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Planetary and Space Science 48 (2000) 175±180

The formation of ionosphere±magnetosphere ducts over the seismic zone
V.M. Sorokin a,*, V.M. Chmyrev a, M. Hayakawa
a

b

Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, Russian Academy of Sciences, IZMIRAN, Troitsk, Moscow Region, 142092, Russia b The University of Electro-Communications, Department of Electronic Engineering, 1-5-1 Chofugaoka, Chofu, Tokyo, 182, Japan Received 13 May 1999; received in revised form 18 November 1999; accepted 22 November 1999

Abstract A physical mechanism of whistler duct formation due to electric ®eld growth in the ionosphere above the seismic zone is considered. The ducts are plasma irregularities, stretched along geomagnetic ®eld, with the transverse spatial scale of the order of 10 km and with the relative plasma density variation over the background value of the order of 10%. It is shown that such structures are formed by the ®eld-aligned currents as a result of the interaction between the ionospheric electric ®eld and the horizontal irregularities of the ionospheric conductivity. The conductivity irregularities are excited by the instability of acousticgravity waves (AGW), developed in the ionosphere when the electric ®eld exceeds a certain critical value. Since the ionosphere conductivity disturbances depend on the AGW parameters, the wave amplitude growth results in modulating the conductivity and forming the additional currents due to the ionospheric electric ®eld. The Joule heat released by these currents ampli®es the AGW amplitude and, hence, the magnitude of the conductivity variations, which resulted in a growth of the oscillations and in the exponential growth of the disturbances, associated with the acoustic-gravity wave. # 2000 Published by Elsevier Science Ltd. All rights reserved.

1. Introduction Numerous observations of anomalous characteristics of ELF/VLF emissions on the ground and in the ionosphere over the seismic zones demonstrate that the processes of preparation and development of earthquakes in¯uence the state of the electromagnetic ®eld and plasma in the ionosphere and the magnetosphere (Chmyrev et al., 1997; Gokhberg et al., 1982; Hayakawa et al., 1993; Larkina et al., 1988; Molchanov et al., 1993; Oike and Ogawa, 1982; Parrot, 1994; Serebryakova et al., 1992; Tate and Daily, 1989). Mechanisms of the disturbance transfer from the earthquake focus to the ionosphere were discussed in a series of publications (Chmyrev et al., 1999; Molchanov and Hayakawa, 1996; Pulinets et al., 1994; Sorokin et al.,
* Corresponding author.

1997, 1998; Sorokin and Chmyrev, 1999a, b) but a consistent model for a comprehensive description of the principal seismic activity eects on the ionosphere has not been built as yet. Hayakawa et al. (1993) found the seismic activity eect on the propagation of magnetospheric whistlers. It was shown from the statistical analysis that abnormal propagation characteristics of whistlers at low latitudes such as increased dispersion value and the enhanced occurrence rate were the consequences of the earthquakes. Hayakawa et al. (1993) discussed the possible mechanisms of such in¯uence. In particular, they considered the seismic eects on the wave trapping in duct (or excitation of duct) at its entrance and the enhanced occurrence of ducts in the ionosphere disturbed by the acoustic or internal gravity waves generated by earthquakes. This idea is experimentally con®rmed by recent satellite observations of small-scale plasma density irregularities and correlated ELF emissions over the seismic zone

0032-0633/00/$20.00 # 2000 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 2 - 0 6 3 3 ( 9 9 ) 0 0 0 9 6 - 3


