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<front>
<journal-meta>
<journal-id journal-id-type="publisher">ANGEO</journal-id>
<journal-title-group>
<journal-title>Annales Geophysicae</journal-title>
<abbrev-journal-title abbrev-type="publisher">ANGEO</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Ann. Geophys.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1432-0576</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/angeo-32-449-2014</article-id>
<title-group>
<article-title>Excitation of planetary electromagnetic waves in the inhomogeneous ionosphere</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Rapoport</surname>
<given-names>Yu.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Selivanov</surname>
<given-names>Yu.</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Ivchenko</surname>
<given-names>V.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Grimalsky</surname>
<given-names>V.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Tkachenko</surname>
<given-names>E.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Rozhnoi</surname>
<given-names>A.</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Fedun</surname>
<given-names>V.</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Kyiv National Taras Shevchenko University, 2, Glushkova Av., Build. 1, 03680 Kyiv, Ukraine</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Space Research Institute NASU-NSAU, 40, Glushkov Av., 03680, Kiev 187, Ukraine</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>University of Morelos, Av. Universidad, 1001, Z.P. 62210, Cuernavaca, Morelos, Mexico</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>Institute of Physics of the Earth, Russian Academy of Sciences, 10 B. Gruzinskaya, Moscow, 123995, Russia</addr-line>
</aff>
<aff id="aff5">
<label>5</label>
<addr-line>Space Systems Laboratory, Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, S1 3JD, UK</addr-line>
</aff>
<pub-date pub-type="epub">
<day>25</day>
<month>04</month>
<year>2014</year>
</pub-date>
<volume>32</volume>
<issue>4</issue>
<fpage>449</fpage>
<lpage>463</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2014 Yu. Rapoport et al.</copyright-statement>
<copyright-year>2014</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://angeo.copernicus.org/articles/32/449/2014/angeo-32-449-2014.html">This article is available from https://angeo.copernicus.org/articles/32/449/2014/angeo-32-449-2014.html</self-uri>
<self-uri xlink:href="https://angeo.copernicus.org/articles/32/449/2014/angeo-32-449-2014.pdf">The full text article is available as a PDF file from https://angeo.copernicus.org/articles/32/449/2014/angeo-32-449-2014.pdf</self-uri>
<abstract>
<p>In this paper we develop a new method for the analysis of excitation and
propagation of planetary electromagnetic waves (PEMW) in the ionosphere of
the Earth. The nonlinear system of equations for PEMW, valid for any height,
from D to F regions, including intermediate altitudes between D and E and
between E and F regions, is derived. In particular, we have found the system
of nonlinear one-fluid MHD equations in the β-plane approximation valid
for the ionospheric F region (Aburjania et al., 2003a, 2005). The
series expansion in a &quot;small&quot; (relative to the local geomagnetic field)
non-stationary magnetic field has been applied only at the last step of the
derivation of the equations. The small mechanical vertical displacement of
the media is taken into account. We have shown that obtained equations can be
reduced to the well-known system with Larichev–Reznik vortex solution in the
equatorial region (see e.g. Aburjania et al., 2002). The excitation of
planetary electromagnetic waves by different initial perturbations has been
investigated numerically. Some means for the PEMW detection and data
