<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article
PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20190208//EN"
       "JATS-journalpublishing1.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" article-type="research-article" dtd-version="1.4" xml:lang="en">
 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Solar-Terrestrial Physics</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Solar-Terrestrial Physics</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Solar-Terrestrial Physics</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="online">2500-0535</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">64587</article-id>
   <article-id pub-id-type="doi">10.12737/stp-93202304</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>Results of current research</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>Results of current research</subject>
    </subj-group>
    <subj-group>
     <subject>Results of current research</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Partial ponderomotive forces of Alfvén waves in near-Earth plasma</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Partial ponderomotive forces of Alfvén waves in near-Earth plasma</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Гульельми</surname>
       <given-names>Анатолий Владимирович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Guglielmi</surname>
       <given-names>Anatol Vladimirovich</given-names>
      </name>
     </name-alternatives>
     <email>guglielmi@mail.ru</email>
     <bio xml:lang="ru">
      <p>доктор физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Фейгин</surname>
       <given-names>Феликс Зеликович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Feygin</surname>
       <given-names>Felix Zelikovich</given-names>
      </name>
     </name-alternatives>
     <email>feygin@ifz.ru</email>
     <bio xml:lang="ru">
      <p>доктор физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Институт физики Земли им. О.Ю. Шмидта РАН</institution>
     <city>Москва</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Schmidt Institute of Physics of the Earth, RAS</institution>
     <city>Moscow</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Институт физики Земли им. О.Ю. Шмидта РАН</institution>
     <city>Москва</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Schmidt Institute of Physics of the Earth, RAS</institution>
     <city>Moscow</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2023-09-30T16:49:41+03:00">
    <day>30</day>
    <month>09</month>
    <year>2023</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2023-09-30T16:49:41+03:00">
    <day>30</day>
    <month>09</month>
    <year>2023</year>
   </pub-date>
   <volume>9</volume>
   <issue>3</issue>
   <fpage>25</fpage>
   <lpage>29</lpage>
   <history>
    <date date-type="received" iso-8601-date="2023-05-19T00:00:00+03:00">
     <day>19</day>
     <month>05</month>
     <year>2023</year>
    </date>
    <date date-type="accepted" iso-8601-date="2023-07-11T00:00:00+03:00">
     <day>11</day>
     <month>07</month>
     <year>2023</year>
    </date>
   </history>
   <self-uri xlink:href="https://zh-szf.ru/en/nauka/article/64587/view">https://zh-szf.ru/en/nauka/article/64587/view</self-uri>
   <abstract xml:lang="ru">
    <p>In the study of the ponderomotive action of Alfvén waves on near-Earth plasma, the general formula for ponderomotive forces, known in classical electrodynamics of continuous media, was previously used. The formula does not explicitly take into account the multi-ion composition of the plasma. Under the action of the waves, significant changes were found in macroscopic parameters — plasma density and velocity. Plasma in Earth’s magnetosphere contains ions with different charge-to-mass ratios. Besides hydrogen and helium ions, the plasma has an admixture of oxygen ions of ionospheric origin, as well as an admixture of other heavy ions. In this connection, a wide range of problems arise on the ponderomotive separation of ions of various types. To solve these problems, it is proposed to use partial ponderomotive forces and to describe the plasma not by hydrodynamic, but by quasi-hydrodynamic equations. In this paper, we discuss the derivation of partial forces for a traveling monochromatic Alfvén wave, and also suggest a method for deriving more general formulas by expanding the classical formula, known in macroscopic electrodynamic, into the sum of partial forces. The ponderomotive separation of ions is illustrated by the example of the problem for diffusion equilibrium of magnetospheric plasma. We propose a hypothesis that Alfvén waves redistribute plasma along geomagnetic field lines in such a way that the plasma at the magnetic field minima is characterized by an increased content of heavy ions. We suggest that a small admixture of heavy ions exists in the polar wind jet stream. The article is dedicated to the 80th anniversary of the discovery of Alfvén waves.