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Cherenkov radiation - Wikipedia
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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Arbitrary_emission_angle"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Arbitrary emission angle</span> </div> </a> <ul id="toc-Arbitrary_emission_angle-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reverse_Cherenkov_effect" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Reverse_Cherenkov_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Reverse Cherenkov effect</span> </div> </a> <ul id="toc-Reverse_Cherenkov_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_vacuum" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_vacuum"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>In vacuum</span> </div> </a> <ul id="toc-In_vacuum-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collective_Cherenkov" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Collective_Cherenkov"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Collective Cherenkov</span> </div> </a> <ul id="toc-Collective_Cherenkov-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Characteristics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Characteristics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Characteristics</span> </div> </a> <ul id="toc-Characteristics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Uses" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Uses</span> </div> </a> <button aria-controls="toc-Uses-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Uses subsection</span> </button> <ul id="toc-Uses-sublist" class="vector-toc-list"> <li id="toc-Detection_of_labelled_biomolecules" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Detection_of_labelled_biomolecules"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Detection of labelled biomolecules</span> </div> </a> <ul id="toc-Detection_of_labelled_biomolecules-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Medical_imaging_of_radioisotopes_and_external_beam_radiotherapy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Medical_imaging_of_radioisotopes_and_external_beam_radiotherapy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Medical imaging of radioisotopes and external beam radiotherapy</span> </div> </a> <ul id="toc-Medical_imaging_of_radioisotopes_and_external_beam_radiotherapy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nuclear_reactors" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nuclear_reactors"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Nuclear reactors</span> </div> </a> <ul id="toc-Nuclear_reactors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Astrophysics_experiments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Astrophysics_experiments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Astrophysics experiments</span> </div> </a> <ul id="toc-Astrophysics_experiments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Particle_physics_experiments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Particle_physics_experiments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Particle physics experiments</span> </div> </a> <ul id="toc-Particle_physics_experiments-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Citations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Citations"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Citations</span> </div> </a> <ul id="toc-Citations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Cherenkov radiation</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 55 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-55" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">55 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Tscherenkow-Strahlung" title="Tscherenkow-Strahlung – Alemannic" lang="gsw" hreflang="gsw" data-title="Tscherenkow-Strahlung" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D8%B4%D8%B9%D8%A7%D8%B9_%D8%AA%D8%B4%D9%8A%D8%B1%D9%86%D9%83%D9%88%D9%81" title="إشعاع تشيرنكوف – Arabic" lang="ar" hreflang="ar" data-title="إشعاع تشيرنكوف" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%9A%E0%A7%87%E0%A6%B0%E0%A7%87%E0%A6%A8%E0%A6%95%E0%A6%AD_%E0%A6%AC%E0%A6%BF%E0%A6%95%E0%A6%BF%E0%A6%B0%E0%A6%A3" title="চেরেনকভ বিকিরণ – Bangla" lang="bn" hreflang="bn" data-title="চেরেনকভ বিকিরণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D1%84%D0%B5%D0%BA%D1%82_%D0%92%D0%B0%D0%B2%D1%96%D0%BB%D0%B0%D0%B2%D0%B0_%E2%80%94_%D0%A7%D0%B0%D1%80%D0%B0%D0%BD%D0%BA%D0%BE%D0%B2%D0%B0" title="Эфект Вавілава — Чаранкова – Belarusian" lang="be" hreflang="be" data-title="Эфект Вавілава — Чаранкова" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%BD%D0%B0_%D0%A7%D0%B5%D1%80%D0%B5%D0%BD%D0%BA%D0%BE%D0%B2" title="Ефект на Черенков – Bulgarian" lang="bg" hreflang="bg" data-title="Ефект на Черенков" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Radiaci%C3%B3_de_Txerenkov" title="Radiació de Txerenkov – Catalan" lang="ca" hreflang="ca" data-title="Radiació de Txerenkov" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C4%8Cerenkovovo_z%C3%A1%C5%99en%C3%AD" title="Čerenkovovo záření – Czech" lang="cs" hreflang="cs" data-title="Čerenkovovo záření" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Cherenkovstr%C3%A5ling" title="Cherenkovstråling – Danish" lang="da" hreflang="da" data-title="Cherenkovstråling" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Tscherenkow-Strahlung" title="Tscherenkow-Strahlung – German" lang="de" hreflang="de" data-title="Tscherenkow-Strahlung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/T%C5%A1erenkovi_kiirgus" title="Tšerenkovi kiirgus – Estonian" lang="et" hreflang="et" data-title="Tšerenkovi kiirgus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BA%CF%84%CE%B9%CE%BD%CE%BF%CE%B2%CE%BF%CE%BB%CE%AF%CE%B1_%CE%A4%CF%83%CE%B5%CF%81%CE%B5%CE%BD%CE%BA%CF%8C%CF%86" title="Ακτινοβολία Τσερενκόφ – Greek" lang="el" hreflang="el" data-title="Ακτινοβολία Τσερενκόφ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Radiaci%C3%B3n_de_Cherenkov" title="Radiación de Cherenkov – Spanish" lang="es" hreflang="es" data-title="Radiación de Cherenkov" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/%C4%88erenkov-radiado" title="Ĉerenkov-radiado – Esperanto" lang="eo" hreflang="eo" data-title="Ĉerenkov-radiado" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Txerenkoven_erradiazio" title="Txerenkoven erradiazio – Basque" lang="eu" hreflang="eu" data-title="Txerenkoven erradiazio" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%A7%D8%A8%D8%B4_%DA%86%D8%B1%D9%86%DA%A9%D9%88%D9%81" title="تابش چرنکوف – Persian" lang="fa" hreflang="fa" data-title="تابش چرنکوف" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Effet_Tcherenkov" title="Effet Tcherenkov – French" lang="fr" hreflang="fr" data-title="Effet Tcherenkov" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Rada%C3%ADocht_%C4%8Cerenkov" title="Radaíocht Čerenkov – Irish" lang="ga" hreflang="ga" data-title="Radaíocht Čerenkov" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Radiaci%C3%B3n_de_Cerenkov" title="Radiación de Cerenkov – Galician" lang="gl" hreflang="gl" data-title="Radiación de Cerenkov" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%B2%B4%EB%A0%8C%EC%BD%94%ED%94%84_%ED%9A%A8%EA%B3%BC" title="체렌코프 효과 – Korean" lang="ko" hreflang="ko" data-title="체렌코프 효과" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8E%D5%A1%D5%BE%D5%AB%D5%AC%D5%B8%D5%BE-%D5%89%D5%A5%D6%80%D5%A5%D5%B6%D5%AF%D5%B8%D5%BE%D5%AB_%D5%A7%D6%86%D5%A5%D5%AF%D5%BF" title="Վավիլով-Չերենկովի էֆեկտ – Armenian" lang="hy" hreflang="hy" data-title="Վավիլով-Չերենկովի էֆեկտ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A5%87%E0%A4%B0%E0%A5%87%E0%A4%A8%E0%A5%8D%E0%A4%95%E0%A5%8B%E0%A4%B5_%E0%A4%B5%E0%A4%BF%E0%A4%95%E0%A4%BF%E0%A4%B0%E0%A4%A3" title="सेरेन्कोव विकिरण – Hindi" lang="hi" hreflang="hi" data-title="सेरेन्कोव विकिरण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/%C4%8Cerenkovljevo_zra%C4%8Denje" title="Čerenkovljevo