processing are discussed.</p>
</abstract>
<counts><page-count count="15"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Aburjania, G. D. and Chargazia, Kh. Z.: Self-organization of large-scale ULF electromagnetic wave structures in their interaction with nonuniform zonal winds in the ionospheric E region, Plasma Phys. Rep., 37, 177–190, &lt;a href=&quot;http://dx.doi.org/10.1134/S1063780X10111017&quot;&gt;https://doi.org/10.1134/S1063780X10111017&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Aburjania, G. D., Khantadze, A. G., and Kharshiladze, O. A.: Nonlinear Planetary Electromagnetic Vortex Structures in the Ionospheric F-Layer, Plasma Phys. Rep., 28, 586–591, &lt;a href=&quot;http://dx.doi.org/10.1134/1.1494057&quot;&gt;https://doi.org/10.1134/1.1494057&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Aburjania, G. D., Jandieri, G. V., and Khantadze, A. G.,: Self-organization of planetary electromagnetic waves in the E-region of the ionosphere, J. Atmos. Sol.-Terr. Phys., 65, 661–671, &lt;a href=&quot;http://dx.doi.org/10.1016/S1364-6826(03)00003-8&quot;&gt;https://doi.org/10.1016/S1364-6826(03)00003-8&lt;/a&gt;, 2003a.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Aburjania, G. D., Khantadze, A. G., and Gvelesiani, A. I.: Physics of generation of the new branches of planetary electromagnetic waves in the ionosphere, Geomagn. Aeron., 42, 193–203, 2003b.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Aburjania, G. D., Chargazia, Kh. D., Jandieri, G. V., Khantadze, A. G., Kharshiladze, O. A., and Lominadze, J. D.: Generation and propagation of the ULF planetary-scale electromagnetic wave structures in the ionosphere, Planet. Space Sci., 53, 881–901, &lt;a href=&quot;http://dx.doi.org/10.1016/j.pss.2005.02.004&quot;&gt;https://doi.org/10.1016/j.pss.2005.02.004&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Alperovich, L. S. and Fedorov, E. N.: Hydromagnetic Waves in the Magnetosphere and the Ionosphere, Astrophysics and Space Science Library, Springer, Vol, 353, 425 pp., 2007.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Arakawa, A.: Self-organization of planetary electromagnetic waves in the E-region of the ionosphere, Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion: Two-Dimensional Incompressible Flow. Part I, J. Comput. Phys., 135, 103–114, &lt;a href=&quot;http://dx.doi.org/10.1006/jcph.1997.5697&quot;&gt;https://doi.org/10.1006/jcph.1997.5697&lt;/a&gt;, 1997.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Boardman, A. D., Hess, O., Mitchell-Thomas, R., Rapoport, Y. G., and Velasco, L.: Temporal solitons in magnetooptic and metamaterial waveguides, Photonic. Nanostruct., 8, 228–243, &lt;a href=&quot;http://dx.doi.org/10.1016/j.photonics.2010.05.001&quot;&gt;https://doi.org/10.1016/j.photonics.2010.05.001&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Boardman, A. D., Grimalsky, V. V., and Rapoport, Yu. G.: The hybrid method of nonlinear transformational and complex geometrical optics for energy concentration in metamaterials, Metamaterials 2011: The Fifth International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, Barcelona, 763–765, 2011a.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Boardman, A. D., Grimalsky, V. V., and Rapoport, Yu. G.: Nonlinear transformational optics and electromagnetic and acoustic fields concentrators, The Fourth International Workshop on Theoretical and Computational Nanophotonics, AIP Conf. Proc., 1398, 120–122, 2011b.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Burmaka, V. P., Lysenko, V. N., Chernogor, L. F., and Chernyak, Yu. V.: Wave-Like Processes in the Ionospheric F Region that Accompanied Rocket Launches from the Baikonur Site, Geomagn. Aeron., 46, 783–800, 2006.