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>In the study of the ponderomotive action of Alfvén waves on near-Earth plasma, the general formula for ponderomotive forces, known in classical electrodynamics of continuous media, was previously used. The formula does not explicitly take into account the multi-ion composition of the plasma. Under the action of the waves, significant changes were found in macroscopic parameters — plasma density and velocity. Plasma in Earth’s magnetosphere contains ions with different charge-to-mass ratios. Besides hydrogen and helium ions, the plasma has an admixture of oxygen ions of ionospheric origin, as well as an admixture of other heavy ions. In this connection, a wide range of problems arise on the ponderomotive separation of ions of various types. To solve these problems, it is proposed to use partial ponderomotive forces and to describe the plasma not by hydrodynamic, but by quasi-hydrodynamic equations. In this paper, we discuss the derivation of partial forces for a traveling monochromatic Alfvén wave, and also suggest a method for deriving more general formulas by expanding the classical formula, known in macroscopic electrodynamic, into the sum of partial forces. The ponderomotive separation of ions is illustrated by the example of the problem for diffusion equilibrium of magnetospheric plasma. We propose a hypothesis that Alfvén waves redistribute plasma along geomagnetic field lines in such a way that the plasma at the magnetic field minima is characterized by an increased content of heavy ions. We suggest that a small admixture of heavy ions exists in the polar wind jet stream. The article is dedicated to the 80th anniversary of the discovery of Alfvén waves.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>electrodynamics</kwd>
    <kwd>plasma</kwd>
    <kwd>Alfvén wave</kwd>
    <kwd>ponderomotive force</kwd>
    <kwd>geomagnetic field</kwd>
    <kwd>ambipolar diffusion</kwd>
    <kwd>height scale</kwd>
    <kwd>resonant acceleration</kwd>
    <kwd>polar wind</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>electrodynamics</kwd>
    <kwd>plasma</kwd>
    <kwd>Alfvén wave</kwd>
    <kwd>ponderomotive force</kwd>
    <kwd>geomagnetic field</kwd>
    <kwd>ambipolar diffusion</kwd>
    <kwd>height scale</kwd>
    <kwd>resonant acceleration</kwd>
    <kwd>polar wind</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">The work was carried out under the Government Assignment of Schmidt Institute of Physics of the Earth Schmidt RAS</funding-statement>
    <funding-statement xml:lang="en">The work was carried out under the Government Assignment of Schmidt Institute of Physics of the Earth Schmidt RAS</funding-statement>
   </funding-group>
  </article-meta>
 </front>
 <body>
  <p></p>
 </body>
 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Alfvén H. Existence of electromagnetic-hydrodynamic waves. Nature. 1942, vol. 150, pp. 405-406.</mixed-citation>
     <mixed-citation xml:lang="en">Alfvén H. Existence of electromagnetic-hydrodynamic waves. Nature. 1942, vol. 150, pp. 405-406.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Alfvén H. Cosmical electrodynamics International Ser. of Monographs on Physics, Oxford: Clarendon Press, 1950.</mixed-citation>
     <mixed-citation xml:lang="en">Alfvén H. Cosmical electrodynamics International Ser. of Monographs on Physics, Oxford: Clarendon Press, 1950.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Banks P.M., Holzer T.E. The polar wind. J. Geophys. Res. 1968, vol. 73 (21), pp. 6846-6854.</mixed-citation>
     <mixed-citation xml:lang="en">Banks P.M., Holzer T.E. The polar wind. J. Geophys. Res. 1968, vol. 73 (21), pp. 6846-6854.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Barnett R.L., Green D.L., Waters C.L., Lore J.D., Smithe D.N., Myra J.R., Lau C., Van Compernolle B., Vincena S. Ponderomotive force driven density modifications parallel to B0 on the LAPD. Phys. Plasmas. 2022, vol. 29, iss. 4, 042508. DOI: 10.1063/5.0071162.</mixed-citation>
     <mixed-citation xml:lang="en">Barnett R.L., Green D.L., Waters C.L., Lore J.D., Smithe D.N., Myra J.R., Lau C., Van Compernolle B., Vincena S. Ponderomotive force driven density modifications parallel to B0 on the LAPD. Phys. Plasmas. 2022, vol. 29, iss. 4, 042508. DOI: 10.1063/5.0071162.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Chugunin D.V., Klimenko M.V., Klimenko V.V. Characteristics of polar wind flows at altitudes of about 20000 km. Russian Journal of Physical Chemistry. 2018, vol. 12, no. 3, pp. 522-526. DOI: 10.1134/S1990793118030077</mixed-citation>
     <mixed-citation xml:lang="en">Chugunin D.V., Klimenko M.V., Klimenko V.V. Characteristics of polar wind flows at altitudes of about 20000 km. Russian Journal of Physical Chemistry. 2018, vol. 12, no. 3, pp. 522-526. DOI: 10.1134/S1990793118030077</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Espinoza-Troni J., Asenjo F.A., Moya P.S. Ponderomotive forces due to electron waves in unmagnetized plasmas described by Kappa distribution functions. Plasma Phys. Control. Fusion. 2023, vol. 65 (6), 06500. DOI: 10.1088/1361-6587/acc68a.</mixed-citation>
