Possibility of magnetospheric VLF response to atmospheric infrasonic waves
 P. A. Bespalov^{1}Email author and
 O. N. Savina^{2, 3}
https://doi.org/10.5047/eps.2011.05.024
© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB 2012
Received: 31 May 2010
Accepted: 6 May 2011
Published: 27 July 2012
Abstract
In this paper, we consider a model of the influence of atmospheric infrasonic waves on VLF magnetospheric whistler wave excitation. This excitation occurs as a result of a succession of processes: a modulation of the plasma density by acousticgravity waves in the ionosphere, a reflection of the whistlers by ionosphere modulation, and a modification of whistler wave generation in the magnetospheric resonator. A variation of the magnetospheric resonator Qfactor has an influence on the operation of the plasma magnetospheric maser, where the active substances are radiation belt particles, and the working modes are electromagnetic whistler waves. The magnetospheric maser is an oscillating system which can be responsible for the excitation of selfoscillations. These selfoscillations are frequently characterized by alternating stages of accumulation and precipitation of energetic particles into the ionosphere during a pulse of whistler emissions. Numerical and analytical investigations of the response of selfoscillations to harmonic oscillations of the whistler reflection coefficient shows that even a small modulation rate can significantly change magnetospheric VLF emissions. Our results can explain the causes of the modulation of energetic electron fluxes and whistler wave intensity with a time scale from 10 to 150 s in the dayside magnetosphere. Such quasiperiodic VLF emissions are often observed in the subauroral and auroral magnetosphere and have a noticeable effect on the formation of space weather phenomena.
Key words
1. Introduction
There have been many studies of the effects of processes in space on the ionosphere and atmosphere. Examples include tidal effects, energetic particle precipitation, the generation of acousticgravity waves by current systems, effects of the current systems on geomagneticallyinduced currents (GIC), and the influence of radiation on the chemistry of the ionosphere. The influence of atmospheric processes on the magnetosphere has received much less attention in the literature. Previous studies have discussed the electromagnetic radiation of lightning discharges, and there are indications of magnetospheric manifestations of earthquakes.

Firstly, acousticgravity waves can change the reflection coefficient of electromagnetic VLF waves from the ionosphere.

Secondly, in the vicinity of intensive ionospheric currents, these variable currents will emit MHD waves at the acousticgravity wave frequency.

Thirdly, and possibly most importantly for our purposes, intensive fluxes of energetic particle precipitation from the magnetosphere to the ionosphere are connected with acousticgravity waves.

Finally, a linear transformation of atmospheric waves into magnetospheric waves is possible in principle. The frequencies and wave vectors of the two types of disturbances must coincide at the appropriate height for this process to occur.

electron density in the ionosphere;

electronic density gradient;

