone is ½ 349 km along the satellite orbit[ Analysis of more than 49 events of such kind enable us to draw the conclusion that the seismic related plasma

density irregularities in the upper ionosphere have characteristic spatial scales of l ½ 3ï09 km and the mag! nitudes dNe:Ne ½ 3ï09)[ One can assume that the observed ~uctuations "dN e# result from spacecraft crossing plasma irregularities stret! ched parallel to geomagnetic _eld[ These irregularities could arise due to formation of the _eld!aligned currents with the transverse scale ¾ 09 km excited in the lower ionosphere[ One of the mechanisms generating a wave of _eld!aligned currents "shear Alfven wave# is a process of formation of the horizontal irregular structure of the ionosphere conductivity and its interaction with iono! spheric DC electric _eld in the region of Sq currents[ Thus the appearance of electron density ~uctuations in the upper ionosphere observed from the spacecraft could originate in the lower ionosphere due to excitation of small scale conductivity variations[ In a frame of such notion these conductivity variations should arise in a localized zone in the ionosphere over a zone of enhanced seismic activity[ A velocity of such disturbances should be considerably less than a satellite velocity[ These properties are characteristic for acoustic!gravity waves "AGW# in the lower ionosphere[ Thus the origination of the observed plasma density ~uctuations can be related to the physical processes resulting in intensi_cation of AGW above the seismic zone[ The dissipative AGW instability in the ionosphere due to Joule heating in the ionospheric currents disturbed by this wave could be considered as such a process[ One can expect\ due to dependence of conductivity variation on AGW parameters\ that the wave propagation leads to


V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

0222

conductivity modulation and appearance of additional currents induced by the ionospheric electric _eld[ Joule heating due to these currents will increase the AGW amplitude and\ hence\ the value of conductivity dis! turbance resulting in their exponential growth[

1[ The electric _eld effect on stability of acoustic! gravity waves in the ionosphere Ingard and Gentle "0854#\ Ingard "0855# and Ingard and Shulz "0856# have examined the instability of acous! tic!gravity waves in a weakly!ionized plasma[ It has been shown that the instability is developed with the condition that the electron temperature is higher than the tem! perature of neutral molecules[ The energy source for the instability is supplied by heated electrons[ Their energy is transferred to the molecules due to elastic collisions[ Similar results were obtained by Rognlien and Self "0860# for the ion!acoustic instability in a two!temperature com! pletely ionized plasma[ In these papers it was assumed that the equilibrium temperature of the neutral or ion component was stationary[ However Kaw "0858#\ Kaw and Sundaram "0861# and McBride and Chu "0861# found that due to energy transfer from more heated elec! trons the equilibrium temperature of neutral or ion com! ponent was increased[ This e}ect results in damping of the acoustic instability[ Another type of instability of acoustic!gravity waves is considered[ This type of instability is considered for isothermic weakly!ionized plasma in the external mag! netic and electric _elds by Sorokin and Chmyrev "0886#[ Strong heat interchange assumes that the electron tem! perature is equal to the temperature of ions and molecules[ Such an approach is generally applied for a model of ionosphere with stabilized thermal balance[ It is realised at the characteristic times t L M:mvei and for the spatial scale l L aM:mvei\ where m\ M are the elec! tron and ion masses and a is a sound velocity[ This balance determines the stationary temperature[ Accord! ing to Piddington "0848#\ in the low!frequency approxi! mation\ the ionosphere can be considered as a continuous medium with a tensor conductivity[ As will be shown later\ propagation of small acoustic oscillations in such a medium is accompanied by a conductivity disturbance and\ hence\ with a perturbation of the currents[ With certain conditions these disturbances have such a charac! ter that Joule heading due to the disturbed currents results in the growth of the acoustic wave amplitude[ In contrast to the results of the quoted papers\ the energy source of the instability under consideration is the elec! tromotive force of the external electric _eld[ The electric _eld energy transforms to the energy of acoustic oscil! lations without a change in the medium thermal balance[ Let us assume that the ionosphere consists of electrons and ions with densities N and of molecules with the den!