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Borries, C., Jakowski, N., Jacobi, Ch., Hoffmann, P., and Pogoreltsev, A.: Spectral analysis of planetary waves seen in ionospheric total electron content (TEC): First results using GPS differential TEC and stratospheric reanalyses, J. Atmos. Sol.-Terr. Phys., 69, 2442–2451, &lt;a href=&quot;http://dx.doi.org/10.1016/j.jastp.2007.02.004&quot;&gt;https://doi.org/10.1016/j.jastp.2007.02.004&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Clark, R. M., Yeh, K. C., and Liu, C. H.: Interaction of internal gravity waves with the ionospheric F2-layer, J. Atmos. Terr. Phys., 33, 1567–1576, &lt;a href=&quot;http://dx.doi.org/10.1016/0021-9169(71)90074-2&quot;&gt;https://doi.org/10.1016/0021-9169(71)90074-2&lt;/a&gt;, 1971.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Gill, A. E.: Atmosphere-Ocean Dynamics, Academic Press, 662 pp., 1982.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Guglielmi, A. V. and Pokhotelov, O. A.: Geoelectromagnetic waves, Taylor &amp; Francis, Bristol, 382 pp., 1996.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Herron, T. J.: Phase Characteristics of Geomagnetic Micropulsations, J. Geophys. Res., 71, 871–889, &lt;a href=&quot;http://dx.doi.org/10.1029/JZ071i003p00871&quot;&gt;https://doi.org/10.1029/JZ071i003p00871&lt;/a&gt;, 1966.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Kaladze, T. D., Pokhotelov, O. A., Sagdeev, R. Z., Stenflo, L., and Shukla, P. K.: Planetary electromagnetic waves in the ionospheric E-layer, J. Atmos. Sol.-Terr. Phys., 65, 757–764, &lt;a href=&quot;http://dx.doi.org/10.1016/S1364-6826(03)00042-7&quot;&gt;https://doi.org/10.1016/S1364-6826(03)00042-7&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Khantadze, A. G.: Some questions of the dynamics of the conducting atmosphere, Metsniereba, Tbilisi, 1973 (in Russian).</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Landau, L. D., Pitaevskii, L. P., and Lifshits, E. M.: Electrodynamics of Continuous Media, 2nd Edn., Volume 8 (Course of Theoretical Physics), Elsevier Butterworth-Heinemann, Oxford, 460 pp., 2004.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Lyubushin, A. A.: Geophysical Monitoring Systems Data Analysis, Moscow, Nauka, 228 pp., 2007 (in Russian).</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Marchuk, G. I.: Numerical Methods and Applications, 1st Edn., CRC Press, Boca Raton, 288 pp., 1994.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Onishchenko, O. and Pokhotelov, O.: Generation of zonal structure by internal gravity waves in the Earths Atmosphere, Doklady Earth Sciences, 445, 845–848, &lt;a href=&quot;http://dx.doi.org/10.1134/S1028334X12070070&quot;&gt;https://doi.org/10.1134/S1028334X12070070&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Onishchenko, O., Pokhotelov, O., and Astafieva, N.: Generation of large-scale eddies and zonal winds in planetary atmospheres, Physics-Uspekhi, 51, 577–589, &lt;a href=&quot;http://dx.doi.org/10.1070/PU2008v051n06ABEH006588&quot;&gt;https://doi.org/10.1070/PU2008v051n06ABEH006588&lt;/a&gt;, 2008.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Onishchenko, O., Pokhotelov, O., and Fedun, V.: Convective cells of internal gravity waves in the earth&apos;s atmosphere with finite temperature gradient, Ann. Geophys., 31, 459–462, &lt;a href=&quot;http://dx.doi.org/10.5194/angeo-31-459-2013&quot;&gt;https://doi.org/10.5194/angeo-31-459-2013&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Pilipenko, V. A., Shalimov, S. L., Fedorov, E. N., Engebretson, M. J., and Hughes, W. J.: Coupling between field-aligned current impulses and Pi1 noise bursts, J. Geophys. Res., 104, 17419–17430, &lt;a href=&quot;http://dx.doi.org/10.1029/1999JA900190&quot;&gt;https://doi.org/10.1029/1999JA900190&lt;/a&gt;, 1999.