zračenje – Croatian" lang="hr" hreflang="hr" data-title="Čerenkovljevo zračenje" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Radiasi_Cherenkov" title="Radiasi Cherenkov – Indonesian" lang="id" hreflang="id" data-title="Radiasi Cherenkov" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Effetto_%C4%8Cerenkov" title="Effetto Čerenkov – Italian" lang="it" hreflang="it" data-title="Effetto Čerenkov" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A8%D7%99%D7%A0%D7%AA_%D7%A6%27%D7%A8%D7%A0%D7%A7%D7%95%D7%91" title="קרינת צ'רנקוב – Hebrew" lang="he" hreflang="he" data-title="קרינת צ'רנקוב" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Radiatio_%C4%8Cerenkov" title="Radiatio Čerenkov – Latin" lang="la" hreflang="la" data-title="Radiatio Čerenkov" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/%C4%8Cerenkova%E2%80%94Vavilova_starojums" title="Čerenkova—Vavilova starojums – Latvian" lang="lv" hreflang="lv" data-title="Čerenkova—Vavilova starojums" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/%C4%8Cerenkovo_spinduliavimas" title="Čerenkovo spinduliavimas – Lithuanian" lang="lt" hreflang="lt" data-title="Čerenkovo spinduliavimas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Cserenkov-effektus" title="Cserenkov-effektus – Hungarian" lang="hu" hreflang="hu" data-title="Cserenkov-effektus" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%9A%E0%B5%86%E0%B4%B1%E0%B5%8D%E0%B4%AF%E0%B5%86%E0%B5%BB%E2%80%8C%E0%B4%95%E0%B5%8B%E0%B4%AB%E0%B5%8D_%E0%B4%B5%E0%B4%BF%E0%B4%95%E0%B4%BF%E0%B4%B0%E0%B4%A3%E0%B4%82" title="ചെറ്യെൻകോഫ് വികിരണം – Malayalam" lang="ml" hreflang="ml" data-title="ചെറ്യെൻകോഫ് വികിരണം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sinaran_Cherenkov" title="Sinaran Cherenkov – Malay" lang="ms" hreflang="ms" data-title="Sinaran Cherenkov" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Tsjerenkoveffect" title="Tsjerenkoveffect – Dutch" lang="nl" hreflang="nl" data-title="Tsjerenkoveffect" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%81%E3%82%A7%E3%83%AC%E3%83%B3%E3%82%B3%E3%83%95%E6%94%BE%E5%B0%84" title="チェレンコフ放射 – Japanese" lang="ja" hreflang="ja" data-title="チェレンコフ放射" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Tsjerenkov-str%C3%A5ling" title="Tsjerenkov-stråling – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Tsjerenkov-stråling" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Tsjerenkovstr%C3%A5ling" title="Tsjerenkovstråling – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Tsjerenkovstråling" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Cherenkov-Vavilov_nurlanishi" title="Cherenkov-Vavilov nurlanishi – Uzbek" lang="uz" hreflang="uz" data-title="Cherenkov-Vavilov nurlanishi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Promieniowanie_Czerenkowa" title="Promieniowanie Czerenkowa – Polish" lang="pl" hreflang="pl" data-title="Promieniowanie Czerenkowa" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Efeito_Tcherenkov" title="Efeito Tcherenkov – Portuguese" lang="pt" hreflang="pt" data-title="Efeito Tcherenkov" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Efectul_Cerenkov" title="Efectul Cerenkov – Romanian" lang="ro" hreflang="ro" data-title="Efectul Cerenkov" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D1%84%D1%84%D0%B5%D0%BA%D1%82_%D0%92%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE%D0%B2%D0%B0_%E2%80%94_%D0%A7%D0%B5%D1%80%D0%B5%D0%BD%D0%BA%D0%BE%D0%B2%D0%B0" title="Эффект Вавилова — Черенкова – Russian" lang="ru" hreflang="ru" data-title="Эффект Вавилова — Черенкова" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Cherenkov_radiation" title="Cherenkov radiation – Scots" lang="sco" hreflang="sco" data-title="Cherenkov radiation" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Cherenkov_radiation" title="Cherenkov radiation – Simple English" lang="en-simple" hreflang="en-simple" data-title="Cherenkov radiation" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C4%8Cerenkovovo_%C5%BEiarenie" title="Čerenkovovo žiarenie – Slovak" lang="sk" hreflang="sk" data-title="Čerenkovovo žiarenie" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Pojav_%C4%8Cerenkova" title="Pojav Čerenkova – Slovenian" lang="sl" hreflang="sl" data-title="Pojav Čerenkova" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B5%D0%BD%D0%BA%D0%BE%D0%B2%D1%99%D0%B5%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D0%B0%D1%82" title="Черенковљев ефекат – Serbian" lang="sr" hreflang="sr" data-title="Черенковљев ефекат" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/%C4%8Cerenkovljevo_zra%C4%8Denje" title="Čerenkovljevo zračenje – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Čerenkovljevo zračenje" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/T%C5%A1erenkovin_s%C3%A4teily" title="Tšerenkovin säteily – Finnish" lang="fi" hreflang="fi" data-title="Tšerenkovin säteily" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Tjerenkovstr%C3%A5lning" title="Tjerenkovstrålning – Swedish" lang="sv" hreflang="sv" data-title="Tjerenkovstrålning" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%BE%E0%AE%B5%E0%AE%BF%E0%AE%B2%E0%AF%8A%E0%AE%B5%E0%AF%8D-%E0%AE%9A%E0%AF%86%E0%AE%B0%E0%AE%A9%E0%AF%8D%E0%AE%95%E0%AF%8B%E0%AE%B5%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%B3%E0%AF%88%E0%AE%B5%E0%AF%81" title="வாவிலொவ்-செரன்கோவ் விளைவு – Tamil" lang="ta" hreflang="ta" data-title="வாவிலொவ்-செரன்கோவ் விளைவு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B5%D0%BD%D0%BA%D0%BE%D0%B2_%D0%BD%D1%83%D1%80%D0%BB%D0%B0%D0%BD%D1%8B%D1%88%D1%8B" title="Черенков нурланышы – Tatar" lang="tt" hreflang="tt" data-title="Черенков нурланышы" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B9%81%E0%B8%9C%E0%B9%88%E0%B8%A3%E0%B8%B1%E0%B8%87%E0%B8%AA%E0%B8%B5%E0%B9%80%E0%B8%8A%E0%B9%80%E0%B8%A3%E0%B8%99%E0%B8%84%E0%B8%AD%E0%B8%9F" title="การแผ่รังสีเชเรนคอฟ – Thai" lang="th" hreflang="th" data-title="การแผ่รังสีเชเรนคอฟ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%87erenkov_radyasyonu" title="Çerenkov radyasyonu – Turkish" lang="tr" hreflang="tr" data-title="Çerenkov radyasyonu" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B5%D1%80%D0%B5%D0%BD%D0%BA%D0%BE%D0%B2%D1%81%D1%8C%D0%BA%D0%B5_%D0%B2%D0%B8%D0%BF%D1%80%D0%BE%D0%BC%D1%96%D0%BD%D1%8E%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F" title="Черенковське випромінювання – Ukrainian" lang="uk" hreflang="uk" data-title="Черенковське випромінювання" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/B%E1%BB%A9c_x%E1%BA%A1_Cherenkov" title="Bức xạ Cherenkov – Vietnamese" lang="vi" hreflang="vi" data-title="Bức xạ Cherenkov" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%A5%91%E5%BF%8D%E5%8F%AF%E5%A4%AB%E8%BC%BB%E5%B0%84" title="契忍可夫輻射 – Chinese" lang="zh" 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Electromagnetic radiation from a charged particle in a medium</div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Advanced_Test_Reactor.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Advanced_Test_Reactor.jpg/220px-Advanced_Test_Reactor.jpg" decoding="async" width="220" height="289" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Advanced_Test_Reactor.jpg/330px-Advanced_Test_Reactor.