sities Nn[ Plasma is weakly ionized N:Nn Ï 0 and is placed in a given uniform magnetic B and electric E _elds[ Let m be the mass of electron and M be the mass of ion and molecule[ The mean velocity of electrons\ ions and molecules and their density\ pressure and temperature are va\ ra\ Pa\ Ta respectively "the index a may be e\ i or n#[ Analysis of stability of acoustic!gravity waves "AGW# will be performed based on the following set of equations "Hines\ 0857^ Hines and Hooke\ 0869^ Gossard and Hooke\ 0864#] rdv:dt 1r: 1t¦9"rv# rcpdT:dt p -9p¦r`¦"0:c#Ï jâBL 9 dp:dt¦" j = E# rRT "0#

and Ohm|s law for the current density j "Alfven and Falthammar\ 0852#] j s>E>¦spE_¦shÏBâE_L:B "1#

The following quantities are introduced in these equa! tions] mean!mass velocity v s rkvk: s rk
k k

characterising the motion of gas as a whole\ its density r mN¦MN¦MNn re¦¦ri¦rn\ and pressure p pe¦pi¦pn[ The temperatures of the gas components are assumed to be equal Te Ti Tn T[ In eqn "0# the following de_nitions were introduced] d:dt 1: 1t¦v9^ R cp-cv is the universal gas constant\ cp and cv are the heat capacities at constant pressure and constant volume\ ` is acceleration due to Earth|s gravity[ In eqn "1# the following notations are used^ s> is the _eld!aligned con! ductivity\ sh and sp are Hall and Pedersen conductivities\ respectively\ and E> is the magnetic _eld!aligned com! ponent of the electric _eld[ The conductivities depend on the collision frequencies "Cowling\ 0834#] s> s
p

e1N"0:mne¦0:Mnin#\
1 1 1 e1NÏne:m"ve ¦ne #¦nin:M"vi1¦nin#L\ 1 1 1 e1NÏve:m"ve ¦ne #-vi:M"vi1¦nin#L\

sh

"2#

where e is electron charge\ ve eB:mc and vi eB:Mc are the gyrofrequencies of electrons and ions\ nab are collision frequencies of particles of the sort a with those of the sort b\ ne nei¦nen[ In the ionosphere s>:sP ½ s>:sh ½093ï094\ hence\ one can assume E> 9[ Above 019 km in the ionosphere the following inequalities are satis_ed] ne Ï ve^ nin Ï vi^ mne:Mnin ½ "m:M#0:1 Ï 0[ Therefore] sp e1Nnin:vi1^ s
h

"vin:vi#sP Ï sP

"3#


0223

V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

where nin qviNn^ vi "7RT:p#0:1[

1r0: 1t¦r99v0¦v0z dr9: dz

9

1p0: 1t¦v0z dp9: dz-gRT9"1r0: 1t¦v0z dr9: dz# "g-0#DspE p
9 1

In eqn "3# q is the cross!section of ion scattering on molecules\ vi is mean thermal velocity of ions[ The depen! dence of the conductivity sP on thermodynamical quan! tities is determined by the equation] s
p

Rr9T9[

"7#

mrir"T #0:1\ m

7qc1:pMB

1

"4#

Let us consider the AGW propagation in a layered irregu! lar isothermic ionosphere in the presence of an external DC electric _eld[ We use the right hand Cartesian coor! dinate system with the z!axis directed vertically upward along the magnetic _eld B and the x!axis along the electric _eld E[ Let us consider the small perturbations of the velocity v0\ density r0\ pressure pl and temperature Tl at the background of their stationary values v9\ r9\ p9 and T9[ From eqns "0#\ "1# and "4# for the stationary state we derive] r9v9z dv9z: dz r9cpv9z dT9: dz p
9