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(Chmyrev et al., 1997). The generation model of such seismic related ®eld-aligned plasma disturbances in terms of dissipative instability of acoustic-gravity waves (AGW) in the ionosphere was presented by (Chmyrev et al., 1999; Sorokin et al., 1998). Further development of this model and its application to the mechanism forming the ionosphere±magnetosphere ducts under in¯uence of seismic activity is given in the present paper. The critical factor of the mechanism is excitation of the super threshold DC electric ®eld in the lower ionosphere that initiates the AGW instability and formation of a periodic structure of Pedersen conductivity, ®eld-aligned electric currents and the related plasma density irregularities in the upper ionosphere. Experimental evidence of the anomalous electric ®elds with signi®cant magnitude in the ionosphere over the seismic zone was reported by (Chmyrev et al., 1989). A physical model for such electric ®eld perturbations, generated in the ionosphere prior to earthquake, was discussed by (Boyarchuk et al. 1998; Sorokin and Chmyrev, 1999a, b; Sorokin et al., 1997; Sorokin and Yaschenko, 1998, 1999). A chain of processes forming the seismic related ionospheric disturbances including the ionosphere± magnetosphere ducts can be presented as follows. According to (Molchanov and Hayakawa, 1996; Pierce, 1976; Sorokin and Yaschenko, 1998, 1999), the injections of radioactive gases and charged aerosols into the atmosphere prior to an earthquake modify the altitude pro®le of the atmosphere conductivity and the current density in the Earth ±ionosphere electric circuit. As a result, the disturbance of DC electric ®eld is formed in the ionosphere E layer as in an element of the global electric circuit. According to Sorokin and Yaschenko (1999) the disturbed electric ®eld can reach 5±10 mV/m, and the spatial scale of the perturbation zone is of the order of 300 km. When the electric ®eld intensity exceeds some threshold value dependent on the sound velocity, the acoustic±gravity wave instability is developed. This instability leads to the spatial modulation of electric conductivity in the ionospheric E layer. In the presence of an external electric ®eld this process forms the periodic structure of growing ®eldaligned electric currents and plasma density irregularities stretched along the geomagnetic lines of force (Sorokin et al., 1998). Taking into account the obtained estimates of the characteristic transverse size H10 km and the density irregularity magnitude DN/No H (1±10)% one can suppose that the small-scale plasma structures excited in this way may play a role in the wave guides or the ducts which channelize the whistler waves along the geomagnetic ®eld. An appearance of such structures above the zone of earthquake focus enhances the probability of the magnetospheric whistler exit into the Earth±ionospheric wave guide in this zone and changes the dispersion characteristics of

the signals mechanism nected with sphere was (1983).

received on the Earth's surface. Another of magnetospheric duct formation cona process of local heating of the ionoconsidered by Borisov and Zolotarev

2. Theory Let us consider the conditions for generating the ducts and estimate their principal characteristics based on analyzing the acoustic ±gravity wave stability in the ionosphere. For this goal we use the equations for the AGW propagation in the ionosphere in the presence of magnetic and electric ®elds (Sorokin et al., 1998). Let us introduce the right hand co-ordinate system with the z-axis directed vertically upward. The magnetic ®eld B is directed along the z-axis, and the electric ®eld E is directed along the x-axis. Small disturbances of the velocity v1, the density r1, the pressure p1 and the temperature T1 of the ionosphere plasma with respect to their stationary values v0, r0, p0 and T0 satisfy the equations: r0 d v1 ad t þrp1 r1 g j1 á B d r1 ad t r0 rv1 v1z dr0 adz 0 d p1 ad t v1z dp0 adz þ gRT0 fd r1 ad t v1z dp0 adzg g þ 1 j1 à E j 1 s p 1 E sp 0 v á B p0 Rr0 T s
p1 0

sp0 a2p1 ap0 2a 1sp0 a2r1 ar0 X

1

Here j1 is the density of ionospheric current associated with the conductivity disturbance sp1 sp þ sp0 ; ri1 ari0 a (r1/r0); ri is the ion density; g is the ratio of heat capacities; R is the universal gas constant. The coecient a characterizes the variation of ion density relatively to variation of neutral gas density in the wave. If a=0, the conductivity disturbance will be determined only by a variation of the collision frequency dependent on the density and the pressure (or the temperature). At a=1, the ion density variation coincides with the relative density variation of the gas as a whole. With a > 1, the conductivity disturbance is mainly determined by the ion density variation. This coecient enables one to estimate the coupling between the ionospheric neutral and ionized components on the wave stability. The system of Eq. (1) is