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Advanced_Test_Reactor.jpg/440px-Advanced_Test_Reactor.jpg 2x" data-file-width="2791" data-file-height="3668" /></a><figcaption>Cherenkov radiation glowing in the core of the <a href="/wiki/Advanced_Test_Reactor" title="Advanced Test Reactor">Advanced Test Reactor</a> at <a href="/wiki/Idaho_National_Laboratory" title="Idaho National Laboratory">Idaho National Laboratory</a></figcaption></figure> <p><b>Cherenkov radiation</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/tʃ/: 'ch' in 'China'">tʃ</span><span title="/ə/: 'a' in 'about'">ə</span><span title="/ˈ/: primary stress follows">ˈ</span><span title="'r' in 'rye'">r</span><span title="/ɛ/: 'e' in 'dress'">ɛ</span><span title="/ŋ/: 'ng' in 'sing'">ŋ</span><span title="'k' in 'kind'">k</span><span title="/ɒ/: 'o' in 'body'">ɒ</span><span title="'f' in 'find'">f</span></span>/</a></span></span><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>) (also known as <b>Čerenkov radiation</b><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>) is <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a> emitted when a <a href="/wiki/Charged_particle" title="Charged particle">charged particle</a> (such as an <a href="/wiki/Electron" title="Electron">electron</a>) passes through a <a href="/wiki/Dielectric" title="Dielectric">dielectric</a> medium (such as <a href="/wiki/Distilled_water" title="Distilled water">distilled water</a>) at a speed greater than the <a href="/wiki/Phase_velocity" title="Phase velocity">phase velocity</a> (speed of <a href="/wiki/Wave_propagation" class="mw-redirect" title="Wave propagation">propagation</a> of a <a href="/wiki/Wavefront" title="Wavefront">wavefront</a> in a medium) of <a href="/wiki/Speed_of_light" title="Speed of light">light</a> in that medium.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> A classic example of Cherenkov radiation is the characteristic blue glow of an underwater <a href="/wiki/Nuclear_reactor" title="Nuclear reactor">nuclear reactor</a>. Its cause is similar to the cause of a <a href="/wiki/Sonic_boom" title="Sonic boom">sonic boom</a>, the sharp sound heard when faster-than-sound movement occurs. The phenomenon is named after Soviet physicist <a href="/wiki/Pavel_Cherenkov" title="Pavel Cherenkov">Pavel Cherenkov</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The radiation is named after the <a href="/wiki/Soviet_Union" title="Soviet Union">Soviet</a> scientist Pavel Cherenkov, the 1958 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize</a> winner, who was the first to detect it experimentally under the supervision of <a href="/wiki/Sergey_Vavilov" title="Sergey Vavilov">Sergey Vavilov</a> at the <a href="/wiki/Lebedev_Physical_Institute" title="Lebedev Physical Institute">Lebedev Institute</a> in 1934. Therefore, it is also known as <b>Vavilov–Cherenkov radiation</b>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Cherenkov saw a faint bluish light around a radioactive preparation in water during experiments. His doctorate thesis was on luminescence of uranium salt solutions that were excited by <a href="/wiki/Gamma_ray" title="Gamma ray">gamma rays</a> instead of less energetic visible light, as done commonly. He discovered the <a href="/wiki/Anisotropy" title="Anisotropy">anisotropy</a> of the radiation and came to the conclusion that the bluish glow was not a fluorescent phenomenon. </p><p>A theory of this effect was later developed in 1937<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> within the framework of <a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a>'s <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> theory by Cherenkov's colleagues <a href="/wiki/Igor_Tamm" title="Igor Tamm">Igor Tamm</a> and <a href="/wiki/Ilya_Frank" title="Ilya Frank">Ilya Frank</a>, who also shared the 1958 Nobel Prize. </p><p>Cherenkov radiation as conical wavefronts had been theoretically predicted by the <a href="/wiki/England" title="England">English</a> <a href="/wiki/Polymath" title="Polymath">polymath</a> <a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Oliver Heaviside</a> in papers published between 1888 and 1889<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> and by <a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Arnold Sommerfeld</a> in 1904,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> but both had been quickly dismissed following the relativity theory's restriction of <a href="/wiki/Faster-than-light" title="Faster-than-light">superluminal</a> particles until the 1970s.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Marie_Curie" title="Marie Curie">Marie Curie</a> observed a pale blue light in a highly concentrated radium solution in 1910,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> but did not investigate its source. In 1926, the French radiotherapist Lucien Mallet described the luminous radiation of <a href="/wiki/Radium" title="Radium">radium</a> irradiating water having a continuous spectrum.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In 2019, a team of researchers from <a href="/wiki/Dartmouth_College" title="Dartmouth College">Dartmouth's</a> and <a href="/wiki/Dartmouth%E2%80%93Hitchcock_Medical_Center" title="Dartmouth–Hitchcock Medical Center">Dartmouth-Hitchcock</a>'s <a href="/wiki/Norris_Cotton_Cancer_Center" class="mw-redirect" title="Norris Cotton Cancer Center">Norris Cotton Cancer Center</a> discovered Cherenkov light being generated in the <a href="/wiki/Vitreous_humor" class="mw-redirect" title="Vitreous humor">vitreous humor</a> of patients undergoing <a href="/wiki/Radiotherapy" class="mw-redirect" title="Radiotherapy">radiotherapy</a>. The light was observed using a camera imaging system called a CDose, which is specially designed to view light emissions from biological systems.<sup id="cite_ref-eureka_11-0" class="reference"><a href="#cite_note-eureka-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Tendler_12-0" class="reference"><a href="#cite_note-Tendler-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> For decades, patients had reported phenomena such as "flashes of bright or blue light"<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> when receiving radiation treatments for brain cancer, but the effects had never been experimentally observed.<sup id="cite_ref-Tendler_12-1" class="reference"><a href="#cite_note-Tendler-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Physical_origin">Physical origin</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=2" title="Edit section: Physical origin"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Basics">Basics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=3" title="Edit section: Basics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> <i>in <a href="/wiki/Vacuum" title="Vacuum">vacuum</a></i> is a <a href="/wiki/Physical_constants" class="mw-redirect" title="Physical constants">universal constant</a> (<span class="nowrap"><i>c</i> = 299,792,458 m/s</span>), the speed in a material may be significantly less, as it is perceived to be slowed by the medium. For example, in <a href="/wiki/Water" title="Water">water</a> it is only 0.75<span style="visibility:hidden; color:transparent; padding-left:2px">‍</span><i>c</i>. <a href="/wiki/Matter" title="Matter">Matter</a> can accelerate to a velocity higher than this (although still less than <i>c</i>, the speed of light in vacuum) during nuclear reactions and in <a href="/wiki/Particle_accelerator" title="Particle accelerator">particle accelerators</a>. Cherenkov radiation results when a charged particle, most commonly an <a href="/wiki/Electron" title="Electron">electron</a>, travels through a <a href="/wiki/Dielectric" title="Dielectric">dielectric</a> (can be polarized electrically) medium with a speed greater than light's speed in that medium. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cherenkov_Radiation_During_Maintainence.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Cherenkov_Radiation_During_Maintainence.jpg/220px-Cherenkov_Radiation_During_Maintainence.jpg" decoding="async" width="220" height="391" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Cherenkov_Radiation_During_Maintainence.jpg/330px-Cherenkov_Radiation_During_Maintainence.