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Prattes, G., Schwingenschuh, K., Eichelberger, H. U., Magnes, W., Boudjada, M., Stachel, M., Vellante, M., Villante, U., Wesztergom, V., and Nenovski, P.: Ultra Low Frequency (ULF) European multi station magnetic field analysis before and during the 2009 earthquake at L&apos;Aquila regarding regional geotechnical information, Nat. Hazards Earth Syst. Sci., 11, 1959–1968, &lt;a href=&quot;http://dx.doi.org/10.5194/nhess-11-1959-2011&quot;&gt;https://doi.org/10.5194/nhess-11-1959-2011&lt;/a&gt;, 2011.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P.: Numerical Recipes in Fortran 77. The Art of Scientific Computing, Cambridge Univ. Press, NY, 1997.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Rapoport, Yu. G., Zaspel, C. E., Mantha, J. H., and Grimalsky, V. V.: Multisoliton formation in magnetic thin films, Phys. Rev. B, 65, 244231–244234, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevB.65.024423&quot;&gt;https://doi.org/10.1103/PhysRevB.65.024423&lt;/a&gt;, 2002.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Rapoport, Yu. G., Gotynyan, O. E., Ivchenko, V. M., Kozak, L. V., and Parrot, M.: Effect of acoustic-gravity wave of the lithospheric origin on the ionospheric F region before earthquakes, Phys. Chem. Earth, 29, 607–616, &lt;a href=&quot;http://dx.doi.org/10.1016/j.pce.2003.10.006&quot;&gt;https://doi.org/10.1016/j.pce.2003.10.006&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Rapoport, Yu. G., Kotsarenko, A. N., Agapitov, A. V., Milinevsky, G. P., and Selivanov, Yu. A.: Planetary electromagnetic waves (PEMW) in the ionospheric region F, in: 7th Ukrainian Conference on Space Research, 4–7 September 2007, Crimea, Evpatoria, Ukraine, Abstracts, 98, 2007.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Rapoport, Yu. G., Hayakawa, M., Gotynyan, O. E., Ivchenko, V. N., Fedorenko, A. K., and Selivanov, Yu. A.: Stable and unstable plasma perturbations in the ionospheric F region, caused by spatial packet of atmospheric gravity waves, Phys. Chem. Earth, Pt. A/B/C, 6–7, 508–515, &lt;a href=&quot;http://dx.doi.org/10.1016/j.pce.2008.09.001&quot;&gt;https://doi.org/10.1016/j.pce.2008.09.001&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Rapoport, Yu. G., Cheremnykh, O. K., Selivanov, Yu. A., Fedorenko, A. K., Ivchenko, V. M., Grimalsky, V. V., and Tkachenko, E. N.: Oscillations of neutral and charged components of near-Earth plasma and effects of active media, in: UK-Ukraine Meeting on Solar Physics and Space Science UKU SPSS/TASS-2011, 29 August–2 September, 2011 Alushta, Crimea, Ukraine, PROGRAMME and ABSTRACTS, 69, 2011.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Rapoport, Yu., Boardman, A., Grimalsky, V., Selivanov, Yu., and Kalinich, N.: Metamaterials for space physics and the new method for modeling isotropic and hyperbolic nonlinear concentrators, in: Mathematical Methods in Electromagnetic Theory (MMET), 2012 International Conference, 76–79, 2012a.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Rapoport, Yu. G., Cheremnykh, O. K., Selivanov, Yu. A., Fedorenko, A. K., Ivchenko, V. M., Grimalsky, V. V., and Tkachenko, E. N.: Modeling AGW and PEMW in inhomogeneous atmosphere and ionosphere, in: Mathematical Methods in Electromagnetic Theory (MMET), 2012 International Conference, IEEE, 577–580, 2012c.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Roache, P. J.: Fundamentals of Computational Fluid Dynamics, Hermosa Publ., NY, 648 pp., 1998.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Saliuk, D. A. and Agapitov, O. V.: Vortex and ULF wave structures in the plasma sheet of the Earth magnetosphere, Advances in Astronomy and Space Physics, 3, 53–57, 2013.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Saliuk, D. A., Agapitov, O., and Milinevsky, G. P.: Magnetized Rossby waves in mid-latitude ionosphere F-layer, Advances in Astronomy and Space Physics, 2, 95–98, 2012.