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177

applicable to the ionospheric E-layer at the altitudes above 120 km where the Hall conductivity can be neglected as compared to the Pedersen conductivity. The Pedersen conductivity dependence on the thermodynamic quantities is determined by the expression sp0 Hri0 r0 T0 1a2 (Sorokin et al., 1998). Since the ion density decreases and the ionospheric temperature increases with the altitude considerably slower than the neutral molecule density, we assume that the Pedersen conductivity sp0 varies with altitude proportionally to r0 . Eliminating sp1 , j1 and v1y in the system of Eq. (1), we derive the following equations describing the AGW propagation in the isothermal conducting ionosphere with the horizontal external electric ®eld: r
0

r0 dad t om v

1x

þd p1 ad x,

d r1 ad t r0 d v1x ad x 0, dad t om fdad t þ o2 p1 þ a2 dad t o1 r1 g om o2 p1 om o1 a2 r1 0X Let in this system the unknown variables be dependent on the co-ordinates and time as expþiot ikxX The system yields the dispersion equation: k2 oo iom o iom þ o2 a2 o iom o1 4

dad t om v

1x

þd p1 ad x,

r0 d v1z ad z þd p1 ad z þ gr1 , d r1 ad t r0 d v1x ad x d v1z ad z v1z dr0 adz 0, dad t om fdad t þ o2 p1 v1z dp0 adz þ a2 dad t o1 r1 v1z dr0 adzg om o2 p1 om o1 a2 r1 0X In Eq. (2) the following symbols are used: o1 2a 1g þ 1sp0 E 2 a2a2 r0 ; a2 gRT0 ; o2 gg þ 1sp0 E 2 a2a2 r0 ; om sp0 B 2 ar0 X 3 2

To analyze the wave stability, let us consider the development with time of the disturbance that was set for the initial time instant. The Fourier transformation for such disturbance includes the components with the real values of the wave vectors. The time dependence of the disturbance is determined by the complex frequencies which are the solutions of Eq. (4). If we assume o=o '+iG where G` o ', Eq. (4) yields: ` o H ak, G þom þ o1 þ o2 a2 5

As a result of Eq. (5), if om > o1+o2, then G < 0, hence, the wave dissipates. With o1=o2=0, the wave dissipation is determined by the parameter om s0 B 2 ar0 that characterizes the induction drag. In the case of om < o1+o2 Eq. (5) yields G > 0 and the amplitude of the initial disturbance is grown up i.e. the instability is developed. The equality om=o1+o2 and Eq. (3) determine the critical electric ®eld value Ec: p 6 Ec aB 2ag þ 12a g 1 This value determines the threshold condition for AGW instability: E >Ec. This inequality could be presented as a condition for plasma drift velocity vd in crossed p electric and magnetic ®elds: vd EaB b vdc a 2ag þ 12a g 1X To estimate the value Ec, we assume a = 3à102 m/s, g=1.4±1.66 (that corresponds to two-atom and one-atom gas molecular), a=2. Since the model deals with vertical magnetic ®eld we assume B=Bz=3à10þ5T; then Eq. (6) yields Ec=(6±8) mV/m. To analyze the AGW stability let us turn in Eq. (2) to the ®eld variables, using the following equations (Gossard and Hooke, 1975): U r0 ars 1a2 v1x ; W r0 ars P r0 ars
þ1a2 1a2

The quantities o1, o2 and om are independent of the altitude z, as it has been assumed above (sp0 H r0). In this case, Eq. (2) forms a system with constant coecients. Assuming o1=0, om=0, we get the well known equation for AGW in the exponentially irregular atmosphere (Gossard and Hooke, 1975). The quantity o1 has a sense of the ratio of the speci®c power of the currents caused by the ionospheric conductivity disturbance to the acoustic wave energy density. This quantity determines the characteristic time of the external source energy transformation to the wave kinetic energy. The value of om characterizes the process of a wave damping due to the magnetic viscosity. Let us analyze the planar wave horizontal propagation along the x-axis. To illustrate the nature of the instability we consider an example of the uniform medium when the free fall acceleration can be neglected in Eq. (2). Assuming g = 0, we have:

v1z ; r1 ;

p1 ;