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Cherenkov_Radiation_During_Maintainence.jpg/440px-Cherenkov_Radiation_During_Maintainence.jpg 2x" data-file-width="1170" data-file-height="2080" /></a><figcaption>Cherenkov radiation during Scheduled Refueling and Maintenance Outage of <a href="/wiki/Arkansas_Nuclear_One" title="Arkansas Nuclear One">Arkansas Nuclear One</a> Unit 2 (ANO-2)</figcaption></figure> <p>The effect can be intuitively described in the following way. From classical physics, it is known that accelerating charged particles emit <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">EM</a> waves and via <a href="/wiki/Huygens%E2%80%93Fresnel_principle" title="Huygens–Fresnel principle">Huygens' principle</a> these waves will form spherical wavefronts which propagate with the <a href="/wiki/Phase_velocity" title="Phase velocity">phase velocity</a> of that medium (i.e. the speed of light in that medium given by <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c/n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c/n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90185828e9033f8d56a91a72415e51117b36b35b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.564ex; height:2.843ex;" alt="{\displaystyle c/n}"></span>, for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>, the <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a>). When any charged particle passes through a medium, the particles of the medium will polarize around it in response. The charged particle excites the molecules in the polarizable medium and on returning to their <a href="/wiki/Ground_state" title="Ground state">ground state</a>, the molecules re-emit the energy given to them to achieve excitation as photons. These photons form the spherical wavefronts which can be seen originating from the moving particle. If <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{p}}<c/n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mo><</mo> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{p}}<c/n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b2e47da5b108024367dada37b0b3bbf16dcb0a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.936ex; height:3.009ex;" alt="{\displaystyle v_{\text{p}}<c/n}"></span>, that is the velocity of the charged particle is less than that of the speed of light in the medium, then the polarization field which forms around the moving particle is usually symmetric. The corresponding emitted <a href="/wiki/Wavefront" title="Wavefront">wavefronts</a> may be bunched up, but they do not coincide or cross, and there are therefore no interference effects to consider. In the reverse situation, i.e. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{p}}>c/n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mo>></mo> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{p}}>c/n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c5e89e639baa481d4cb13fcc10bb45debd8f3e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.936ex; height:3.009ex;" alt="{\displaystyle v_{\text{p}}>c/n}"></span>, the <a href="/wiki/Polarization_(waves)" title="Polarization (waves)">polarization</a> field is asymmetric along the direction of motion of the particle, as the particles of the medium do not have enough time to recover to their "normal" randomized states. This results in overlapping waveforms (as in the animation) and <a href="/wiki/Wave_interference" title="Wave interference">constructive interference</a> leads to an observed cone-like light signal at a characteristic angle: Cherenkov light. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Cherenkov_radiation-animation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Cherenkov_radiation-animation.gif/220px-Cherenkov_radiation-animation.gif" decoding="async" width="220" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Cherenkov_radiation-animation.gif/330px-Cherenkov_radiation-animation.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Cherenkov_radiation-animation.gif/440px-Cherenkov_radiation-animation.gif 2x" data-file-width="467" data-file-height="260" /></a><figcaption>Animation of Cherenkov radiation</figcaption></figure> <p>A common analogy is the <a href="/wiki/Sonic_boom" title="Sonic boom">sonic boom</a> of a <a href="/wiki/Supersonic" class="mw-redirect" title="Supersonic">supersonic</a> <a href="/wiki/Aircraft" title="Aircraft">aircraft</a>. The <a href="/wiki/Sound" title="Sound">sound</a> waves generated by the aircraft travel at the speed of sound, which is slower than the aircraft, and cannot propagate forward from the aircraft, instead forming a conical <a href="/wiki/Shock_wave" title="Shock wave">shock front</a>. In a similar way, a charged particle can generate a "shock wave" of visible light as it travels through an insulator. </p><p>The velocity that must be exceeded is the <a href="/wiki/Phase_velocity" title="Phase velocity">phase velocity</a> of light rather than the <a href="/wiki/Group_velocity" title="Group velocity">group velocity</a> of light. The phase velocity can be altered dramatically by using a periodic medium, and in that case one can even achieve Cherenkov radiation with <i>no</i> minimum particle velocity, a phenomenon known as the <a href="/wiki/Smith%E2%80%93Purcell_effect" title="Smith–Purcell effect">Smith–Purcell effect</a>. In a more complex periodic medium, such as a <a href="/wiki/Photonic_crystal" title="Photonic crystal">photonic crystal</a>, one can also obtain a variety of other anomalous Cherenkov effects, such as radiation in a backwards direction (see below) whereas ordinary Cherenkov radiation forms an acute angle with the particle velocity.<sup id="cite_ref-Luo03_14-0" class="reference"><a href="#cite_note-Luo03-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Reactor-core-from-above-1400-opt_tcm18-278435.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Reactor-core-from-above-1400-opt_tcm18-278435.jpg/220px-Reactor-core-from-above-1400-opt_tcm18-278435.jpg" decoding="async" width="220" height="268" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Reactor-core-from-above-1400-opt_tcm18-278435.jpg/330px-Reactor-core-from-above-1400-opt_tcm18-278435.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Reactor-core-from-above-1400-opt_tcm18-278435.jpg/440px-Reactor-core-from-above-1400-opt_tcm18-278435.jpg 2x" data-file-width="657" data-file-height="800" /></a><figcaption>Cherenkov radiation in the <a href="/wiki/University_of_Massachusetts_Lowell_Radiation_Laboratory" title="University of Massachusetts Lowell Radiation Laboratory">University of Massachusetts Lowell Radiation Laboratory</a></figcaption></figure> <p>In their original work on the theoretical foundations of Cherenkov radiation, Tamm and Frank wrote, "This peculiar radiation can evidently not be explained by any common mechanism such as the interaction of the fast electron with individual atom or as radiative scattering of electrons on atomic nuclei. On the other hand, the phenomenon can be explained both qualitatively and quantitatively if one takes into account the fact that an electron moving in a medium does radiate light even if it is moving uniformly provided that its velocity is greater than the velocity of light in the medium."<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Emission_angle">Emission angle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=4" title="Edit section: Emission angle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Cherenkov.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Cherenkov.svg/220px-Cherenkov.svg.png" decoding="async" width="220" height="204" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Cherenkov.svg/330px-Cherenkov.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Cherenkov.svg/440px-Cherenkov.svg.png 2x" data-file-width="378" data-file-height="351" /></a><figcaption>The geometry of the Cherenkov radiation shown for the ideal case of no dispersion.