On the modification of light ion concentration profiles above seismically active regions : a qualitative consideration

\ PERGAMON

Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0914Ð0922

On the modi_cation of light ion concentration pro_les above seismically active regions ] a qualitative consideration D[ R[ Shklyara\\ V[ Truhl(kb b

a IZMIRAN\ Troitsk\ Moscow Re`ion\ 031981\ Russia Institute of Atmospheric Physics\ Acad[ Sci[ Czech Republic\ Boc³n( II\ 030 20 Pra`ue 3\ Czech Republic

Received 0 April 0886 ^ revised form 10 November 0886 ^ accepted 16 February 0887

Abstract A simpli_ed model of di}usive equilibrium is used to reveal the parameters of the light ion distribution in the topside ionosphere which are most sensitive to any kind of perturbations[ The role of particle drift\ caused by a localized\ quasi! static electric _eld\ modifying the concentration pro_les is investigated[ Other factors a}ecting the ion distribution in the upper ionosphere are also mentioned[ The relation of the results to the problem of earthquake predictions is discussed[ Þ 0887 Elsevier Science Ltd[ All rights reserved[

0[ Introduction and statement of the problem In recent decades\ the problem of earthquake pre! diction from its geophysical precursors has been in the focus of many studies[ Geophysical phenomena like the anomalous increase in the critical frequency f9F1 "Sobolev and Husamiddinov\ 0874#\ the peculiarities in the spectrum of ELF and VLF emissions observed on satellites over seismic regions "see\ for instance\ Larkina et al[\ 0873\ 0878 ^ Parrot and Lefeuvre\ 0874 ^ Ser! ebryakova et al[\ 0881# have been considered as possible precursors of an earthquake[ Some e}ects in the E region of the ionosphere before the earthquake have been con! sidered by Kim and Khegay "0874# and Kim et al[ "0883#[ A number of recent papers on earthquake electro! magnetic e}ects\ together with the literature on this subject\ can be found in a Special Issue of the Journal of Atmospheric Electricity "0885#[ The problem of longitudinal variations in the lati! tudinal distribution of light ions observed on a satellite over a seismically active region has been raised by Bos³kova et al[ "0882#[ The experimental data presented in that paper give the latitudinal distribution of light ions H¦ and He¦ along the Intercosmos 13 satellite orbit at heights from about 1999 to 1499 km[ Since the variation of longitude along a given orbit is small the variations in

 Corresponding author[ E!mail ] davidÝizmiran[rssi[ru

the latitudinal distribution of light ion concentration from one orbit to another re~ect the longitudinal "and:or time# variations of the pro_les[ The following results have been obtained ] "0# An increase in the light ion concentration over a narrow latitudinal region above the focus of the forthcoming earthquake\ or somewhat to the North of it[ "1# A general increase in the light ion density in the relevant latitudinal region as a whole\ at longitudes close to the future epicentre\ as compared to curves related to other longitudes[ "2# A decrease in the light ion density over a seismically inactive zone in cases when the neighbouring longi! tude region was in the preparatory stage for an earth! quake[ We believe that the signi_cance of the paper by Bos³kova et al[ "0882# consists of presenting original experimental results and discussing new possible physical signs of earthquakes\ although their statistical reliability and physical explanation have not been discussed[ However\ the possible role of the electric _eld of seismic origin\ and related particle drift in the ionosphere\ was pointed out[ In relation to the experimental results mentioned above\ in the present paper we\ in the main\ investigate the role of one factor\ the quasi!static transverse electric _eld\ which can modify the light ion concentration pro_les[ Such _elds have been observed over seismic regions some

S0253Ð5715:87 ,*see front matter Þ 0887 Elsevier Science Ltd[ All rights reserved PII ] S 0 2 5 3 Ð 5 7 1 5 " 8 7 # 9 9 9 3 0 Ð 7