     <mixed-citation xml:lang="en">Espinoza-Troni J., Asenjo F.A., Moya P.S. Ponderomotive forces due to electron waves in unmagnetized plasmas described by Kappa distribution functions. Plasma Phys. Control. Fusion. 2023, vol. 65 (6), 06500. DOI: 10.1088/1361-6587/acc68a.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Feygin F.Z., Pokhotelov O.A., Pokhotelov D.O., Braysy T., Kangas J., Mursula K. Exo-plasmaspheric refilling due to ponderomotive forces induced by geomagnetic pulsations. J. Geophys. Res. 1997, vol. 102, pp. 4841-4845.</mixed-citation>
     <mixed-citation xml:lang="en">Feygin F.Z., Pokhotelov O.A., Pokhotelov D.O., Braysy T., Kangas J., Mursula K. Exo-plasmaspheric refilling due to ponderomotive forces induced by geomagnetic pulsations. J. Geophys. Res. 1997, vol. 102, pp. 4841-4845.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Feygin F.Z., Pokhotelov O.A., Pokhotelov D.O., Mursula K., Kangas J., Braysy T., Kerttula R. Effect of heavy ions on pondedromotive forces due to ion cyclotron waves. J. Geophys. Res. 1998, vol. 103, pp. 20481-20486.</mixed-citation>
     <mixed-citation xml:lang="en">Feygin F.Z., Pokhotelov O.A., Pokhotelov D.O., Mursula K., Kangas J., Braysy T., Kerttula R. Effect of heavy ions on pondedromotive forces due to ion cyclotron waves. J. Geophys. Res. 1998, vol. 103, pp. 20481-20486.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Ginzburg V.L. The Propagation of Electromagnetic Waves in Plasmas. Pergamon Press, 1970. 615 p.</mixed-citation>
     <mixed-citation xml:lang="en">Ginzburg V.L. The Propagation of Electromagnetic Waves in Plasmas. Pergamon Press, 1970. 615 p.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Ginzburg V.L. Theoretical Physics and Astrophysics. Moscow, Lenand Publ., 2020, 488 p. (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Ginzburg V.L. Theoretical Physics and Astrophysics. Moscow, Lenand Publ., 2020, 488 p. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Guglielmi A.V. MHD Waves in Near-Earth Plasma. Moscow, Nauka Publ., 1979, 139 p. (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Guglielmi A.V. MHD Waves in Near-Earth Plasma. Moscow, Nauka Publ., 1979, 139 p. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Guglielmi A.V. Ponderomotive forces in Earth’s core and magnetosphere. Izvestiya, Physics of the Solid Earth. 1992, no. 7, pp. 35-40. (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Guglielmi A.V. Ponderomotive forces in Earth’s core and magnetosphere. Izvestiya, Physics of the Solid Earth. 1992, no. 7, pp. 35-40. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Guglielmi A.V., Feygin F.Z. The effect of ponderomotive forces on Earth’s magnetosphere. 2018, no. 5, pp. 53-60. DOI: 10.1134/S1069351318050075. (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Guglielmi A.V., Feygin F.Z. The effect of ponderomotive forces on Earth’s magnetosphere. 2018, no. 5, pp. 53-60. DOI: 10.1134/S1069351318050075. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Landau L.D., Lifshitz E.M. Electrodynamics of Continious Media. Moscow, Fizmatlit Publ., 2003a, 656 p.</mixed-citation>
     <mixed-citation xml:lang="en">Landau L.D., Lifshitz E.M. Electrodynamics of Continious Media. Moscow, Fizmatlit Publ., 2003a, 656 p.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Landau L.D., Lifshitz E.M. The Classical Theory of Fields. Moscow, Fizmatlit Publ., 2003b, 536 p. (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Landau L.D., Lifshitz E.M. The Classical Theory of Fields. Moscow, Fizmatlit Publ., 2003b, 536 p. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B16">
    <label>16.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Lifshitz E.M. Pitaevsky L.P. Physical Kinetics. Moscow, Nauka Publ., 1979, 528 p. (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Lifshitz E.M. Pitaevsky L.P. Physical Kinetics. Moscow, Nauka Publ., 1979, 528 p. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B17">
    <label>17.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Nekrasov A.K., Feygin F.Z. Ponderomotive modification of multicomponent magnetospheric plasma due to electromagnetic ion cyclotron waves. Astrophys. Space Sci. 2013, vol. 346, pp. 203-212.</mixed-citation>
     <mixed-citation xml:lang="en">Nekrasov A.K., Feygin F.Z. Ponderomotive modification of multicomponent magnetospheric plasma due to electromagnetic ion cyclotron waves. Astrophys. Space Sci. 2013, vol. 346, pp. 203-212.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B18">
    <label>18.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Nishida A. Geomagnetic Diagnosis of the Magnetosphere. Moscow, Nauka Publ., 1980, 299 p. (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Nishida A. Geomagnetic Diagnosis of the Magnetosphere. Moscow, Nauka Publ., 1980, 299 p. (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B19">
    <label>19.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Potapov A.S., Guglielmi A.V. Upward acceleration of magnetospheric ions by oscillatory centrifugal force. Geomagnetism and Aeronomy. 2011, vol. 51, pp. 843-847.</mixed-citation>
     <mixed-citation xml:lang="en">Potapov A.S., Guglielmi A.V. Upward acceleration of magnetospheric ions by oscillatory centrifugal force. Geomagnetism and Aeronomy. 2011, vol. 51, pp. 843-847.</mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