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Sèbe, O., Bard, P.-Y., and Guilbert, J.: Single station estimation of seismic source time function from coda waves: The Kursk disaster, Geophys. Res. Lett., 32, L14308, &lt;a href=&quot;http://dx.doi.org/10.1029/2005GL022799&quot;&gt;https://doi.org/10.1029/2005GL022799&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Slavin, A. N., Büttner, O., Bauer, M., Demokritov, S. O., Hillebrands, B., Kostylev, M. P., Kalinikos, B. A., Grimalsky, V. V., and Rapoport, Yu.: Collision properties of quasi-one-dimensional spin wave solitons and two-dimensional spin wave bullets, Chaos, 13, 693–701, &lt;a href=&quot;http://dx.doi.org/10.1063/1.1557961&quot;&gt;https://doi.org/10.1063/1.1557961&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Sorokin, V. M. and Fedorovich, G. V.: Physics of Slow MHD Waves in the Ionospheric Plasma, Energoizdat, Moscow, 1982 (in Russian).</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Southwood, D. J. and Kivelson, M. G.: Vortex motion in the ionosphere and nonlinear transport, J. Geophys. Res., 98, 11459–11466, &lt;a href=&quot;http://dx.doi.org/10.1029/93JA00434&quot;&gt;https://doi.org/10.1029/93JA00434&lt;/a&gt;, 1993.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Sun, J., Burns, S. P., Vandemark, D., Donelan, M. A., Mahrt, L., Crawford, Timothy, L., Herbers, T. H. C., Crescenti, G. H., and French, J. R.: Measurement of Directional Wave Spectra Using Aircraft Laser Altimeters, J. Atmos. Ocean. Tech., 22, 869–885, &lt;a href=&quot;http://dx.doi.org/10.1175/JTECH1729.1&quot;&gt;https://doi.org/10.1175/JTECH1729.1&lt;/a&gt;, 2005.</mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple">Szegö, K., Glassmeier, K.-H., Bingham, R., Bogdanov, A., Fischer, C., Haerendel, G., Brinca, A., Cravens, T., Dubinin, E., Sauer, K., Fisk, L., Gombosi, T., Schwadron, N., Isenberg, P., Lee, M., Mazelle, C., Möbius, E., Motschmann, U., Shapiro, V. D., Tsurutani, B., and Zank, G.: Physics of Mass Loaded Plasmas, Space Sci. Rev., 94, 429–671, &lt;a href=&quot;http://dx.doi.org/10.1023/A:1026568530975&quot;&gt;https://doi.org/10.1023/A:1026568530975&lt;/a&gt;, 2000.</mixed-citation>
</ref>
<ref id="ref44">
<label>44</label><mixed-citation publication-type="other" xlink:type="simple">Tolstoy, I.: Hydromagnetic Gradient Waves in the Ionosphere, J. Geophys. Res., 72, 1435–1442, &lt;a href=&quot;http://dx.doi.org/10.1029/JZ072i005p01435&quot;&gt;https://doi.org/10.1029/JZ072i005p01435&lt;/a&gt;, 1967.</mixed-citation>
</ref>
<ref id="ref45">
<label>45</label><mixed-citation publication-type="other" xlink:type="simple">Verkhoglyadova, O. P., Agapitov, A. V., and Ivchenko, V. N.: Model of vortex tubes in the low-latitude plasma sheet of the Earth magnetosphere, Adv. Space Res., 28, 801–806, &lt;a href=&quot;http://dx.doi.org/10.1016/S0273-1177(01)00511-7&quot;&gt;https://doi.org/10.1016/S0273-1177(01)00511-7&lt;/a&gt;, 2001.</mixed-citation>
</ref>
<ref id="ref46">
<label>46</label><mixed-citation publication-type="other" xlink:type="simple">Wright, D. M., Yeoman, T. K., and Chapman, P. J.: High-latitude HF Doppler observations of ULF waves. 1. Waves with large spatial scale sizes, Ann. Geophys., 15, 1548–1556, &lt;a href=&quot;http://dx.doi.org/10.1007/s00585-997-1548-2&quot;&gt;https://doi.org/10.1007/s00585-997-1548-2&lt;/a&gt;, 1997.</mixed-citation>
</ref>
<ref id="ref47">
<label>47</label><mixed-citation publication-type="other" xlink:type="simple">Zaspel, C. E., Mantha, J. H., Rapoport, Yu. G., and Grimalsky, V. V.: Evolution of solitons in magnetic thin films, Phys. Rev. B, 64, 064416, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevB.64.064416&quot;&gt;https://doi.org/10.1103/PhysRevB.64.064416&lt;/a&gt;, 2001.</mixed-citation>
</ref>
</ref-list>
</back>
</article>