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D[R[ Shklyar\ V[ Truhl(k:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0914Ð0922

time before the earthquakes "Chmyrev et al[\ 0878#[ Model calculations of the electric _eld penetration into the ionosphere have been performed by Kim et al[ "0883#[

dn0 M0 `>−eo> − n0 ^ dS T

"0#

M1 `>−eo> dn1 − n1\ dS T 1[ Some qualitative features of light ion distribution in upper ionosphere The thermal plasma distribution in the Earth|s iono! sphere is determined by many di}erent physical and chemical processes[ This distribution is nonstationary and depends on many factors\ in particular\ season\ time\ place\ solar activity\ etc[ All sophisticated mathematical models of thermal plasma distribution are numerical ones\ since\ accounting for the main physical and chemi! cal processes\ the distribution of plasma is described by a complicated set of nonlinear equations "see\ for instance\ Bailey and Sellek\ 0889\ and references therein#[ In the frame of such elaborate models\ it is rather di.cult to investigate the in~uence of particular factors on the dis! tribution of di}erent plasma components[ For this pur! pose simpler models are usually used\ which lead to a qualitative understanding of the role of di}erent factors[ In this paper we consider a simpli_ed model which per! mits us to understand some important qualitative fea! tures of the topside light ion distribution along the geo! magnetic _eld line[ We consider a plasma consisting of electrons and two kinds of ions with masses M0 and M1\ respectively\ assuming that M0 ³ M1[ In the following\ the quantities related to electrons\ light ions and heavy ions are indi! cated by the indices {e|\ {0| and {1|\ respectively[ We denote by S the length along the _eld line on which the plasma distribution is calculated[ The equations of di}usive equi! librium represent the balance of the sum equal to zero of longitudinal "along the ambient geomagnetic _eld# components of all forces\ namely due to the pressure\ gravity and polarization electric _eld acting upon a given plasma component in a volume element "e[g[ Angerami and Thomas\ 0853#[ As is well known\ a small longi! tudinal electric _eld\ called the polarization _eld\ inevi! tably appears due to di}erent mobility of {fast| electrons and {slow| ions[ This _eld balances the di}erence in the gravity of electrons and ions and keeps the plasma dis! tribution quasi!neutral "see below#[ In fact\ one can neg! lect the gravity force acting on electrons "in comparison with the pressure and electric force#[ Keeping in mind that a partial pressure of plasma components is equal to pa  naT "where na is the concentration of plasma species\ the index a taking the values {e|\ {0| and {1|#\ and putting the temperature T constant and equal for all plasma species\ we have an initial set of equations in the form ] dne eo>  − ne ^ dS T

where o> is the longitudinal component of the polarization electric _eld\ and `> is the longitudinal component of the sum of gravitational and centrifugal accelerations[ This set of three equations for four quantities ne\ n0\ n1 and o>\ is usually completed by the quasi!neutrality condition ne  n0¦n1[ This is nothing but an approximate solution of the Poisson equation for the conditions when the Debye radius is much less than a characteristic scale of the electric _eld variation[ We transform eqn "0# to dimensionless variables choos! ing as the units of length\ electric _eld and density the quantities T:M1 `>\ M1 `>:e\ and ne"9#\ respectively\ where ne"9# is the electron density at some initial level at which we put the coordinate S equal to zero[ Introducing dimen! sionless variables s  M1 `>S:T ^ E  eo>:M1 `> ^

"1#

na  na:ne"9# ^ m0  M0:M1 we rewrite the set of eqn"0# in the form ] dne  −Ene ^ ds dn0  −"m0−E#n0 ^ ds

"2#

dn1  −"0−E#n1[ ds In numerical calculations we put m0  0:05\ assuming O¦ and H¦ as heavy and light ions\ respectively[ The requirement that the neutrality condition is ful_lled along the coordinate s leads to the relation E

m0n0¦n1 ne¦n0¦n1

"3#

which determines the polarization electric _eld through the concentrations of the di}erent plasma components[ Putting this _eld into eqn "2#\ we obtain a closed set of three equations for three quantities ne\ n0\ and n1\ the solution of which is determined by the values of the concentration of all plasma components at the initial level[ We should underline that it automatically gives the value of the polarization _eld at this level\ and that\ in general\ the polarization electric _eld is always positive in the region where di}usive equilibrium with quasi!neu! trality holds[ Since due to the normalization ne"9# is always equal to 0\ and ne"9#  n0"9#¦n1"9#\ the quantity n0"9# appears to be the only parameter of the plasma distribution in this model[ Obviously to have the ion

