Possibility of magnetospheric VLF response to atmospheric infrasonic waves
© 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
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 acoustic-gravity 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 Q-factor 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 self-oscillations. These self-oscillations 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 self-oscillations 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 day-side magnetosphere. Such quasi-periodic VLF emissions are often observed in the sub-auroral and auroral magnetosphere and have a noticeable effect on the formation of space weather phenomena.
Key wordsMagnetosphere-ionosphere interactions wave propagation wave-particle interactions
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 acoustic-gravity waves by current systems, effects of the current systems on geomagnetically-induced 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, acoustic-gravity 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 acoustic-gravity 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 acoustic-gravity 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;
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 post-noon 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 day-side 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 Ground-Based 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 n0. 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 magneto-spheric 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 ray-tracing 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
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., acoustic-gravity waves.
4.2 Model problem statement and initial equations
4.3 Day and night conditions
Whistler-mode waves attenuate more effectively in the day-side ionosphere. This is related to the fact that the day-side lower boundary of the ionosphere is less sharp than the night-side boundary, and whistler-mode 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 day-time 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 whistler-mode waves from the ionosphere affects the Q-factor 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 night-time conditions), whereas the dynamic quasi-periodic regimes take place at a lower Q-factors (in the dawn and day-time mag-netosphere).
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 “quasi-optical” 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 day-time 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 QJ defines the resonant response of the radiation belts to external effects. The system is ready for the generation of quasi-periodic 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
Infrasound in the atmosphere is excited by different sources (Le Pichon et al., 2009), for example, by earthquakes, and by meteors, etc. In high-latitude regions, in-frasound 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 day-side magnetosphere;
process can occur at sub-auroral 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.
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. 12-02-00344.
- Artru, J., P. Lognonne, and E. Blanc, Normal modes modelling of post-seismic ionospheric oscillations, Geophys. Res. Lett., 28, 697–700, 2001.View ArticleGoogle Scholar
- Bespalov, P. A. and V. G. Mizonova, Reflection coefficient of whistler mode waves normally incident on the ionosphere, Geomagn. Aeron., 44, 49–53, 2004.Google Scholar
- Bespalov, P. A. and O. N. Savina, Global synchronization of the fluctuations of the level of whistler emissions near Jupiter as the consequence of the three-dimensional rectification of the quality of the magneto-spheric resonator, JETP Lett., 81, 151–155, 2005.View ArticleGoogle Scholar
- Bespalov, P. A. and V. Yu. Trakhtengerts, Dynamics of cyclotron instability in the Earth–s radiation belts, in Rev. Plasma Phys., edited by Leon-tovich, M. A., 10, 155–292, Consultants Bureau, New York, London, 1986.Google Scholar
- Bespalov, P. A., V. G. Mizonova, and O. N. Savina, Magnetospheric VLF response to the atmospheric infrasonic waves, Adv. Space Res., 31, 1235–1240, 2003.View ArticleGoogle Scholar
- Bespalov, P. A., O. N. Savina, and S. W. H. Cowley, Synchronized oscillations in whistler wave intensity and energetic electron fluxes in Jupiter’s middle magnetosphere, J. Geophys. Res., 110, A09209, doi:10:1029/2005JA011147, 2005.Google Scholar
- Gershman, B. N., Dynamics of Ionospheric Plasma, Nauka, Moscow, 1974 (in Russian).Google Scholar
- Ginzburg, V. L., The Propagation of Electromagnetic Wave in Plasma, Pergamon, New York, 1970.Google Scholar
- Gossard, E. and W. Hooke, Waves in the Atmosphere, Elsevier Scientific Publishing Company, Amsterdam-Oxford-New York, 1975.Google Scholar
- Gurevich, A. V. and A. B. Shvartsburg, Nonlinear Theory of Radio Wave Propagation in the Ionosphere, Nauka, Moscow, 1973 (in Russian).Google Scholar
- Hamlin, D. A., R. Karplus, R. C. Vik, and K. M. Watson, Mirror and azimuthal drift frequencies for geomagnetically trapped particles, J. Geophys. Res., 66, 1–4, 1961.View ArticleGoogle Scholar
- Le Pichon, A., E. Blanc, and A. Hauchecorne (eds.), Infrasound Monitoring for Atmospheric Studies, Hardcover, 2009.Google Scholar
- Rapoport, V. O., P. A. Bespalov, N. A. Mityakov, M. Parrot, and N. A. Ryzhov, Feasibility study of ionospheric perturbations triggered by monochromatic infrasonic waves emitted with a ground-based experiment, J. Atmos. Sol.-Terr. Phys., 66, 1011–1017, 2004.View ArticleGoogle Scholar
- Savina, O. N., Acoustic-gravity waves in the atmosphere with a realistic temperature distribution, Geomagn. Aeron., 36, 218–224, 1996.Google Scholar
- Savina, O. N., P. A. Bespalov, V. O. Rapoport, and N. A. Ryzhov, Generalized polarization relationships for acoustic gravity waves in the non-isothermic atmosphere with the wind, Geomagn. Aeron., 46, 247–253, 2006.View ArticleGoogle Scholar
- Tsuruda, K., Penetration and reflection of VLF waves through the ionosphere full wave calculations with ground effect, J. Atmos. Terr. Phys., 35, 1377–1405, 1973.View ArticleGoogle Scholar
- Tverskoy, B. A., Dynamics of Earth Radiation Belts, Nauka, Moscow, 1968 (in Russian).Google Scholar