In eqn "7# Dsp sp-sp9 is a perturbation of the iono! sphere conductivity and g cp:cy[ Using formula "4#\ the equation of state and the linear dependence between the relative variations of ion and neutral component densities ri0:ri9 a "r0:r9#\ we obtain] sp mri"Pr:R#0:1 sp9"0¦ar0:r#"0¦p0:p9#0:1"0¦r0:r9#0:1 m"T9#0:1ri9r9"z#[

sp9Ï0¦p0:1p9¦"1a¦0#r0:1r9L\ sp9 Hence] Dsp "sp9:1#p0:p9¦Ï"1a¦0#sp9:1Lr0:r9[

"8#

- dp9 dz-`r

9 0:1 1

v9z dp9:dz¦mri9r9"T9# E Rr9T9^ dr9v9z: dz 9[

"5#

The generally accepted model of stationary ionosphere applied for studying the AGW properties is the iso! thermic "T9 const# exponentially strati_ed medium "Gossard and Hooke\ 0864#] p9 ½ r9 ½ exp "-z:H#^ H RT9:`[ "6#

Ion density varies with altitude substantially slower than the atmosphere density r9 with the scale H\ therefore it could be assumed constant[ The ionosphere stationarity is provided by various processes of cooling such as ther! mal conductivity\ radiation\ convection\ etc[ which do not result in considerable e}ects on the atmosphere waves in the AGW range[ The corresponding summands could be added to the second eqn "5# of the law of energy conservation[ In eqn "5# the stationarity of temperature is provided by slow vertical mass transfer with the vel! ocity v9z[ If v9z Ï "`H#0:1 ½ 2â093 cm s-0 "` ¼ 092 cm s-1\ H ¼ 095 cm# then we obtain from the _rst eqn "5# dp9:dz -`r9[ Assuming dT9:dz 9 in the second eqn "5# and substituting the derivating value dp9:dz we shall obtain an estimate of the velocity value v9z ½ sp9E1:gr9[ Taking\ for the conducting lower ionosphere\ the values sp9 ½ 095 s-0\ E ½ 2 mV m-0 09-6 cgse\ r9 ½ 09-01 g cm-2\ we obtain v9z ½ 09 cm s-0[ Thus\ when deducing the equations for perturbations\ one can assume the iono! sphere to be at rest[ Neglecting the Hall conductivity as compared to Pedersen conductivity and saving in eqn "0# the perturbations of the _rst order of smallness\ we obtain] r9 1v0: 1t -9p0¦r0`

The coe.cient a characterises the variation of ion density relatively to variation of neutral gas density in the wave[ If a 9 the conductivity perturbation will be determined only by a variation of the collision frequency which depends on neutral gas density and temperature[ At a 0 the variation of ion density coincides with relative vari! ation of gas density as a whole[ At a â 0 the conductivity perturbation is mainly determined by ion density vari! ation[ This coe.cient enables one to estimate the e}ect of a degree of interaction between the neutral and ionized components on the wave stability[ Substituting equality "8# in the third eqn "7#\ we obtain] " 1: 1t-v1#p0¦v0z dp9: dz-a1"" 1: 1t¦v0#r
0

¦v0z dr9: dz# In eqn "09# it is de_ned that] v0 v1 "1a¦0#"g-0#sp9E1:1a1r9^ a g"g-0#sp9E1:1a1r9^ v
0 1

9

"09#

gRT9^ "00#

Ï"1a¦0#:gLv1[

Since sp9"z# ½ r9"z#\ the quantities v0\ v1 and a1 are inde! pendent of the altitude z[ The _rst two eqns "7# and "09# describe the AGW propagation in isothermic conducting ionosphere with the horizontal external electric _eld[ Taking v0 9\ we obtain the well known equations for the AGW in exponentially strati_ed atmosphere "Gos! sard and Hooke\ 0864#[ The quantity v0 has the meaning of the ratio of speci_c power released by the currents due to perturbation of the ionosphere conductivity in the electric _eld to the energy density of the acoustic wave[ It determines the characteristic time during which the energy of external DC electric _eld is transformed to the wave energy[


V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

0224

2[ Formation of the horizontal irregularities of the ionosphere conductivity Let us consider the horizontal propagation of the planar wave along the x!axis[ First of all we analyze the case when the terms with acceleration due to gravity in eqns "7# and "09# can be neglected[ Assuming ` 9 we obtain] r9 1v0x: 1t - 1p0: 1x\ 1r0: 1t¦r9 1v0x: 1x
0