D[R[ Shklyar\ V[ Truhl(k:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0914Ð0922

distribution in dimensional variables\ the dimensionless quantities should be multiplied by the dimensional elec! tron concentration at the base level[ We will return to this point later on\ and now we discuss general features of the set of eqn "2#[ If the base concentration of all ions and electrons increases "decreases# by some factor\ and the temperature pro_les remain unchanged\ the electron and ion con! centration at any point will increase "decrease# by the same factor[ Thus\ the shape of the concentration pro_les is determined only by relative concentrations at the base level\ while the absolute concentrations determine only the scale[ It should be stressed that\ at the base level\ as well as along the whole pro_le\ the quasi!neutrality condition ne  Sni is ful_lled[ From "2#\ "3# we easily _nd the following relations for the polarization electric _eld E ] 0 n0"0−m0# dE n0n1 E − ^ "0−m0#1\ − 1 1ne ds 1ne1

"4#

which shows that E monotonically decreases from its initial value "which is always less than 0:1# to the asymp! totic value m0:1 corresponding to n1 ¹ 9 and n0 ¹ ne[ Since m0:1 ³ E ³ 0:1\ the concentrations of electrons and heavy ions always decrease with increasing s\ while the pro_le of light ions may have a characteristic maximum[ Rewriting the equation for n0 in the form

0

1

0 dn0 "0−m0# 0−1m0 n0 −  n0 ds 1 0−m0 ne

"5#

0916

we notice that the light ion concentration increases for n0:ne values in the interval "9\ 03:04# and decreases in the interval "03:04\ 0#\ where m0  0:05 has been used[ Thus\ if the initial value of n0"9# is less than 03:04\ the light ion concentration pro_le has a characteristic maximum at some point s × 9\ while for n0"9# × 03:04 the maximum is at s  9[ "We remind the reader that we consider the pro_les only for s × 9\ taking the base values of con! centrations at s  9[ In fact\ for n0"9# × 03:04\ a maximum in the light ion concentration formally lies at s ³ 9[# We should stress that the heavy ion concentration drops faster than that for light ions "which can even increase#[ Thus\ for n0"9# ³ n1"9#\ there always exists a transition point\ str\ at which n0"str#  n1"str# and after which n0"s# × n1"s#[ This consideration shows that\ apart from the scaling similarity mentioned above\ the set of eqn "2# has another important property as follows[ Imagine that we want to determine the pro_les cor! responding to certain base values ne9\ n09\ n19  ne9−n09 at s  9[ As was mentioned above\ for this aim it is necessary to solve the set of eqn "2# in the interval 9 ³ s ³  with the boundary value n0"9#  n09:ne9 "and\ correspondingly\ ne"9#  0 n1"9#  0−n0"9## and then multiply the pro_les by ne9[ Instead\ one can always use another _xed pro_le corresponding to su.ciently small value of n0"9#\ _nd the point si where n0"si #:n1"si #  n09:n19 "which always exists according to the consideration above# and choose the point si as a new base level[ Then the required pro_les are obtained by a simple scaling of the _xed pro_les\ namely by multiplication of all concentrations by

Fig[ 0[ Typical plasma concentration pro_les of di}erent plasma components and the polarization electric _eld in the upper ionosphere in the model[ According to traditional way of drawing such pro_les\ the dimensionless length along the _eld line of the ambient magnetic _eld is put along the y axis\ while the concentrations and the polarization electric _eld are along the x axis[