R r0 ars

þ1a2

r0 rs expþzaH , where rs is the density value at the level z = 0. For the


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®eld variables we obtain the system of uniform equations with the constant coecients: rs dad t om U þd Pad x; rs d Wad t þd Pad z Pa2H þ gR; d Rad t rs d Uad x d Wad z þ Wa2H 0; dad t om dad t þ o2 P þ a2 dad t o1 R g þ 1grs W om o2 P a2 om o1 R 0X Let us consider the horizontal AGW propagation along the x-axis, assuming d/dz = 0. Substituting in the equation system the dependence of unknown variables of the co-ordinates and time as exp(þiot+ikx ), we derive the dispersion equation: 2 ak o o iom fo2 o iom þ o2 þ o iom o2 io2 o2 g a 3 ofo2 o iom o1 þ o iom o2 g g

Bo o2 þ o2 oo1 o2 þ o2 o2 þ o2 o2 ao, a g 3 Oo f2o2 þ o2 2 o2 o2 g g 1
1a2

X

Fig. 1 presents the result of calculations of dependencies n=n(o ) and k=k(o ), performed in the vicinity of the spectral frequency og with the use of Eq. (8). As seen from the graphs, the absorption coecient is negative and has the maximum absolute value at the frequencies o H og. This means that the waves with frequency of the order og are exponentially growing and standing out the background in their amplitude forming a periodic structure. Along with oscillations of the density and pressure in the wave, the conductivity variations occur according to the last equation of system (1). Hence, the wave instability is followed with forming the horizontal periodic structure of ionospheric conductivity with the scale l H l/2 where l is the wavelength corresponding to o H og. At these frequencies the refraction index reaches its maximum value n(og), corresponding to lowest phase velocity of the wave as compared with the sound velocity (vg=a/ n(og) < a ). The horizontal scale of the conductivity variation has the value: l la2 pvg aog paaog nog X 9

where o2 gga4H is the boundary acoustic frequency, a o2 g þ 1gagH is the Brunt±Vaisala frequency, and g o2 o2 2a 3agX At g = 0, equality of Eq. (7) trans3 a forms to the formula of Eq. (4) that describes the acoustic wave propagation in the uniform medium. The case of vanishing electric ®eld and the absorption corresponds to the transition o1=o2=om=0: k2 o2 o2 þ o2 aa2 o2 þ o2 a g This dispersion equation is satis®ed with the AGW propagated in the horizontal direction (Gossard and Hooke, 1975). Let us introduce in Eq. (7) the refraction index k=(n+ik )o/a. The unstable regime is realised when o1 > om and o2 > om. The correspondent threshold electric ®eld can be determined from these inequalities. Numerical estimates show that its value insigni®cantly diers from the case of g = 0 (see equality of Eq. (6)). In the case where the electric ®eld enables one to neglect the absorption, Eq. (7) yields: no fA2 o B 2 o
1a2

The horizontal irregularities of conductivity in the ionosphere interact with the electric ®eld. High con-

Aog

1a2

aOo aOo 8
Fig. 1. Frequency dependence of the refraction and absorption indexes for the AGW horizontal propagation. The following values of the parameters were set: g=1.4; g = 10 m/s2; sp0 5 á 10þ4 S/m; r0 5 á 10þ10 kg/m3; E = 9 mV/m; og 2 á 10þ2 sþ1. Curve 1 corresponds to a=0.2 o1 aog 1X4 á 10þ2 ; o3 aog 2X7 and curve 2 corresponds to a=1.0 o1 aog 3 á 10þ2 ; o3 aog 3X9X

ko þfA2 o B 2 o

1a2

þ Aog

1a2

In Eq. (8) the following symbols were used: Ao o2 þ o2 o2 þ o2 þo2 þ o2 o1 o2 , a g 3