1r0: 1t¦r9" 1v0x: 1x¦ 1v0z: 1z#-"r9:H#v

0z

9\
0

"1: 1t-v1#p0-" p9:H#v0z-a1"Ï"1: 1t¦v0#r

-"r9:H#v0z#

9[

"05#

Let us pass to the _eld variables through the formulas "Gossard and Hooke\ 0864#] U P r9 "r9:rs#0:1v0x\ W "r9:rs#
-0:1

9\

"r9:rs#0:1v0z\ "r9:rs#-0:1r0\ "06#

" 1: 1t-v1#p0-a1" 1: 1t¦v0#r

9[

p0\ R

Assuming the dependance on coordinates and time as exp "-ivt¦ikx# we derive the dispersion equation] k1 v1"v-iv1#:a1"v¦iv0# "01#

rs exp "-z:H#\

where rs is the density value at the level corresponding to z 9[ For the _eld variables we derive the system of uniform equations with constant coe.cients] rs 1U: 1t - 1P: 1x^ rs 1W: 1t - 1P: 1z¦P:1H-`R^ 9^ 9[ "07#

For v0 v1 9 we obtain the equation k v:a descri! bing the acoustic wave propagation in a uniform medium with the velocity a without dispersion[ Let us introduce the complex refraction index from the formula] k "n¦ik#v:a "02#

1R: 1t¦rs" 1U: 1x¦ 1W: 1z-W:1H#

" 1: 1t-v1#P-a1" 1: 1t¦v0#R¦"g-0#`rsW

where n is the refraction index and k is the absorption coe.cient[ Substituting eqn "02# into eqn "01# and sepa! rating the real and imaginary parts\ we obtain] n"v#
1 "Ï"v1¦v1#0:1"v1¦v1#0:1¦v1-v0v1L:1"v1¦v1##0:1:k"v# 0 0 1 1 -"Ï"v1¦v0#0:1"v1¦v1#0:1-v1¦v0v1L:1"v1¦v0##0:1 1

Let us consider the horizontal AGW propagation along the x!axis assuming 1: 1z 9[ Using again the coordinate and time dependence of all functions according to exp "-ivt¦ikx# we derive the dispersion equation]
1 k1a1Ïv"v¦iv0#-vg L 1 1 v1Ïv"v-iv1#-va L¦ivv1v2

"08# gg:3H is the boundary acoustic frequency\ where v 1 vg "g-0#g:gH is the BruntïVaisala frequency and 1 1 v2 va "1a¦2#:g[ Taking\ in "08#\ va vg 9\ we obtain formula "01# describing the acoustic wave dis! persion in a uniform medium[ The case of electric _eld vanishing corresponds to the transition to v0 v1 9 in "08#] k1
1 1 v1"v1-va #:a1"v1-vg # 1 a

"03# The character of n"v# and k"v# dependencies in eqn "03# practically will be not changed if we take formally v0 v1 that is satis_ed when 1a¦0 g\ see eqn "00#[ Assuming the perfect gas approximation we put g 0[3 and accordingly a 9[1[ In this case eqn "03# is simpli_ed] n"v# k"v#
1 v:"v1¦v0#0:1\ 1 -v0:"v1¦v0#0:1[

"04#

This dispersion equation is satis_ed for the AGW pro! pagating in the horizontal direction "Gossard and Hooke\ 0864#[ Using in "08# the complex refraction index "02# and separating the real and imaginary parts\ we obtain] n"v# k"v# "ÏA1"v#¦B1"v#L0:1¦A"v##0:1:V"v# -"ÏA1"v#¦B1"v#L0:1-A"v##0:1:V"v# "19#

These equations give a negative absorption coe.cient k ¨ 9 that means the instability development and exponential growth of the wave amplitude[ Since the refraction index n ¨ 0\ the phase velocity vph a:n of a wave propagating with a dispersion exceeds the acoustic velocity a[ This case gives evidence to possible instability of the AGW because the limit ` 9 describes the high! frequency range of the spectrum of these waves[ To ana! lyze the AGW instability let us write the components of eqns "7# and "09#] r9 1v0x: 1t r9 1v0z: 1t - 1p0: 1x\ - 1p0: 1z-`r0\

