Strong atmospheric disturbances as a possible origin of inner zone particle diffusion

A new mechanism of the atmosphere-magnetosphere interaction, which might be called “acoustic-magnetospheric cyclotron accelerator”, is proposed. The idea of this mechanism stems from the fact that strong acoustical perturbations in the ionosphere (e.g., due to earthquakes, thunderstorms, etc.) may generate magnetic disturbances in the magnetosphere. Then, the latter will induce local resonant acceleration and subsequent inward diffusion of trapped particles. This idea may be fruitful in the interpretation of some occasional increases in inner zone particle fluxes which do not correlate with the solar or magnetospheric activities.


Introduction
Experimental evidence is mounting for the mutual in¯uence of processes in dierent geophysical media. Consequently a modern understanding of geophysical phenomena requires consideration of the eects in more than one medium. Some eects of the mutual in¯uence in the lithosphere-atmosphere-ionosphere-magnetosphere system are known and have been extensively studied: 1. Ionosphere-magnetosphere coupling ± ionospheremagnetosphere interaction is an essential part of aurora dynamics in the night-side magnetosphere (Goertz and Boswell, 1979). 2. Technogenic in¯uence on the ionosphere ± modi®cation of the ionosphere caused by additional precipitation of magnetospheric energetic particles induced by radio emission from ground radio transmitters, industrial facilities, etc. (Fraser-Smith, 1981;Parrot and Zaslavski, 1996). 3. Meteorological control of the ionosphere ± dependence of the parameters of the lower ionosphere on large-scale motions of neutral atmosphere . 4. Terrogenic eects in the ionosphere ± in¯uence of the Earth's crustal features on the dynamical processes in the ionosphere (Popov et al., 1989). 5. Ionospheric precursors of earthquakes ± in¯uence of seismic-related electromagnetic phenomena on the VLF noise background and on the ionospheric parameters (Gokhberg et al., 1995;Gal'perin et al., 1992;Molchanov et al., 1995;Hayakawa et al., 1996).
It is impossible to disregard the eects of the interaction between dierent geophysical domains and, though some progress in this direction has been made, all these eects should be studied further. The present paper addresses one more possible eect of geophysical media interaction: additional radial diusion and acceleration of inner zone particles, induced by strong acoustical motions in the upper atmosphere. The proposed mechanism of particle acceleration and inward diusion is related to transformation of acoustical wave energy into MHD modes in the ionospheric i-layer. Essentially, according to our estimates, the ground eect of excited MHD disturbances is small, whereas in the magnetosphere the corresponding magnetic disturbance may have substantial magnitude. Finally, we discuss some experimental indications on the feasibility of the considered mechanism.
2 Physical mechanism of MHD wave generation in the ionosphere by an acoustic disturbance The key element of the scenario in hand lies in the fact that atmosphere-magnetosphere interaction results in the excitation of electric currents and magnetic ®elds by acoustic disturbances in the ionospheric i-layer. The problem of magnetic disturbance generation by acous-tical waves has been already treated within the framework of dierent theoretical models (Belov et al., 1973;Al'perovich et al., 1979;Jacobson and Bernhardt, 1985;Borisov and Moiseyev, 1989;Pokhotelov et al., 1994). At a more simple and physically obvious level, it is attempted to demonstrate in the following the general idea of acoustic-magnetohydrodynamic coupling in the mid-latitude ionosphere. Various natural and man-made phenomena in the lower atmosphere can be a source of strong acoustical disturbances, e.g. severe tropospheric weather storms, Rayleigh surface waves or tsunami from earthquakes, volcano eruptions, large rocket launches,¯ights of supersonic aircrafts or chemical and nuclear explosions (for references see reviews by Karlov et al., 1980;Blanc, 1985;Pokhotelov et al., 1995;Guglielmi and Pokhotelov, 1996). Emitted acoustic waves increase in amplitude as they propagate upward through the atmosphere, passing progressively through layers with exponentially decreasing density. In this process the upper atmosphere acts as a ®lter, allowing only a certain frequency band of acoustic noise to pass. At low-frequency edge atmospheric pass-band ®lter is limited by the cut-o frequency. The high-frequency cuto is controlled by a stronger attenuation of higher frequencies ($ f 2 ) due to dissipation processes. Doppler soundings of the i-and p -layers (Prasad et al., 1975;Okuzawa et al., 1983Okuzawa et al., , 1986 actually showed that the ionospheric response constituted band-limited oscillations with prevailing periods from several seconds up to several minutes.