</figcaption></figure> <p>In the figure on the geometry, the particle (red arrow) travels in a medium with speed <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c597064a184e56328af49003c920c966e0d160c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.274ex; height:2.343ex;" alt="{\displaystyle v_{\text{p}}}"></span> such that <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {c}{n}}<v_{\text{p}}<c,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>n</mi> </mfrac> </mrow> <mo><</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mo><</mo> <mi>c</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {c}{n}}<v_{\text{p}}<c,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65de91982018ad991c82946ad4abf3211896418d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.355ex; height:4.676ex;" alt="{\displaystyle {\frac {c}{n}}<v_{\text{p}}<c,}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is <a href="/wiki/Speed_of_light_in_vacuum" class="mw-redirect" title="Speed of light in vacuum">speed of light in vacuum</a>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> is the <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a> of the medium. If the medium is water, the condition is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 0.75c<v_{\text{p}}<c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0.75</mn> <mi>c</mi> <mo><</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mo><</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0.75c<v_{\text{p}}<c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3bfe41dd8e02eecca4b2428f7da0cf0f1b623872" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.619ex; height:2.843ex;" alt="{\displaystyle 0.75c<v_{\text{p}}<c}"></span>, since <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\approx 1.33}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≈<!-- ≈ --></mo> <mn>1.33</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\approx 1.33}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01c14bbcc9a2948ab0a2e1dc51c506a63f20426f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.627ex; height:2.176ex;" alt="{\displaystyle n\approx 1.33}"></span> for water at 20 °C. </p><p>We define the ratio between the speed of the particle and the speed of light as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta ={\frac {v_{\text{p}}}{c}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β<!-- β --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta ={\frac {v_{\text{p}}}{c}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f48a51faaa3183534251bd94252343b462ae5ca" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:8.187ex; height:5.009ex;" alt="{\displaystyle \beta ={\frac {v_{\text{p}}}{c}}.}"></span> The emitted <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">light waves</a> (denoted by blue arrows) travel at speed <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{em}}={\frac {c}{n}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>em</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>n</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{em}}={\frac {c}{n}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fa9d3315c1b0985ed16271c0a9ad7ca664a481f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.435ex; height:4.676ex;" alt="{\displaystyle v_{\text{em}}={\frac {c}{n}}.}"></span> </p><p>The left corner of the triangle represents the location of the superluminal particle at some initial moment (<span class="nowrap"><i>t</i> = 0</span>). The right corner of the triangle is the location of the particle at some later time t. In the given time <i>t</i>, the particle travels the distance <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{\text{p}}=v_{\text{p}}t=\beta \,ct}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mi>t</mi> <mo>=</mo> <mi>β<!-- β --></mi> <mspace width="thinmathspace" /> <mi>c</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{\text{p}}=v_{\text{p}}t=\beta \,ct}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cb980fd5a4f6f50e028acf803cf727293d9e4a3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.352ex; height:2.843ex;" alt="{\displaystyle x_{\text{p}}=v_{\text{p}}t=\beta \,ct}"></span> whereas the emitted electromagnetic waves are constricted to travel the distance <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{\text{em}}=v_{\text{em}}t={\frac {c}{n}}t.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>em</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>em</mtext> </mrow> </msub> <mi>t</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <mi>n</mi> </mfrac> </mrow> <mi>t</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{\text{em}}=v_{\text{em}}t={\frac {c}{n}}t.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f1ce6096afd7c7f6bd2d21b776c4d14c4bc0ad3" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.873ex; height:4.676ex;" alt="{\displaystyle x_{\text{em}}=v_{\text{em}}t={\frac {c}{n}}t.}"></span> </p><p>So the emission angle results in <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \theta ={\frac {1}{n\beta }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mi>β<!-- β --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \theta ={\frac {1}{n\beta }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0107b3d0767cb06d5b82432fa80bbea33df22461" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.25ex; height:5.676ex;" alt="{\displaystyle \cos \theta ={\frac {1}{n\beta }}}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Arbitrary_emission_angle">Arbitrary emission angle</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=5" title="Edit section: Arbitrary emission angle"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cherenkov radiation can also radiate in an arbitrary direction using properly engineered one dimensional <a href="/wiki/Metamaterial" title="Metamaterial">metamaterials</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The latter is designed to introduce a gradient of phase retardation along the trajectory of the fast travelling particle (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d\phi /dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>ϕ<!-- ϕ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\phi /dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b239ace67a2d97c2bf80183ccdb220f7a8eebc61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.309ex; height:2.843ex;" alt="{\displaystyle d\phi /dx}"></span>), reversing or steering Cherenkov emission at arbitrary angles given by the generalized relation: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \theta ={\frac {1}{n\beta }}+{\frac {n}{k_{0}}}\cdot {\frac {d\phi }{dx}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>n</mi> <mi>β<!-- β --></mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>n</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>ϕ<!-- ϕ --></mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \theta ={\frac {1}{n\beta }}+{\frac {n}{k_{0}}}\cdot {\frac {d\phi }{dx}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5517aa1e5e28ee140891789a1a7e1e2897667aa" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.309ex; height:5.843ex;" alt="{\displaystyle \cos \theta ={\frac {1}{n\beta }}+{\frac {n}{k_{0}}}\cdot {\frac {d\phi }{dx}}}"></span> </p><p>Note that since this ratio is independent of time, one can take arbitrary times and achieve <a href="/wiki/Similarity_(geometry)" title="Similarity (geometry)">similar triangles</a>. The angle stays the same, meaning that subsequent waves generated between the initial time <span class="nowrap"><i>t</i> = 0</span> and final time <i>t</i> will form similar triangles with coinciding right endpoints to the one shown. </p> <div class="mw-heading mw-heading3"><h3 id="Reverse_Cherenkov_effect">Reverse Cherenkov effect</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=6" title="Edit section: Reverse Cherenkov effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A reverse Cherenkov effect can be experienced using materials called negative-index <a href="/wiki/Metamaterial" title="Metamaterial">metamaterials</a> (materials with a subwavelength microstructure that gives them an effective "average" property very different from their constituent materials, in this case having negative <a href="/wiki/Permittivity" title="Permittivity">permittivity</a> and negative <a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">permeability</a>). This means that, when a charged particle (usually electrons) passes through a medium at a speed greater than the phase velocity of light in that medium, that particle emits trailing radiation from its progress through the medium rather than in front of it (as is the case in normal materials with, both permittivity and permeability positive).