In eqn "19# it is de_ned that] A"v# B"v# V"v#
1 1 1 "v1-va #"v1-vg #-"v1-v2#v0v1\ 1 1 1 "v1-va #vv0¦"v1-vg #"v1-v2#v1:v\ 1 1 "1Ï"v1-vg #1¦v1v0L#0:1[

"10#

The dependencies n n"v# and k k"v# calculated from eqns "19# are presented in Fig[ 1 for the following set of


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V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

Fig[ 1[ The frequency dependence of the refractive index "n# and the absorption coe.cient "k# of acoustic!gravity wave in the ionosphere in the presence of an external electric _eld[

parameters] g 0[3^ g 092 cm s-0^ H 095 cm^ sp9 4â095 s-0^ r9 4â09-02 g cm-2^ E 2â09-6 cgse^ vg 1â09-1 s-0[ The curve 0 corresponds to the case of a 9\1 "v0:vg 0[3â09-1^ v2:vg 1[6#\ and the curve 1 corresponds to the case of a 0 "v0:vg 2â09-1^ v2:vg 2[8#[ As seen from these curves the absorption coe.cient is negative and has the maximum value at the frequencies v ½ vg[ Thus the instability and the wave growth occur in the relatively

narrow region around the BruntïVaisala frequency[ This process results in creation of the periodic structure of ionospheric perturbation[ Parallel with the variations of plasma density and pressure in the wave the oscillations of conductivity take place according to formula "8#[ The horizontal periodic structure of the ionospheric con! ductivity is formed with the scale l ½ l:1 where l is wave! length of AGW at the frequencies v ½ vg corresponding to the maximum k value[ At these frequencies the waves


V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

0226

have maximum values of refraction index n"vg# or mini! mum phase velocities vg a:n:"vg# ¨ a[ The horizontal scale of the conductivity variations is] 0 l:1 pvg:v
g

pa:v`n"v`#

"11#

where ni is the collision frequency of ions\ vex -cEy9:B is the velocity of electron drift and Ex Ex9¦DEx is the electric _eld within the band[ Substituting eqn "13# into eqn "12# we obtain the density ratio in the following form] N:N9 ""0-niEx9:viEy9#-"0¦ni1:vi1#vg:vex#: "Ï0-ni"Ex9¦DEx#:viEy9L-"0¦ni1:vi1#vg:vex# "14#

Thus the dissipative instability of AGW in the presence of an external electric _eld in the ionosphere results in excitation of plasma density variations and formation of periodic horizontal structure of conductivity with charac! teristic scale\ eqn "11#[

3[ Formation of _eld!aligned currents and plasma inhomogeneities in the upper ionosphere as a result of AGW instability in the lower ionosphere One can expect that the AGW related wave of con! ductivity in the ionosphere in the presence of an external electric _eld will excite an obliquely propagating hyd! romagnetic wave into the upper ionosphere and the mag! netosphere[ The _eld!aligned current in this wave is car! ried by electrons while the closing current is carried by ions[ It is shown below that transferring such dis! turbances from the E!layer to the upper ionosphere induces there the variations of plasma density[ According to Section 2 we consider the AGW propa! gation along the x!axis[ Therefore\ the irregularities of conductivity are stretched along the y!axis[ Let the elec! tric _eld E9 be located in the x!y plane and the magnetic _eld B directed along the z!axis[ Let us consider the simpli_ed model of formation of plasma irregularity in the upper ionosphere caused by a motion of the con! ductivity irregularity DsP\h in a form of isolated band with the width l l:1 stretched along the y!axis in the ionospheric E!layer "Lyatsky and Maltsev\ 0872#[ The horizontal velocity of the band motion along the x!axis is vg[ The wave propagation in the magnetosphere is characterized by the Alfven velocity u or by the integral wave conductivity Sw c1:3pu[ The conducting band in the ionospheric E!layer causes the appearance of pol! arization electric _eld DE which is transferred along the magnetic _eld lines to the upper ionosphere and results in a change of plasma density in this region[ Since ions can move in the electric _eld in horizontal direction\ integrating along the x!axis the stationary equation of continuity for ions on the band boundary gives] N"vi-vg# N9"vi9-vg9#\ "12#