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Fig[ 1[ Absolute "a#\ and relative "b#\ numbers of light ions for the pro_le as functions of the base concentration of light ions n0"9#[ N0 and Ne are the integrals over s of n0"s# and ne"s#\ respectively[

n09:n0"si# and by shifting the point si to the base level s  9[ The concentration pro_les for the three plasma com! ponents and the polarization electric _eld obtained from the numerical solution of eqn "2# for n0"9#  9[90 are displayed in Fig[ 0 as functions of the dimensionless length along the _eld line[ As we have seen above\ due to the scaling and shifting the base level\ Fig[ 0 represents typical concentration pro_les in the considered model[ We proceed by discussing the peculiarities of the light ion distribution assuming that s  9 at the base level and ne"9#  0[ Figure 1"a# shows the total light ion number\ that is the integral of n0 over s\ and Fig[ 1"b# shows the

ratio of the total light ion number to the total electron number for the pro_le\ as functions of the base light ion concentration n0"9#[ We see that there is a one to one correspondence between n0"9# and "N0:Ne#\ and that a very sharp increase of "N0:Ne# at small n0"9# is changed to a very slow increase of "N0:Ne# for the rest of the curve[ Since during a perturbation the quantity "N0:Ne# is expected to be more conservative than n0"9#\ the former is used as the independent variable in further curves[ Figure 2"a#\ "b# show the maximum concentration n0max and the coordinate smaxn0 of the concentration maximum of light ions as the functions of "N0:Ne#[ From Fig[ 2 we

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Fig[ 2[ Maximum concentration "a#\ and the coordinate smaxn0 if concentration maximum "b#\ in the light ion distribution as a function of their relative total number for the pro_le[

can see that\ for "N0:Ne# close to 0\ the quantities n0max and smaxn0 are very sensitive to variations of "N0:Ne#[ Before proceeding to the analysis of the response of such concentration pro_les to perturbations\ the fol! lowing remark is in order[ Equation "2# determines con! centration of plasma species as a function of length s along a given _eld line[ On that _eld line\ the length s can be expressed as a function of the height h from the Earth[ In this sense we can speak about the concentration pro! _les as functions of height[ But\ even a circularly orbiting satellite will not measure constant concentrations\ since it crosses di}erent _eld lines along its orbit[ However\ in

unperturbed conditions\ the latitudinal density dis! tribution for nearby longitudes could be expected to show only little di}erences[ That is why strong longitudinal variations in the latitudinal ion distribution\ if they could be related to some processes in seismically active regions\ are of the utmost interest[ In analyzing the reaction of concentration pro_les to perturbations\ we should keep in mind the following fea! tures of the plasma distribution\ which are revealed in the frame of this simple model[ If we determine an e}ec! tive length se} as the length containing\ say\ 88) of the total number of light ions\ this quantity appears to be

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practically independent of n0"9# "or N0:Ne# and close to 049 "in dimensionless units#[ This means that the majority of light ions is concentrated in the region where the heavy ion concentration is practically zero\ and the electrons and light ions are distributed according to an exponential law\ with the index of the exponent being equal to m0:1[ At the same time\ the most sensitive region of the pro_les containing the light ion maximum and the transition point is situated at s less than\ or about\ 09[ Thus\ while interpreting satellite data\ we should be very cautious in distinguishing between real changes in the pro_les and variations of the observation height and\ thus\ the length s[ In general\ there could be two di}erent kinds of per! turbations a}ecting the concentration pro_les of di}erent plasma species ] those which change and those which do not change the total number of particles of each plasma species in the pro_les[ In the second case\ all observable changes in ion concentration can be attributed to the variation of the height of the base level[ The perturbations of such kind can be produced by ponderomotive forces[ The perturbations of other kinds change the total number of particles in the pro_les[ However\ both kinds of per! turbations could be considered in a similar way if we _x the base level of the pro_les and permit variations of the total number of particles of each plasma species[ The variations of the total number of particles in a pro_le may be connected\ for instance\ with light gas injection from the earthquake focus\ alteration of the ionization balance\ or with a plasma drift across the magnetic _eld tubes due to a transverse electric _eld[ The last possibility is discussed in detail in the next Section[