In the ionospheric plasma, where collisions do occur, the motion of neutral particles transverse to the geomagnetic ®eld line forces the ionized particles to oscillate; hence currents are induced. These oscillating currents act as a source for MHD waves, which then may propagate along the ionosphere or into the magnetosphere.
At ®rst, it seems that the transformation must be very weak due to the enormous dierence between the AlfveÂ n velocity in the ionosphere, e 9 5 Á 10 2 km/s, and the sound velocity s 9 5 Á 10 À1 km/s. Actually, the pressure variation dp in acoustic wave yields to the relationship: where v n is the perturbation of a neutral particle bulk velocity and p stands for the unperturbed pressure. The disturbed magnetic ®eld df in the MHD wave can be estimated as follows where v i is the velocity of the ionized plasma component and f stands for the unperturbed magnetic ®eld (for these rough estimates we neglect the dierence between v i , v i , and v e ). For the most favorable conditions, i.e. when v n $ v i , the transformation coecient becomes equal to dfafadpap 9 s a e $ 10 À3 X 3 Thus, when an acoustic impulse with an amplitude of dpap $ 10 À1 enters the ionosphere, it would generate magnetic disturbances with an amplitude no larger than several nT; that is df $ 3nT for f 3 Â 10 4 nT (Danilov and Dovzhenko, 1987). The above elementary consideration illustrates the basic problem of an ecient coupling between the acoustic waves and MHD disturbances. However, in the ionospheric plasma the properties of MHD waves are modi®ed considerably, as compared to collisionless plasma. The simplest way to understand the properties of these waves is to consider their propagation along a magnetic ®eld B in a homogeneous plasma, where all the disturbances can be considered as plane waves propagating along the ®eld lines, where x is the wave angular frequency, and k is the wave vector.
In the frequency range m in ( x ( x i (where m in is the ion-neutral collision frequency and x i is the ion angular gyrofrequency), which holds in the ionized plasma of the upper ionosphere, a wave propagates with the ordinary AlfveÂ n velocity e . The neutrals with density x n are practically not disturbed by the wave. As the frequency decreases, the MHD wave becomes attenuated due to ion-neutral collisions.
At very low frequencies, when m ni $ x ( x i (m ni is a neutral-ion collision frequency: m ni x 0 ax n m in , where x 0 is a total ion density), multicomponent plasma starts to move as a whole, without slipping between the velocities of ionized and neutral plasma components. It was suggested to call this wave regime a``slow MHD wave'' (Sorokin and Fedorovich, 1982), which is not to be confused with the slow ion acoustic mode. The phase velocity of the wave for the case when ions drag the neutrals, i.e. when v n $ v i , turns out to be (Al'perovich et al., 1979) v ph fa4pw i x n 1a2 e x 0 ax n 1a2 X 5 However, in the realistic ionosphere, even at altitudes of the p -layer, the expected periods of the slow MHD disturbances are too long, that is about several hours. In the i-layer, where the plasma conductivity transverse to the magnetic ®eld becomes highly anisotropic (local Hall conductivity is much larger than Pedersen conductivity), a new modi®ed MHD mode appears, called the gyrotropic MHD mode (Sorokin and Fedorovich, 1982). The phase velocity of this gyrotropic MHD mode in the non-dissipative plasma diers essentially from the ordinary AlfveÂ n velocity: v ph e xax i 1a2 6 in the range of parameters x e ) m en (m en is the electron-neutral collision frequency and x e is the electron gyrofrequency) and x ( x i ( m in , that are typical for the i-layer. A characteristic feature of the gyrotropic MHD mode, namely the velocity decrease by a factor xax i 1a2 , predicts a high transformation coecient, up to $ 5 Â 10 À2 , in the i-layer in accordance with Eq. (3). For this case magnetic distur-bances with amplitudes up to hundreds of nT may be expected; e.g. for dpap $ 10 À1 and f 3 Â 10 4 nT, df $ 1X5 Â 10 2 nT. The above simpli®ed consideration should be considered only as some intuitive guess, indicating that in the ionospheric i-layer the coupling between an acoustic impact and MHD disturbances might be substantial. In fact, more advanced theoretical models (Belov et al., 1973;Pokhotelov et al., 1994) support this notion. But the most convincing argument, in our opinion, is presented by the experimental results obtained during the MASSA experiment (Gal'perin et al., 1985;Gal'perin and Hayakawa, 1996). The low-orbiting eureol-3 satellite actually recorded magnetic impulses in the upper ionosphere with amplitudes of 10 2 nT resulting from ground-based explosions. Polarization of the electromagnetic impulse showed that it was an AlfveÂ n wave, propagating upwards from the ionosphere. Then, AlfveÂ n impulse oscillated between the conjugate ionospheres and shifted due to dispersion to lower v-shells. As a result, the lower latitude magnetosphere became à`w ell'' for AlfveÂ n disturbances that were triggered by the ionospheric acoustical motion.