It is seen from eqn "14# that the plasma density N is determined by the electric _eld change DE and the vel! ocity of the band motion vg[ The quantity N depends on the altitude of the layer determined by the altitudinal variation of ni:vi[ Thus\ electric _eld variations at certain altitudes in the ionosphere are accompanied by the vari! ations of plasma density[ The polarization electric _eld in the band is determined by the condition of current continuity in each of the ionospheric layers]
9 Jx-Jx

Jz\

"15#

9 where Jx\ Jx and Jz\ are the surface densities of iono! spheric and _eld!aligned currents[ The _eld!aligned cur! rent Jz is considered as positive when it ~ows up of the layer[ Equation "15# determines Jz on the frontal "when moving along the x!axis# boundary of the band[ On the back boundary the sign of Jz should be inverse[ According to the Ohm|s law the surface density of transverse iono! spheric current Jx in each layer is determined by the integral "over the layer# Pedersen "Sp# and Hall "Sh# con! ductivities]

J

x

SpEx¦ShE

y

"16#

Taking into account that the Hall conductivity in the upper ionosphere is close to zero and applying eqns "15# and "16# to the E!layer\ we obtain] SpEx-Sp9Ex9¦"Sh-Sh9#Ey SFEx-SF9Ex
9

JE z JF z "17#

9

where Sp and Sh are the integral Pedersen and Hall con! ductivities of the E!layer\ SF is the integral Pedersen conductivity of the upper ionosphere\ index 9 cor! responds to undisturbed values\ JE and JF are the _eld! z z aligned currents in the E!layer and in the upper iono! sphere[ The resulting _eld!aligned current ~owing out from the ionosphere to the magnetosphere is] Jz JE¦J z
F z

where N\ vi^ N9\ vi9 are the balanced densities and vel! ocities along the x!axis of ions inside and outside the band[ To determine the ion velocities we use the equa! tions of motion for ions and electrons "Sorokin and Fedo! rovich\ 0871#[ In quasi!static approximation "d:dt 9# when : u : L :vg :\ we obtain] vix vex"0-niEx:viEy9#:"0¦n :v #\
1 i 1 i

"18#

Let us determine the connection between Jz and the horizontal electric _eld[ Current densities and _elds in the magnetosphere satisfy the Maxwell|s equations] Ï9âbL Ï9âEL 3pj:c¦ 1E:c 1t - 1b:c 1t "29#

"13#


0227

V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

From the equations of electron and ion motion we obtain the Ohm|s law] j_ "c1MN:B1#" 1E:1t# "20#

v

ex

-cEy9:B\ v

g

a:n"vg#[

"27#

The density variation DN N-N9 as follows from eqn "26# is determined by the equation] DN:N9 "D0-D1#:"0¦D1-vg:vex#[ "28#

where MN is magnetospheric plasma density and j_ is the transverse component of current density[ When deducing the Ohm|s law\ the conditions 1: 1t Ï vi and E> 9 have been used[ The polarization electric _eld arising within the band is transferred along the magnetic _eld lines into the magnetosphere[ The polarization currents in the magnetosphere corresponding to eqn "20# is] jx "c1:3pu1# 1Ex: 1t "c1:3pu1#vg 1Ex: 1x[ "21#

In the case of a uniform band these currents arise only on the band boundaries where 1E: 1x ä 9[ To provide the coupling of the Alfven wave with AGW and related disturbances of conductivity the transverse velocity of Alfven wave should be equal to the AGW velocity] vg u tan 8\ "22#

Let the electric _eld be directed along the x!axis "Ey9 9#[ In the ionosphere the equality Sw SP9 is satis_ed with the su.cient degree of accuracy[ For example\ at the u ½ 4â096ï7â096 cm s-0 and sp9"zmax# ½ 2â094ï2â095 s-0\ we obtain Sp9 ï dzsp9"z# ½ sp9"zmax# = Dz ½ 0901ï 0902 cm s-0 for Dz ½ 2â095 cm and Sw c1:3pu ½ 0901ï 1â0901 cm s-0[ If we assume DSp:Sp9 Dsp:sp9 and nicEx9:vivgB Ï 0 then\ for estimating the value of the plasma density change\ we obtain the formula] DN:N9 "nicEx9:vivgB#"Dsp:sp9#:"1¦Dsp:sp9#[ "39#