2[ Variation of plasma tube contents due to electric _eld As has been shown above\ of all plasma components\ the light ion concentration pro_les are most sensitive to perturbations of the relative number of di}erent plasma species[ For instance\ if the total number of particles on di}erent magnetic tubes depends on longitude\ then both the concentration pro_les along the _eld line and the latitudinal pro_les along a satellite orbit may show strong variations with longitude[ In this Section\ we investigate E×B9 drift as a possible cause of plasma density per! turbations[ In a stationary state which assumes\ in particular\ the absence of the particle drift\ the concentration of di}erent plasma species along the geomagnetic _eld line is deter! mined by the partial balance of the pressure\ gravity and the longitudinal "along the ambient geomagnetic _eld# polarization electric _eld forces[ The corresponding relation is nothing but the equation for the _rst moment of the distribution function[ In this case\ the continuity equation gives no new information\ since it reduces to the condition of zero average velocity\ assuming also the

absence of any ~ux[ On the other hand\ the continuity equation is important for the description of a non! stationary process of the modi_cation of the electron and ion distributions[ Since thermal plasma is strongly magnetized\ the cur! vature of the ambient geomagnetic _eld may play a sig! ni_cant role[ However\ for the sake of simplicity\ in the present consideration we neglect the curvature of B9[ We choose an orthogonal Cartesian coordinate system with the z!axis along the ambient magnetic _eld\ so that the "x\ z#!plane coincides with the meridional plane[ The continuity equation for each particle species has the form ] 1na 1 "n V #  9\ ¦ 1t 1xk a ak

"6#

where na is the a type particle density "a  e for electrons\ a  i for ions#\ Vak is the average velocity component for the particles of the type a determined by

g

Vak  vk fa"t\r\v#dv\

"7#

fa"t\r\v# is the distribution function of the particles of the type a\ and it is assumed that the summation is made over the index k\ so that xk takes the values x\y\z[ The continuity eqn "6# is obtained by integrating the kinetic equations over all velocities\ the collision integral St" fa# giving zero contribution since the collisions do not change the number of particles[ It should be stressed that\ although the form of the continuity equation dos not depend on the collision integral\ the distribution function itself and\ thus\ the average velocity Vak "7# entering "6# is essentially determined by the collisions[ Now\ let us consider the following model problem[ Let a stationary distribution of plasma particles in the ionosphere be perturbed by an electric _eld arising from the region of the forthcoming earthquake[ We describe ł U[ While this _eld by the potential U\ so that E  −9 analysing the plasma motion under the in~uence of the _eld E we can neglect its longitudinal component\ which is rapidly removed by a small shift of charges along the magnetic _eld ^ thus we can suppose that U  U"x\y#[ We should underline that the last statement concerns only the _eld connected with the earthquake which is assumed to be much larger than the polarization electric _eld[ Needless to say\ the latter remains also in perturbed con! ditions[ In a collisionless plasma\ the transverse electric _eld ł _U leads to the drift of all plasma components E_  −9 with the velocity Vd  c

ðE×B9Ł B91

\

cgs units\ or\ in component form

"8#

D[R[ Shklyar\ V[ Truhl(k:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 0914Ð0922

Vdx  −

c 1U c 1U \ Vdy  B9 1y B9 1x

"09#

Putting "09# into "6# we obtain the continuity equation in the form 1na 1na 1na ¦Vdx ¦Vdy  9\ 1t 1x 1y

"00#

where Vdx\Vdy are determined in "09#[ The terms con! taining the derivatives of the drift velocity over the coor! dinates are cancelled because of the relations "09#[ Equa! tion "00# is similar to the one!dimensional kinetic equation in which the role of conjugate variables is played by the coordinates x\y\ the role of the Hamiltonian from which the equations of motion can be derived is played by the function −cU:B9\ and the role of the phase volume\ which is conserved along the particle phase tra! jectory\ is played by the volume in the plane "x\y#[ Due to the similarity mentioned above\ we can write a general solution of eqn "00# based on Liouville|s theorem n"t\x\y#  n9ðx9"t\x\y#\ y9"t\x\y#Ł\

