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<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" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Journal of Communications Technology and Electronics</journal-id><journal-title-group><journal-title xml:lang="en">Journal of Communications Technology and Electronics</journal-title><trans-title-group xml:lang="ru"><trans-title>Радиотехника и электроника</trans-title></trans-title-group></journal-title-group><issn publication-format="print">0033-8494</issn><issn publication-format="electronic">3034-5901</issn><publisher><publisher-name xml:lang="en">The Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">650702</article-id><article-id pub-id-type="doi">10.31857/S0033849424030078</article-id><article-id pub-id-type="edn">JUZAEZ</article-id><article-categories><subj-group subj-group-type="toc-heading"><subject>ЭЛЕКТРОННАЯ И ИОННАЯ ОПТИКА</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">Studying the accuracy of geometrized models of ribbon electron beams</article-title><trans-title-group xml:lang="ru"><trans-title>Исследование точности геометризованных моделей плоских электронных пучков</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Sapronova</surname><given-names>T. M.</given-names></name><name xml:lang="ru"><surname>Сапронова</surname><given-names>Т. М.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>All-Russian Electrotechnical Institute</p></bio><bio xml:lang="ru"><p>ВЭИ</p></bio><email>red@cplire.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Syrovoy</surname><given-names>V. A.</given-names></name><name xml:lang="ru"><surname>Сыровой</surname><given-names>В. А.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><bio xml:lang="en"><p>All-Russian Electrotechnical Institute</p></bio><bio xml:lang="ru"><p>ВЭИ </p></bio><email>red@cplire.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Russian Federal Nuclear Center All-Russian Scientific Research Institute of Technical Physics named after academician E.I. Zababakhin</institution></aff><aff><institution xml:lang="ru">ВНИИТФ им. академ. Е.И. Забабахина”</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2024-03-14" publication-format="electronic"><day>14</day><month>03</month><year>2024</year></pub-date><volume>69</volume><issue>3</issue><fpage>260</fpage><lpage>287</lpage><history><date date-type="received" iso-8601-date="2025-01-31"><day>31</day><month>01</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2024, Russian Academy of Sciences</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2024, Российская академия наук</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="en">Russian Academy of Sciences</copyright-holder><copyright-holder xml:lang="ru">Российская академия наук</copyright-holder></permissions><self-uri xlink:href="https://innoscience.ru/0033-8494/article/view/650702">https://innoscience.ru/0033-8494/article/view/650702</self-uri><abstract xml:lang="en"><p>Using a set of standard exact solutions described by ordinary differential equations and elementary functions, geometrized models of plane electron beams in <italic>l</italic>-, and <italic>W</italic>-representations were studied. A comparison is made of the capabilities of the geometrized approach and the paraxial theory.</p></abstract><trans-abstract xml:lang="ru"><p>На наборе эталонных точных решений, описываемых обыкновенными дифференциальными уравнениями и элементарными функциями, исследованы геометризованные модели плоских электронных пучков в <italic>l</italic>-, φ- и <italic>W</italic>-представлениях. Проведено сопоставление возможностей геометризованного подхода и параксиальной теории.</p></trans-abstract><kwd-group xml:lang="en"><kwd>plane electron beams</kwd><kwd>geometrized models</kwd><kwd>reference exact solutions</kwd><kwd>geometrized approach</kwd><kwd>paraxial theory</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>плоские электронные пучки</kwd><kwd>геометризованные модели</kwd><kwd>эталонные точные решения</kwd><kwd>геометризованный подход</kwd><kwd>параксиальная теория</kwd></kwd-group><funding-group/></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Сыровой В.А. // Прикл. физика. 1997. № 2–3. С. 69.</mixed-citation></ref><ref id="B2"><label>2.</label><mixed-citation>Акимов П.И., Гаврилин А.А., Никитин А.П. и др. // РЭ. 2018. Т. 63. № 11. С. 1303.</mixed-citation></ref><ref id="B3"><label>3.</label><mixed-citation>Гамаюнов Ю.Г., Патрушева Е.В., Тореев А.И., Шаталина С.А. // РЭ. 2008. Т. 53. № 3. 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