With growing the relative conductivity disturbance Dsp:sp9 eqn "39# tends to the limiting value] DN:N9 nicEx9:vivgB nicEx9n"vg#:viaB "30#

where 8 is wave front inclination angle of the hyd! romagnetic disturbance relatively to external magnetic _eld[ The transverse and the _eld!aligned currents are determined by the equations] jx jz "c1vg:3pu1# 1Ex: 1x Jx tan 8 Sw"vg:u# 1Ex: 1x[ "23#

When a satellite moving with the velocity vs crosses the plasma irregularities of the scale l "see Fig[ 2#\ plasma density ~uctuations are registered with the period] Dt 0:vs pa:vsvgn"vg# "31#

Sw 1Ex: 1x\

where Sw c1:3pu is the magnetospheric integral con! ductivity for the Alfven wave[ Integrating the expression for current jz over the thickness of the layer boundary and introducing the surface density of _eld!aligned cur! rents Jz\ we obtain] Jz Sw"Ex9-Ex# "24#

Equations "17# and "24# result in the equation for the electric _eld within the band] Ex ÏSF9Ey9:"Sp¦Sw#L"Ï0¦"Sp9¦Sw#:SF9LEx9:E
y9

¦"Sh-Sh9#:SF9#[

"25#

When deducing eqn "25#\ we used the fact that the con! ductivity of the upper ionosphere is much less than the E!layer conductivity ÏSF Ï "Sp¦Sw#L[ Equations "14# and "25# make it possible to derive a change of plasma density in the upper ionosphere above the band of increased conductivity in the E!layer] N:N9 where] D0 D1 niEx9:viEy9\ "ni:vi#Ï"Sp9¦Sw#Ex9:"Sp¦Sw#E
y9

"0¦D0-vg:vex#:"0¦D1-vg:Vex#\

"26#

¦"Sh-Sh9#:"Sp¦Sw#L\

Equations "30# and "31# enable us to estimate the mag! nitude and the characteristic period of plasma density variations due to disturbances of conductivity in the iono! spheric E!layer that should be observed onboard the sat! ellite in the upper ionosphere[ These values depend on the altitude as ni ni"z#[ Thus\ the excitation of horizontal spatial structure of the ionosphere conductivity results in forming the plasma layers stretched along the geo! magnetic _eld[ The argument for formation of the _eld!aligned cur! rents in the ionosphere resulting in formation of plasma irregularity can be found in the satellite data presented by Chmyrev et al[ "0878#[ Figure 3 from this paper shows the variations of two horizontal magnetic _eld com! ponents Bx and By in the frequency range 9[0ï7 Hz along with the vertical component of quasistatic electric _eld Ez which were observed onboard the {Intercosmos!Bulgaria 0299| satellite within the 04 min interval before the earth! quake occurred on 01 January 0871 at 06[49[15 UT[ The quasistatic electric _eld 2ï6 mV m-0 was observed in two zones] above the focus and in the magnetically conjugated region[ The size of the zones was 0ï0[4> in latitude[ The amplitude of geomagnetic pulsations at the frequency about 0 Hz observed in these regions was ½ 2 nT[ According to the physical model presented above a growth of the electric _eld in the ionosphere observed above the zone of developing earthquake leads to the AGW dissipative instability[ As a result the horizontal irregularities of the ionospheric conductivity are formed


V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

0228

Fig[ 2[ The scheme of satellite observations of plasma density inhomogeneities and ULF magnetic _eld oscillations] 0[ Earthquake zone^ 1[ Lower ionosphere^ 2[ Horizontal inhomogenities of ionospheric conductivity] 3[ Field!aligned electric currents^ 4[ Field!aligned plasma density inhomogenities^ 5[ Satellite[

and the _eld!aligned currents arise[ The satellite moving through the periodic current sheets will observe the related magnetic _eld oscillations with the period Dt l:vs and the amplitude] b "1p:c#J
z