Magnetospheric and ground eects of magnetic disturbances induced by an acoustic wave
After all the above considerations a very appropriate question arises: if the magnetic disturbances induced by acoustic waves might be so strong, why only small eects are observed by ground-based magnetometers, particularly after explosions and earthquakes ? To answer this question we now estimate the eects expected above the ionosphere and on the ground.
Since we are only interested in the region near the source, we may limit our analysis to a quasi-static approximation. We suppose that in the northern ionosphere a neutral velocity disturbance v n arises, perpendicular to B, with a wave vector k x k (Fig. 1). We also assume, that the disturbance scale in the vertical direction z is larger than the scale of the current-carrying layer of the ionosphere.
Then from the electrodynamic point of view, the ionosphere can be imagined as a thin ®lm with an anisotropic tensor conductivity: where the subscripts P and H refer to Pedersen and Hall height-integrated conductivities, respectively. The electric ®eld E x in the northern ionosphere is comprised of the dynamo and polarization ®elds according to: The local ionosphere is connected by equipotential ®eld lines to the conjugate southern ionosphere, i.e. u x u , while E c Àr c u . Now, proceeding from the current conservation condition: and Ohm's law for the height-integrated transverse we may obtain the equations for the potential u of the polarization ®eld and for the ®eld-aligned current From Eq. (12) it follows that the ®eld-aligned current j z can be excited either by an acoustical wave (for which r Â v n z 0 and r Á v n T 0) due to Hall conductivity, or by a non-compressional gravity wave (for which r Â v n z T 0 and r Á v n 0) due to Pedersen conductivity. The polarization of horizontally strati®ed p -region plasma and perturbations of plasma density induced by acoustic and gravity waves were also studied in electrostatic approximation by Jacobson (1986), and Jacobson and Bernhardt (1985), who demonstrated that at low latitudes electrostatic eects should be mirrored in the conjugated ionosphere.
We further concentrate on estimates of the current, induced by an acoustical wave, in the i-layer. For the qualitative estimates let us limit ourselves by considering the simple one-dimensional model (d/dy=0) illustrated in Fig. 1.
The transverse current can be decomposed into the potential (Pedersen) and the solenoidal (Hall) parts with the potentials U and W, respectively: where z is the unit vector along the ambient magnetic ®eld, i.e. z Baf.
According to Fukushima's (1969) theorem the resultant eect of ®eld-aligned and Pedersen currents is zero at the ground. The magnetic disturbance at the Earth's surface is only produced by the Hall part containing the W potential.