<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> One can also obtain such reverse-cone Cherenkov radiation in non-metamaterial periodic media where the periodic structure is on the same scale as the wavelength, so it cannot be treated as an effectively homogeneous metamaterial.<sup id="cite_ref-Luo03_14-1" class="reference"><a href="#cite_note-Luo03-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="In_vacuum">In vacuum</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=7" title="Edit section: In vacuum"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Cherenkov effect can occur in vacuum.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> In a slow-wave structure, like in a <a href="/wiki/Traveling-wave_tube" title="Traveling-wave tube">traveling-wave tube</a> (TWT), the <a href="/wiki/Phase_velocity" title="Phase velocity">phase velocity</a> decreases and the velocity of charged particles can exceed the phase velocity while remaining lower than <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span>. In such a system, this effect can be derived from conservation of the energy and momentum where the momentum of a <a href="/wiki/Photon" title="Photon">photon</a> should be <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\hbar \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi class="MJX-variant">ℏ<!-- ℏ --></mi> <mi>β<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\hbar \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/808e88a516cd633249ab865b1c22a2d377d5ca00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:6.996ex; height:2.509ex;" alt="{\displaystyle p=\hbar \beta }"></span> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>β<!-- β --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \beta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="{\displaystyle \beta }"></span> is <a href="/wiki/Phase_constant" class="mw-redirect" title="Phase constant">phase constant</a>)<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> rather than the <a href="/wiki/De_Broglie_relation" class="mw-redirect" title="De Broglie relation">de Broglie relation</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=\hbar k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <mi class="MJX-variant">ℏ<!-- ℏ --></mi> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=\hbar k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24fee69175538303b28ac54e907baf53d0a58dbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:6.875ex; height:2.509ex;" alt="{\displaystyle p=\hbar k}"></span>. This type of radiation (VCR) is used to generate high-power microwaves.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Collective_Cherenkov">Collective Cherenkov</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=8" title="Edit section: Collective Cherenkov"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Radiation with the same properties of typical Cherenkov radiation can be created by structures of electric current that travel faster than light. <sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> By manipulating density profiles in <a href="/wiki/Plasma_acceleration" title="Plasma acceleration">plasma acceleration</a> setups, structures up to nanocoulombs of <a href="/wiki/Charge_density" title="Charge density">charge</a> are created and may travel faster than the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> and emit optical shocks at the Cherenkov angle. Electrons are still subluminal, hence the electrons that compose the structure at a time <span class="nowrap"><i>t</i> = <i>t</i><sub>0</sub></span> are different from the electrons in the structure at a time <span class="nowrap"><i>t</i> > <i>t</i><sub>0</sub></span>. </p> <div class="mw-heading mw-heading2"><h2 id="Characteristics">Characteristics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=9" title="Edit section: Characteristics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Frequency_spectrum" class="mw-redirect" title="Frequency spectrum">frequency spectrum</a> of Cherenkov radiation by a particle is given by the <a href="/wiki/Frank%E2%80%93Tamm_formula" title="Frank–Tamm formula">Frank–Tamm formula</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d^{2}E}{dx\,d\omega }}={\frac {q^{2}}{4\pi }}\mu (\omega )\omega {\left(1-{\frac {c^{2}}{v^{2}n^{2}(\omega )}}\right)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>E</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>ω<!-- ω --></mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>4</mn> <mi>π<!-- π --></mi> </mrow> </mfrac> </mrow> <mi>μ<!-- μ --></mi> <mo stretchy="false">(</mo> <mi>ω<!-- ω --></mi> <mo stretchy="false">)</mo> <mi>ω<!-- ω --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <msup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>ω<!-- ω --></mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d^{2}E}{dx\,d\omega }}={\frac {q^{2}}{4\pi }}\mu (\omega )\omega {\left(1-{\frac {c^{2}}{v^{2}n^{2}(\omega )}}\right)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8fad75897691866f3969bd76e3123cddf5912131" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:35.108ex; height:6.509ex;" alt="{\displaystyle {\frac {d^{2}E}{dx\,d\omega }}={\frac {q^{2}}{4\pi }}\mu (\omega )\omega {\left(1-{\frac {c^{2}}{v^{2}n^{2}(\omega )}}\right)}}"></span> </p><p>The Frank–Tamm formula describes the amount of energy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> emitted from Cherenkov radiation, per unit length traveled <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> and per frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω<!-- ω --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span>. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu (\omega )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ<!-- μ --></mi> <mo stretchy="false">(</mo> <mi>ω<!-- ω --></mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu (\omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b8e1f91fc5d2f2d87892247dde5e44bb675e4c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.657ex; height:2.843ex;" alt="{\displaystyle \mu (\omega )}"></span> is the <a href="/wiki/Permeability_(electromagnetism)" title="Permeability (electromagnetism)">permeability</a> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n(\omega )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo stretchy="false">(</mo> <mi>ω<!-- ω --></mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n(\omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cd5670e77c35314472dcea1ba1651b58538d0d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.65ex; height:2.843ex;" alt="{\displaystyle n(\omega )}"></span> is the <a href="/wiki/Refractive_index" title="Refractive index">index of refraction</a> of the material the charged particle moves through. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.07ex; height:2.009ex;" alt="{\displaystyle q}"></span> is the <a href="/wiki/Electric_charge" title="Electric charge">electric charge</a> of the particle, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> is the speed of the particle, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a> in vacuum. </p><p>Unlike <a href="/wiki/Fluorescence" title="Fluorescence">fluorescence</a> or <a href="/wiki/Stimulated_emission" title="Stimulated emission">emission</a> <a href="/wiki/Electromagnetic_spectrum" title="Electromagnetic spectrum">spectra</a> that have characteristic spectral peaks, Cherenkov radiation is continuous. Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency. That is, higher frequencies (shorter <a href="/wiki/Wavelength" title="Wavelength">wavelengths</a>) are more intense in Cherenkov radiation. This is why visible Cherenkov radiation is observed to be brilliant blue. In fact, most Cherenkov radiation is in the <a href="/wiki/Ultraviolet" title="Ultraviolet">ultraviolet</a> spectrum—it is only with sufficiently accelerated charges that it even becomes visible; the sensitivity of the human eye peaks at green, and is very low in the violet portion of the spectrum. </p><p>There is a cut-off frequency above which the equation <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos \theta =1/(n\beta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mo>=</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mi>β<!-- β --></mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \theta =1/(n\beta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf544395c40d2c43164ce5e9559b034b92974258" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.548ex; height:2.843ex;" alt="{\displaystyle \cos \theta =1/(n\beta )}"></span> can no longer be satisfied. The <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> varies with frequency (and hence with wavelength) in such a way that the intensity cannot continue to increase at ever shorter wavelengths, even for very relativistic particles (where <i>v</i>/<i><a href="/wiki/Speed_of_light" title="Speed of light">c</a></i> is close to 1). At <a href="/wiki/X-ray" title="X-ray">X-ray</a> frequencies, the refractive index becomes less than 1 (note that in media, the phase velocity may exceed <i>c</i> without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as <a href="/wiki/Gamma_ray" title="Gamma ray">gamma rays</a>) would be observed. However, X-rays can be generated at special frequencies just below the frequencies corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonant frequency <style data-mw-deduplicate="TemplateStyles:r1033199720">.mw-parser-output div.crossreference{padding-left:0}</style><style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><span role="note" class="hatnote navigation-not-searchable crossreference">(see <i><a href="/wiki/Kramers%E2%80%93Kronig_relation" class="mw-redirect" title="Kramers–Kronig relation">Kramers–Kronig relation</a></i> and <i><a href="/wiki/Anomalous_dispersion" class="mw-redirect" title="Anomalous dispersion">Anomalous dispersion</a></i>)</span>. </p><p>As in sonic booms and bow shocks, the angle of the shock <a href="/wiki/Cone_(geometry)" class="mw-redirect" title="Cone (geometry)">cone</a> is directly related to the velocity of the disruption. The Cherenkov angle is zero at the threshold velocity for the emission of Cherenkov radiation. The angle takes on a maximum as the particle speed approaches the speed of light. Hence, observed angles of incidence can be used to compute the direction and speed of a Cherenkov radiation-producing charge. </p><p>Cherenkov radiation can be generated in the eye by charged particles hitting the <a href="/wiki/Vitreous_humour" class="mw-redirect" title="Vitreous humour">vitreous humour</a>, giving the impression of flashes,<sup id="cite_ref-Tendler_Hartford_Jermyn_LaRochelle_2020_pp._422–429_22-0" class="reference"><a href="#cite_note-Tendler_Hartford_Jermyn_LaRochelle_2020_pp._422–429-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> as in <a href="/wiki/Cosmic_ray_visual_phenomena" title="Cosmic ray visual phenomena">cosmic ray visual phenomena</a> and possibly some observations of <a href="/wiki/Criticality_accident" title="Criticality accident">criticality accidents</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Uses">Uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=10" title="Edit section: Uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Detection_of_labelled_biomolecules">Detection of labelled biomolecules</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=11" title="Edit section: Detection of labelled biomolecules"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cherenkov radiation is widely used to facilitate the detection of small amounts and low concentrations of <a href="/wiki/Biomolecule" title="Biomolecule">biomolecules</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Radioactive atoms such as phosphorus-32 are readily introduced into biomolecules by enzymatic and synthetic means and subsequently may be easily detected in small quantities for the purpose of elucidating biological pathways and in characterizing the interaction of biological molecules such as affinity constants and dissociation rates. </p> <div class="mw-heading mw-heading3"><h3 id="Medical_imaging_of_radioisotopes_and_external_beam_radiotherapy">Medical imaging of radioisotopes and external beam radiotherapy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=12" title="Edit section: Medical imaging of radioisotopes and external beam radiotherapy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cherenkov-breast.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Cherenkov-breast.png/220px-Cherenkov-breast.png" decoding="async" width="220" height="186" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Cherenkov-breast.png/330px-Cherenkov-breast.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Cherenkov-breast.png/440px-Cherenkov-breast.png 2x" data-file-width="472" data-file-height="400" /></a><figcaption>Cherenkov light emission imaged from the chest wall of a patient undergoing whole breast irradiation, using 6 <a href="/wiki/MeV" class="mw-redirect" title="MeV">MeV</a> beam from a linear accelerator in radiotherapy.</figcaption></figure> <p>More recently, Cherenkov light has been used to image substances in the body.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> These discoveries have led to intense interest around the idea of using this light signal to quantify and/or detect radiation in the body, either from internal sources such as injected <a href="/wiki/Radiopharmaceutical" title="Radiopharmaceutical">radiopharmaceuticals</a> or from external beam radiotherapy in oncology. Radioisotopes such as the <a href="/wiki/Positron_emission" title="Positron emission">positron</a> emitters <a href="/wiki/Fluorine-18" title="Fluorine-18"><sup>18</sup>F</a> and <a href="/wiki/Nitrogen-13" title="Nitrogen-13"><sup>13</sup>N</a> or <a href="/wiki/Beta_decay#.CE.B2.E2.88.92_decay" title="Beta decay">beta</a> emitters <a href="/wiki/Phosphorus-32" title="Phosphorus-32"><sup>32</sup>P</a> or <a href="/wiki/Yttrium-90" title="Yttrium-90"><sup>90</sup>Y</a> have measurable Cherenkov emission<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> and isotopes <sup>18</sup>F and <a href="/wiki/Iodine-131" title="Iodine-131"><sup>131</sup>I</a> have been imaged in humans for diagnostic value demonstration.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p><p>External beam radiation therapy has been shown to induce a substantial amount of Cherenkov light in the tissue being treated, due to electron beams or photon beams with energy in the 6 MV to 18 MV ranges. The secondary electrons induced by these high energy x-rays result in the Cherenkov light emission, where the detected signal can be imaged at the entry and exit surfaces of the tissue.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> The Cherenkov light emitted from patient's tissue during radiation therapy is a very low light level signal but can be detected by specially designed cameras that synchronize their acquisition to the linear accelerator pulses.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> The ability to see this signal shows the shape of the radiation beam as it is incident upon the tissue in real time.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Nuclear_reactors">Nuclear reactors</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=13" title="Edit section: Nuclear reactors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:TrigaReactorCore.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/TrigaReactorCore.jpeg/220px-TrigaReactorCore.jpeg" decoding="async" width="220" height="162" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/68/TrigaReactorCore.jpeg/330px-TrigaReactorCore.