4[ Conclusion In the ionosphere with magnetic and electric _elds the dissipative instability of acoustic!gravity waves can arise[ In case " 1sp: 1r# â 9 the plasma density variations in the wave result in growth of the conductivity disturbances and the Joule heating connected with the disturbed currents[ The instability increment is proportional to the square of external electric _eld and to the value of deriva! tive " 1sp: 1r#[ The dissipative instability leads to growth of waves with the frequencies of the order of Bruntï Vaisala frequency[ As a result the conductivity irregu! larities with the horizontal spatial scale l determined by eqn "11# are excited in the lower ionosphere[ The wave related irregularities of conductivity change the ionospheric electric _elds[ High conductivity along magnetic _eld lines results in the electric _eld propagation to the upper ionosphere and the magnetosphere[ The _elds are transferred by the _eld!aligned currents which are closed by the transverse currents in the ionosphere due to Pedersen conductivity[ Since the _eld!aligned cur!

"32#

where Jz is the surface density of the _eld!aligned current sheet[ Substituting eqns "24# and "25# into eqn "32#\ we obtain] b "1p:c#ExSw"DSp:ÏSp9¦Sw¦DSpL# "33#

In eqn "33# it is assumed Ey 9[ Taking Sw Sp9\ DSp:Sp9 Dsp:sp9\ we obtain from eqn "33# the formula for estimating the amplitude of geomagnetic pulsations] b "p:c#ExSp9ÏDsp:"1sp9¦Dsp#L "34#

Thus\ the satellite passing through the considered struc! ture of _eld!aligned currents will observe the plasma den! sity ~uctuations\ eqn "30# and the ULF!oscillations of the geomagnetic _eld\ eqn "34# with the characteristic period eqn "31#[


0239

V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

Fig[ 3[ An example of DC electric _eld "vertical component# and ULF magnetic _eld "horizontal components# observations over the earthquake zone and in the magnetically conjugate region ½ 04 minutes before an earthquake[

rents are carried by electrons\ while the transverse cur! rents are carried by ions\ the upward propagation of the transverse electric _eld is followed by the local variations of plasma density[ This means that the excitation of hori! zontal spatial structure of conductivity in the lower iono! sphere results in the formation of plasma layers stretched

along the geomagnetic _eld[ Transverse spatial scale of the layers coincides with the scale of conductivity irregu! larities[ When a satellite crosses the _eld!aligned currents and related _eld!aligned plasma inhomogeneities the oscillations of plasma density and ULF!oscillations of geomagnetic _eld are registered with amplitude whose


V[M[ Sorokin et al[:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0220ï0231

0230

order of value is determined by eqns "30# and "34#[ The oscillation period Dt is determined by eqn "31#[ Let us estimate these quantities[ At the altitude of the order of 0999 km the total number of ions collisions is ni ni"n¦i# ½ 9[4 s-0 "Schunk and Nagy\ 0879# and the ion gyrofrequency vi ½ 29 s-0[ Let us assume a 2â093 cm s-0^ E 8 mV m-0 2â09-6 cgse^ B 2â093 nT 9[2 cgsm^ refractive index n 0ï09\ from eqn "30# we obtain] DN:N9 ¼ nicnE:viaB Assuming S
P9

"0[5ï05#)[
01 -0

"35#

1â09 cm s 4nT[

in eqn "34# we obtain]

b ¼ "p:c#ESP9

Equation "31# gives the estimate for the oscillation period Dt at vg 1â09-1 s-0 and vs ½ 095 cm s-0] Dt ¼ pa:vsvgn"vg# "9[2ï2#s[

These values in their order of magnitude are in agreement with the satellite data presented in Figs[ 0 and 3[ These values correspond to seismic related ionospheric dis! turbances observed onboard the COSMOS!0798 satellite over the zone of Spitak earthquake "Chmyrev et al[\ 0886#[ We believe that the mechanism of dissipative insta! bility of acoustic!gravity waves in the ionosphere developed in this paper can be used as a basis for the theory of electromagnetic and plasma response of the ionosphere to the earthquake preparation processes[

Acknowledgements This work was partly supported by NASA through NASA!RSA contract NAS04ï09009 and by RFFI under contracts 85ï94ï54293 and 86ï94ï53248[

References
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0231

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