smallscale instabilities.
Here, ν is the average rate of decay of whistler waves in the magnetospheric resonator, T_{ l } is the mean life time of energetic electrons in the magnetic trap, taking into account all factors. For typical conditions in the pre and postnoon local time sectors of the Earth’s magnetosphere, the period of these oscillations (T_{ j }) is between 10 and 150 s, and the Q_{ J }factor of the oscillations (Q_{ J } = Ω_{ J }/2ν_{ J }) is of the order of several tens in the dayside magnetosphere. Such a high quality factor Q_{ J } defines the resonant response of the radiation belts to external effects. Let us note that the oscillations of Eq. (1) can actually be excited by different external actions. For example, in the magnetosphere of Jupiter such oscillations are excited by the daily rotation of the planet (Bespalov and Savina, 2005; Bespalov et al., 2005).
The frequency Ω_{ J } is that of the atmospheric infrasonic wave. Therefore, it is natural to begin our analysis with the study of infrasound propagation in the Earth’s atmosphere. We take the infrasound source to be on the Earth’s surface.
2. The Propagation of Infrasonic Waves in the Atmosphere from a GroundBased Source
3. Variation in the Electronic Density and Total Electrons Content in the Ionosphere
The solution presented in Eq. (9) shows that the variation of the plasma density becomes large in regions with large gradients of undisturbed density n_{0}. Let us note that the infrasonic waves, considered in this paper, modulate not only the local, but also the total content of electronic density in the lower region of the ionosphere. Variation of the plasma density causes a modification of the reflection coefficient of VLF waves from the ionosphere R, and its rate of decay in the magnetospheric resonator.
4. Whistler Waves: Rate of Decay in the Magnetospheric Resonator
The rate of decay of whistler waves in the magnetospheric resonator is determined by many factors, such as refraction, local damping and damping in the ionosphere. There is an uncertainty in the estimation of the first two factors due to raytracing problems. Here, we will examine damping in the ionosphere as the basic loss mechanism.
4.1 Reflection coefficient of whistler mode waves normally incident on the ionosphere
Important preliminary results about the reflection coefficient were obtained analytically by Tverskoy (1968) and numerically by Tsuruda (1973) based on computing the signal at the Earth’s surface.
In this paper, we analyze analytical expressions for the reflection coefficient of whistler mode waves with frequency ω and wave number κ which are normally incident on the ionosphere from above. The form of these expressions makes it relatively simple to take into account the effect of different ionospheric factors, e.g., acousticgravity waves.
4.2 Model problem statement and initial equations
4.3 Day and night conditions
Whistlermode waves attenuate more effectively in the dayside ionosphere. This is related to the fact that the dayside lower boundary of the ionosphere is less sharp than the nightside boundary, and whistlermode waves can penetrate to the region of intense attenuation where ν_{ en } ~ ω_{ B }. Moreover, the ionospheric density of charged particles and the collision frequency of electrons with neutrals are higher under daytime conditions. Note that expressions for ǀln Rǀ and the corresponding figures have been obtained under the assumption that the conditions and c/h_{ i } ≤ ω are satisfied.
The coefficient of reflection of whistlermode waves from the ionosphere affects the Qfactor of the magnetospheric resonator. A detailed analysis (Bespalov and Trakhtengerts, 1986) indicates that the regime of stationary generation of whistler emissions occurs when the magnetospheric resonator quality is comparatively high (under nighttime conditions), whereas the dynamic quasiperiodic regimes take place at a lower Qfactors (in the dawn and daytime magnetosphere).
5. Dynamics of Plasma Magnetospheric Maser
5.1 Basic equations
Previous research has shown that the cyclotron instability of a whistler wave in a separate magnetic flux tube in the electron radiation belts is similar to laboratory masers and lasers in many aspects (Bespalov and Trakhtengerts, 1986). In the plasma magnetospheric maser (PMM), a rather dense magnetized plasma, and conjugate areas of the ionosphere, form a “quasioptical” resonator for whistler waves. The active particles are energetic electrons of the radiation belts. The role of the pump is carried out by sources of energetic electrons in the magnetic flux tube. There are several processes responsible for the formation of the particle source power, namely the diffusion of particles on magnetic shells, convection across magnetic field, and other factors.
For typical conditions in the daytime sectors in the Earth’s magnetosphere, the period of these oscillations T_{ J } = 2π/Ω_{ J } is between 10 and 150 s, and the quality factor of the oscillations Q_{ J } = Ω_{ J }/2ν_{ J } in these regions is of the order of several tens. Such a high quality factor Q_{J} defines the resonant response of the radiation belts to external effects. The system is ready for the generation of quasiperiodic VLF emissions, if there is a suitable external action.
In principle, it is possible to try to explain the strongest influences on the work of the PMM. For this purpose, it is necessary to assume that there are modulations of the power of the source of particles, the exterior wave source and the magnetospheric resonator quality. Additional calculations show that if the depth of modulation of these values is of a similar order, then the modulation of the magnetospheric resonator quality produces the strongest effects.
5.2 Some results of numerical calculations
6. Conclusion
Infrasound in the atmosphere is excited by different sources (Le Pichon et al., 2009), for example, by earthquakes, and by meteors, etc. In highlatitude regions, infrasound is excited also by moving auroral arcs.

the infrasonic wave must have a period between 30 and 150 s:

the horizontal scale of the infrasonic wave must not be less than 100 km;

process can occur in the dayside magnetosphere;

process can occur at subauroral latitudes.
We do not know of any publications in which experimental results about the influence of atmospheric infrasonic waves on the magnetospheric processes are discussed, and one of the basic purposes of this paper is draw attention of researchers to this possibility.
Declarations
Acknowledgments
We are grateful to Prof. S. W. H. Cowley and Dr. R. Fear for help in the evolution of this work. This work was partly funded by ISSI 2006/2007 grant, by Program no. 22 of RAS, and by RFBR grant no. 120200344.
Authors’ Affiliations
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