"01#

where n9"x\y# is the initial density\ that is n"t  9\x\y#\ and x9"t\x\y#\ y9"t\x\y# are initial coordinates expressed as functions of current coordinates and time from the equations of motion dx  Vdx ^ dt

b

b

dy  Vdy [ dt

"02#

Proceeding to the solution of the model problem\ we place the origin of the coordinate system at some base height in the plasma on the _eld line crossing the focus of the forthcoming earthquake[ Obviously\ in such a case the electric _eld\ as well as the drift velocities\ will be localized in some region of the "x\y#!plane[ One should remember that\ in the chosen simpli_ed geometry\ the coordinate y corresponds to the azimuthal coordinate[ Let us suppose that the initial density n9 does not depend on y\ i[e[ n9  n9"x#\ and in the restricted region under consideration the density n9"x# is\ for example\ a mon! otonically decreasing function "which it is natural to assume if the positive direction of x corresponds to the increase of the radial distance from the Earth#[ Let there be a dominant direction of the x!drift in the region of the forthcoming earthquake[ Evidently\ this direction depends on the sign of the y!component of the electric _eld\ V ÞdxEy\ where the bar denotes the average value[ Using "01#\ "02# we obtain n"t\x\y#  n9ðx−V Þdx"t\x\y#tŁ[

"03#

It follows from "03# that\ in the region where a dominant direction of the drift exists\ the particle density varies according to

1n ÞdxtŁV Þdx\ ¹ −n?9ðx−V 1t

0920

"04#

where n?9 is the derivative of the initial density over the coordinate x ] n?9  dn9:dx[ We see that the character of the density variation with time is determined by the sign of V ł dx × 9[ Since according to ÞdxEy[ Let\ for instance\ V our assumption n?9 ³ 9\ it follows from "04# that the par! ticle density increases over part of the region of localised electric _eld[ As will be seen from the example given below\ the particle density slightly decreases in the region adjacent to that of the electric _eld localization[ In the case of V ÞdxEy ³ 9 and n?9 ³ 9\ the situation is inverse\ i[e[\ the particle density decreases in the region of the _eld localization and increases in the adjacent region[ We must consider whether assumptions about the _eld localization\ its potential character\ and the existence of the dominant drift direction are consistent[ To show this\ and to understand some peculiarities of the particle den! sity redistribution\ we consider a particular example[ The following expression is just a possible model satisfying the requirements formulated above ^ it by no means pre! tends to describe the real electric _eld above the region of future earthquake[ Let the quantity cU:B9\ which is proportional to the electric _eld potential\ be of the form ] cU 1 1  A = tanh "by# = e−d"x ¦y #\ "za u b#[ B9

"05#

The corresponding equations of the motion are "cf "02#\ "09## ]

$

%

dx b 1 1  −A −1ay = tanh "by# e−d"x ¦y #\ 1 dt ch "by# dy 1 1  −1Aax tanh "by# = e−a"x ¦y #[ dt

"06#

We see that for small y in the region of the _eld local! ization the sign of dx:dt is opposite to the sign of A for all values of x and y[ Plasma drift trajectories in the "x\y#! plane\ which correspond to the lines U"x\y#  constant are shown in Fig[ 3[ In the dashed part of the region\ the sign of the quantity dx:dt is opposite to that in the remaining part[ From the conservation of the total num! ber of particles "which is always valid# and the con! servation of the phase space volume "which takes place only in the absence of collisions#\ it follows that\ in a relatively small region close to the _eld maximum\ sig! ni_cant plasma density variation takes place at the expense of a small density variation of the opposite sign in the adjacent region[ 3[ Modi_cation of thermal plasma distribution in the topside ionosphere The results given above suggest a possible mechanism for the modi_cation of thermal plasma concentration

