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<article article-type="research-article" dtd-version="1.3" 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" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2015-6-5-661-671</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-990</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>The motion of a charged particle in the field by a frequency-modulated electromagnetic wave</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Kopytov</surname><given-names>G. F.</given-names></name></name-alternatives><bio xml:lang="en"><p>Krasnodar</p></bio><email xlink:type="simple">g137@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Martynov</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Krasnodar</p></bio><email xlink:type="simple">martynov159@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Akintsov</surname><given-names>N. S.</given-names></name></name-alternatives><bio xml:lang="en"><p>Krasnodar</p></bio><email xlink:type="simple">akintsov777@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Kuban State University</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2015</year></pub-date><pub-date pub-type="epub"><day>15</day><month>08</month><year>2025</year></pub-date><volume>6</volume><issue>5</issue><fpage>661</fpage><lpage>671</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Kopytov G.F., Martynov A.A., Akintsov N.S., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Kopytov G.F., Martynov A.A., Akintsov N.S.</copyright-holder><copyright-holder xml:lang="en">Kopytov G.F., Martynov A.A., Akintsov N.S.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/990">https://nanojournal.ifmo.ru/jour/article/view/990</self-uri><abstract><p>In this article, the exact solutions of equations of motion for a charged particle in a frequency-modulated wave are presented. We performed an analysis of the results for the motion of a charged particle in the field of frequencymodulated electromagnetic waves. A point of interest was a solution for the equations of the motion for a charged particle in the field of a plane electromagnetic wave. We investigated the interaction of high intensity laser pulses with solid targets in relation to the practical development of multi-frequency lasers and laser modulation technology. This study was undertaken because of the wide practical application of high-temperature plasma formed on the surface of the target and the search for new modes of laser plasma interaction </p></abstract><kwd-group xml:lang="en"><kwd>charged particle</kwd><kwd>plane electromagnetic wave</kwd><kwd>modulation frequency</kwd><kwd>average kinetic energy</kwd><kwd>ultrashort laser pulse</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Mourou G., Tajima T., Bulanov S.V. Optics in the Relativistic Regime. Rev. Mod. Phys., 2006, 78, P. 309–371.</mixed-citation><mixed-citation xml:lang="en">Mourou G., Tajima T., Bulanov S.V. Optics in the Relativistic Regime. Rev. Mod. Phys., 2006, 78, P. 309–371.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Yariv A. Quantum Electronics and Nonlinear Optics. 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