The magnetic disturbance in the magnetosphere can be calculated from the AmpeÂ re's law and Eq. (12), and results in df y af Àl 0 a2R r v n Y 14 where l 0 is the permeability of a free space. Then, for the W part we obtain from Eqs. (10)±(13) Finally, for the Hall current induced by the acoustic wave we have: The ground magnetic eect from the current system in hand is given by: where u 1 f is the modi®ed Bessel function, f kh, and h is the height of the current carrying layer. Estimates, which follow from Eqs. (16) and (17) for R r 2R , R 10 S, f 3 Â 10 4 nT, h 100 km, v n 50 m/s and k 2pa100 km À1 yield df y 90X5Â10 2 nT in the magnetosphere and df x 9 3nT on the ground. The given estimates show that the ground magnetic eect of the ionospheric currents induced by an acoustic impulse is small as compared with that in the magnetosphere. The reason of this fact is that a satellite detects the direct eect of a localized ®eld-aligned current, while ground-based magnetometer records the spatially integrated eect of small-scale ionospheric current system.

Inner zone particle acceleration and diusion
Now we consider what kind of in¯uence may be exerted on the energetic trapped particles from locally excited hydromagnetic disturbances. This process has to be described by a diusion-type system of equations in the quasi-linear approximation. Just for simplicity, our consideration of the eect is based on the relationships for typical wave and particle parameters, which actually are the characteristics of the relevant quazi-linear dierential equations.
Due to the conservation of the ®rst two adiabatic invariants the radial displacement dv of trapped parti-cles is directly related to the variation of energy d as follows (Lyons and Williams, 1984): For simplicity herein we only consider the particles mirroring near the geomagnetic equator. As it can be deduced from Eq. (18) any transfer of energy from MHD disturbances to particles will be accompanied by their inward radial diusion. The energy imparted to the charged non-relativistic particles in a time-varying ®eld can be estimated from the well known formula (e.g. Sturrock, 1994): Here df k is ®eld aligned perturbation of the magnetic ®eld, e is the magnitude of the particle charge, l is the particle magnetic moment, v d is the azimuthal drift velocity, i / is the azimuthal component of the wave electric ®eld, and integration is made along particle trajectories. The appearance of the second term in the brackets on the right side of Eq. (19) is connected with the fact, that in the time-dependent magnetic ®eld, there must be an accompanying electric ®eld according to the Faraday's law. If we expand the wave ®elds E and dB into Fourier integral over time t and azimuthal angle /, then for particles moving along trajectories /t / 0 x d t, where / 0 is the initial particle phase and x d is the magnetic drift frequency, the energy gain per one pass through the disturbed region will be where m is the azimuthal wave number, and the superscripts in the initial values are omitted. Remembering that The appearance of a delta function in Eq. (23) means that the average energy gain is non-vanishing only for resonant particles. The resonance condition x mx d means that an energy transfer from the wave to the particles occurs only when the period of the wave is equal to multiples of the particle drift period. The factor expim/ 0 relates to the proper phasing between the particles and the oscillating ®eld: depending on the initial phase some particles will give energy to the wave, while others will extract energy from the wave. Further we will consider Eq. (23) only averaged over group of particles with such phases that d ! 0. Now we consider the particle acceleration induced by a localized disturbance, such as where D/ stands for the azimuthal extent of the source in hand.
For such disturbance we have from Eqs. (22) and (23) The expression in Eq. (25) shows that the group of particles with energies such that the period of transit through a disturbed region is about the disturbance period will be resonantly accelerated in the most eective way. A typical period of magnetic drift of non-relativistic particles in the inner magnetosphere can be estimated as (Lyons and Williams, 1984): The actual resonant period depends, as follows from Eq. (25), on the scale of disturbance localization. For example, an acoustically generated disturbance with the periods s $ 1 mn and localized in the region D/v i $ 10 3 km can resonantly interact with electrons of MeV energy. Scaling of Eq. (25) gives an estimate for resonant particle energy gain per one revolution d i c a 9 e axdf c afY d df k a 9 df k af 27 Supposing that the curvature radius of geomagnetic ®eld 9 i , x 9 10 À1 s À1 , e 9 3 Â 10 3 km/s, and f 10 4 nT, for the disturbance with magnitude df c 9 10nT we get from Eq. (27) d a 9 5 Â 10 À3 . An evaluation of the total energy gain d and consequent particle displacement dv may require the consideration of several drift periods. For x 5 periods the relationship Eq. (27) would yield a value between 10 À2 ±10 À1 . So, the considered disturbance will accelerate some group of electrons up to additional energies 3 Â 10 2 keV. As was indicated by Falthammar (1965) particle acceleration in the magnetosphere via magnetic drift resonance is physically similar to the particle acceleration in a cyclotron or to the transit-time heating in a stellarator. Following Falthammar (1965) the discussed above process may be called``acoustic-magnetospheric cyclotron acceleration''.