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Fig[ 3[ Plasma drift trajectories in the "x\y#!plane[ In the calculations\ the following values of parameters have been used ] A  099\ a  2\ b  0[ The value of the quantity cU"x\y#:B9 corresponding to each trajectory is shown in the gap in each line[

pro_les over a seismically active region[ Let us suppose that\ in the process of earthquake preparation\ a large scale quasi!static electric _eld arises from the seismic region[ The transverse component of this _eld penetrates ionospheric heights and gives rise to the drift of all plasma species across the geomagnetic _eld[ This process is non! stationary\ and takes place during a limited time[ Due to this transverse drift\ plasma redistribution takes place in some region over a forthcoming earthquake[ As a result\ both the total and relative number of electrons and ions change in this region[ Under quite general assumptions about the plasma radial distribution in the ionosphere and the character of the electric _eld\ the plasma drift leads to a signi_cant variation of the base concentration and the total number of electrons and ions on some magnetic tube connected to the seismic region ^ the vari! ation of plasma parameters in the adjacent region is smal! ler and of the opposite sign[ As has been shown above\ the most crucial changes take place in the light ion dis! tribution at heights close to the transition point where the concentrations of light and heavy ions are of the same order[ Thus\ when crossing a seismically active region\ a satellite may measure a latitudinal pro_le of the light ion distribution which signi_cantly di}ers from the cor!

responding pro_les at other longitudes beyond the region of the earthquake preparation[ We should underline that the transversal electric _eld and related particle drift constitute only one possible mechanism for the modi_cation of plasma distribution\ in particular\ of the light ion pro_le[ The important point is the variation of the number of particles above some level or\ which is the same\ the variation of the base concentration of the plasma components[ Such variations could take place under the in~uence of factors connected with the earthquake preparation\ but di}erent from par! ticle drift[ Here we mention another possible scenario\ following the model of lithosphere!ionosphere inter! action that has been put forward by Martynenko et al[ "0885# for the explanation of anomalous changes in VLF signal characteristics[ We believe that the same processes may play a part in the problem studied in the present paper[ According to that model\ radioactive releases during the time preceding the earthquake increase the atmo! spheric conductivity[ This changes the current ~owing between the ionosphere and the Earth and\ thus\ the electric _eld at the lower boundary of the ionosphere[ Since the e}ective collision frequency ve} depends on the

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magnitude of the electric _eld E \ the variation of E changes ve}\ which in turn changes the ionization balance and\ thus\ plasma parameters in the lower ionosphere[ We may then speculate that these perturbations {propa! gate| upwards through the ionosphere\ and slightly change the total number of charged particles along a plasma tube[ As we have shown above\ this can sig! ni_cantly change the plasma concentration pro_les\ especially of light ions in the region near the transition point[

4[ Summary and conclusions The aim of the present paper is to continue discussions of the possible relation between seismic activity preceding earthquakes and ion concentration pro_les in the outer ionosphere\ started by Bos³kova et al[ "0882#[ Basing on a simpli_ed model of di}usive equilibrium\ we have underlined the sensitivity of the light ion pro_les\ especially near the transition point\ to small variations of plasma parameters[ We have investigated the role of a quasi!static transverse electric _eld in modifying the plasma density distribution[ Such _elds have been observed experimentally by Chmyrev et al[ "0878#\ though the origin of such _elds is not yet clear[ We have also pointed out another possible mechanism for mod! ifying the ion concentration pro_les connected with radioactive releases preceding earthquakes[

Acknowledgements One of the authors "D[R[S[# wishes to acknowledge many useful and stimulating discussions with Dr V[ M[ Chmyrev[ This work was partly supported by NASA through NASA!RSA contract NAS04Ð09009[

References Angerami\ J[J[\ Thomas\ J[O[\ 0853[ Studies of planetary atmo! sphere\ 0[ The distribution of electrons and ions in the Earth|s exosphere[ Journal of Geophysical Research 58\ 3426Ð3459[ Bailey\ G[J[\ Sellek\ R[\ 0889[ A mathematical model of the

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