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179

ductivity along the magnetic ®eld lines results in transferring the electric ®eld disturbances to the upper ionospheric layers and to the magnetosphere. The electric circuit arising in this case includes the ®eld-aligned currents and the closure currents due to the Pedersen conductivity. We note that the ®eld-aligned currents are transferred by electrons while ions are the carriers of the transverse currents. Therefore the electric ®eld propagation along the magnetic lines of force and the appearance of the closing currents is accompanied by plasma density variations. If the wave is propagated along the x-axis, the conductivity irregularities are stretched along the y-axis. The electric ®eld E lies in the (x, y )-plane while the magnetic ®eld B is directed along the z-axis. Lyatsky and Maltsev (1983) have considered the formation of plasma irregularity stretched along the geomagnetic ®eld in the upper ionosphere. They analyzed the eects of motion in the ionospheric E layer of the conductivity irregularity, having a form of a lengthened band with the amplitude DsP,H and the width l=l/2, stretched in the y-direction. The horizontal velocity of the band motion along the x-axis in this case coincides with the AGW velocity and has the value vg aanog X The conducting band in the E layer excites the polarisation electric ®eld that is transferred along geomagnetic lines of force to the upper ionosphere where this ®eld initiates plasma density variations. In the case ni E0 aoi vg B ( 1, we obtain the formula for evaluating the magnitude of plasma density variations DN=NþNo across the plasma layer in the upper ionosphere (Sorokin et al., 1998): DNaNo Ini E0 a2oi vg BIni nog E0 a2oi aBX 10

The theoretical analysis has shown that the instability of acoustic-gravity waves in the lower ionosphere can lead to the formation of magnetic ®eld aligned plasma density irregularities in the upper ionosphere. These irregularities can play a role of whistler ducts. The estimated transverse size of ducts and the separation between them are H10 km, the relative plasma density enhancement within the duct is of the order of a few percent. The model predicts the following eects which could be identi®ed in the experiment: 1. the movement of plasma irregularities (ducts) in the horizontal direction with the velocity less than or of the order of the velocity of sound in the E layer; 2. the multi-ray (®ne) structure of whistlers associated with the structure of the distribution of plasma irregularities excited by AGW; 3. the correlation of anomalous whistlers with the enhancement of DC electric ®eld and plasma density oscillations as well as with formation of the ®eldaligned electric currents and associated transverse magnetic ®eld disturbances (ULF magnetic pulsations). So we studied the principle possibility of duct formation and modi®cation of whistler propagation characteristics under in¯uence of seismic related disturbances of DC electric ®eld in the lower ionosphere. Such a possibility was demonstrated on the simplest model with the vertical magnetic ®eld. The more realistic model for oblique magnetic ®eld and the detailed comparison of theoretical results with the experimental data is a subject of a separate paper.

The formula of Eq. (10) enables one to evaluate the order of magnitude of plasma irregularities caused by conductivity disturbances in the E layer of the ionosphere. This magnitude depends on altitude as ni=ni(z). The transverse spatial scales of plasma layers coincide with the scales of the horizontal spatial structure of conductivity. Let us present the numerical estimates. At the altitude of the order of 900 km at low latitudes the total rate of the ion collisions with ions and molecules is ni nini H1 sþ1 (Schunk and Nagy, 1980), and BH2 á 10þ5 T. With a 3 á 102 m/c; n 1 ± 10; og 2 á 10þ2 sþ1, for the oxygen plasma and the super-threshold electric ®eld E = 9 mV/m Eqs. (9) and (10) yield: l H (4 6 40) km; DN/No H (0.5 ±5)%.

Acknowledgements This work was partly supported by RFBR under contract 99-05-65650 and by ISTC under contract 41798.

References
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3. Conclusion The aim of this paper was to search the possible physical mechanism that could be responsible for the modi®cation of propagation characteristics of whistlers observed on the Earth's surface before earthquakes.


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