Discussion
The mechanism of electron acceleration presented above has much in common with that proposed by Cladis (1966) for the interpretation of the transient¯uxes of 0X75 MeV electrons observed by Imhof and Smith (1965) in the inner magnetosphere at v 1X15. In his approach, Cladis (1966) suggested the locally increased equatorial electrojet variations as an origin of MeV electron acceleration. In due course, we propose oscillations of the ionosphere-magnetosphere current system, induced by acoustical oscillatory motion, as an origin of the similar eects.
A particular source of acoustical disturbances may be, for example, surface Rayleigh waves emanating from earthquakes or severe weather storms. Preliminary analysis of data from the ximus-6 satellite indicated the existence of certain correlation of seismic activity with sporadic bursts of electrons in the gap between inner edge of inner radiation belt and atmosphere (Stassinopoulos and Vette, private communication, 1981). Similar eects were noticed by Gal'per et al. (1989) on board the ws station, by Pustovetov and Malyshev (1993) on board the weteor-3 satellite, and by BoskovaÂ et al. (1994) in the course of the processing the sg-19 data.
The comparison of electron precipitation from radiation belts as measured by qmm satellite with the occurrence of tropical cyclones was made by Melioransky et al. (1996). They noticed that tropical cyclones are regularly accompanied by electron precipitation, whereas the maximum of precipitation corresponds to the most intense phase of cyclone evolution.
The result of resonant periodic action on the trapped radiation will be the formation of nearly monoenergetic group of electrons. Electron distribution function of this type (``bump on the tail'' distribution) will be unstable under excitation of some high-frequency electrostatic turbulence. Thus, the described scenario represents the channel of transformation of the large-scale atmospheric motion into small-scale plasma turbulence in the magnetosphere. Then low-latitude regions of strong thunderstorm activity may be one of the sources of equatorial electrostatic VLF hiss, observed on board the yqy-6 satellite (Laaspere et al., 1971).
An interesting sub-class of near-equatorial electrostatic VLF hiss was discovered by sg-19 low-orbiting satellite (Larkina et al., 1983(Larkina et al., , 1988Molchanov et al., 1993). The v-shell projection of this noise corresponded to the earthquake epicenters. Electrostatic noise lasted for many hours after a seismic shock. We may speculate that the process of energy transformation following the scheme``acoustical disturbance 3 MHD wave 3 electron acceleration 3 electrostatic VLF noise generation'' may be responsible for the events observed on board sg-19 satellite.

Conclusion
The additional possible mechanism of the atmospheremagnetosphere coupling is proposed. Strong acoustic oscillations, reaching the ionospheric i-layer, may result in the generation of ®eld-aligned currents. The magnetic eect of these currents in the magnetosphere might have a considerable magnitude ($10±10 2 nT), whereas the ground signature of these magnetic disturbances is essentially weaker ($several nT). AlfveÂ n waves, generated by acoustic disturbances in the upper atmosphere, may induce resonant energizing and subsequent diusion across v-shells of particles, trapped in the magnetosphere. As a whole, a physical picture described above represents some kind of an``acoustic-magnetospheric cyclotron accelerator''. Using this conception we may provide a reasonable explanation for a number of satellite observations of occasional increases in inner zone particle¯uxes (Gal'per et al., 1989;Gal'perin et al., 1992;Pustovetov andMalyshev, 1993, BoskovaÂ et al., 1994;Melioransky et al., 1996) which do not explicitly relate to solar or magnetospheric processes.
Summarizing we hope to draw the attention of space physicists to the possibility (practically never taken into account) that some of magnetospheric disturbances may be driven by processes in the upper atmosphere. De®nitely, all the problems related to this problem cannot be solved in one paper, and further studies, both experimental and theoretical, are necessary.