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/68/TrigaReactorCore.jpeg/440px-TrigaReactorCore.jpeg 2x" data-file-width="550" data-file-height="405" /></a><figcaption>Cherenkov radiation in a <a href="/wiki/TRIGA" title="TRIGA">TRIGA</a> <a href="/wiki/Open_pool_reactor" class="mw-redirect" title="Open pool reactor">reactor pool</a>.</figcaption></figure> <p>Cherenkov radiation is used to detect high-energy charged particles. In <a href="/wiki/Open_pool_reactor" class="mw-redirect" title="Open pool reactor">open pool reactors</a>, <a href="/wiki/Beta_particles" class="mw-redirect" title="Beta particles">beta particles</a> (high-energy electrons) are released as the <a href="/wiki/Fission_products" class="mw-redirect" title="Fission products">fission products</a> decay. The glow continues after the chain reaction stops, dimming as the shorter-lived products decay. Similarly, Cherenkov radiation can characterize the remaining <a href="/wiki/Radioactivity" class="mw-redirect" title="Radioactivity">radioactivity</a> of spent fuel rods. This phenomenon is used to verify the presence of spent nuclear fuel in spent fuel pools for nuclear safeguards purposes.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Astrophysics_experiments">Astrophysics experiments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=14" title="Edit section: Astrophysics experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When a high-energy (<a href="/wiki/TeV" class="mw-redirect" title="TeV">TeV</a>) <a href="/wiki/Gamma_photon" class="mw-redirect" title="Gamma photon">gamma photon</a> or <a href="/wiki/Cosmic_ray" title="Cosmic ray">cosmic ray</a> interacts with the <a href="/wiki/Earth%27s_atmosphere" class="mw-redirect" title="Earth's atmosphere">Earth's atmosphere</a>, it may produce an electron–<a href="/wiki/Positron" title="Positron">positron</a> <a href="/wiki/Pair_production" title="Pair production">pair</a> with enormous velocities. The Cherenkov radiation emitted in the atmosphere by these charged particles is used to determine the direction and energy of the cosmic ray or gamma ray, which is used for example in the <a href="/wiki/IACT" title="IACT">Imaging Atmospheric Cherenkov Technique</a> (<a href="/wiki/IACT" title="IACT">IACT</a>), by experiments such as <a href="/wiki/VERITAS" title="VERITAS">VERITAS</a>, <a href="/wiki/H.E.S.S." class="mw-redirect" title="H.E.S.S.">H.E.S.S.</a>, <a href="/wiki/MAGIC_(telescope)" title="MAGIC (telescope)">MAGIC</a>. Cherenkov radiation emitted in tanks filled with water by those charged particles reaching earth is used for the same goal by the Extensive Air Shower experiment <a href="/wiki/High_Altitude_Water_Cherenkov_Experiment" title="High Altitude Water Cherenkov Experiment">HAWC</a>, the <a href="/wiki/Pierre_Auger_Observatory" title="Pierre Auger Observatory">Pierre Auger Observatory</a> and other projects. Similar methods are used in very large <a href="/wiki/Neutrino" title="Neutrino">neutrino</a> detectors, such as the <a href="/wiki/Super-Kamiokande" title="Super-Kamiokande">Super-Kamiokande</a>, the <a href="/wiki/Sudbury_Neutrino_Observatory" title="Sudbury Neutrino Observatory">Sudbury Neutrino Observatory (SNO)</a> and <a href="/wiki/IceCube" class="mw-redirect" title="IceCube">IceCube</a>. Other projects operated in the past applying related techniques, such as <a href="/wiki/STACEE" title="STACEE">STACEE</a>, a former solar tower refurbished to work as a non-imaging Cherenkov observatory, which was located in <a href="/wiki/New_Mexico" title="New Mexico">New Mexico</a>. </p><p>Astrophysics observatories using the Cherenkov technique to measure air showers are key to determining the properties of astronomical objects that emit very-high-energy gamma rays, such as <a href="/wiki/Supernova_remnant" title="Supernova remnant">supernova remnants</a> and <a href="/wiki/Blazar" title="Blazar">blazars</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Particle_physics_experiments">Particle physics experiments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=15" title="Edit section: Particle physics experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Cherenkov_detector" title="Cherenkov detector">Cherenkov detector</a> and <a href="/wiki/Ring_imaging_Cherenkov_detector" class="mw-redirect" title="Ring imaging Cherenkov detector">Ring imaging Cherenkov detector</a></div> <p>Cherenkov radiation is commonly used in experimental <a href="/wiki/Particle_physics" title="Particle physics">particle physics</a> for particle identification. One could measure (or put limits on) the <a href="/wiki/Velocity" title="Velocity">velocity</a> of an electrically charged elementary particle by the properties of the Cherenkov light it emits in a certain medium. If the <a href="/wiki/Momentum" title="Momentum">momentum</a> of the particle is measured independently, one could compute the <a href="/wiki/Mass" title="Mass">mass</a> of the particle by its momentum and velocity (see <a href="/wiki/Four-momentum" title="Four-momentum">four-momentum</a>), and hence identify the particle. </p><p>The simplest type of particle identification device based on a Cherenkov radiation technique is the threshold counter, which answers whether the velocity of a charged particle is lower or higher than a certain value (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{0}=c/n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{0}=c/n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/940cb3f024408b218db75ebce68da24a80e06560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.844ex; height:2.843ex;" alt="{\displaystyle v_{0}=c/n}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is the <a href="/wiki/Speed_of_light" title="Speed of light">speed of light</a>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span> is the <a href="/wiki/Refractive_index" title="Refractive index">refractive index</a> of the medium) by looking at whether this particle emits Cherenkov light in a certain medium. Knowing particle momentum, one can separate particles lighter than a certain threshold from those heavier than the threshold. </p><p>The most advanced type of a detector is the RICH, or <a href="/wiki/Ring-imaging_Cherenkov_detector" title="Ring-imaging Cherenkov detector">ring-imaging Cherenkov detector</a>, developed in the 1980s. In a RICH detector, a cone of Cherenkov light is produced when a high-speed charged particle traverses a suitable medium, often called radiator. This light cone is detected on a position sensitive planar photon detector, which allows reconstructing a ring or disc, whose radius is a measure for the Cherenkov emission angle. Both focusing and proximity-focusing detectors are in use. In a focusing RICH detector, the photons are collected by a spherical mirror and focused onto the photon detector placed at the focal plane. The result is a circle with a radius independent of the emission point along the particle track. This scheme is suitable for low refractive index radiators—i.e. gases—due to the larger radiator length needed to create enough photons. In the more compact proximity-focusing design, a thin radiator volume emits a cone of Cherenkov light which traverses a small distance—the proximity gap—and is detected on the photon detector plane. The image is a ring of light whose radius is defined by the Cherenkov emission angle and the proximity gap. The ring thickness is determined by the thickness of the radiator. An example of a proximity gap RICH detector is the High Momentum Particle Identification Detector (HMPID),<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> a detector currently under construction for ALICE (<a href="/wiki/A_Large_Ion_Collider_Experiment" class="mw-redirect" title="A Large Ion Collider Experiment">A Large Ion Collider Experiment</a>), one of the six experiments at the LHC (<a href="/wiki/Large_Hadron_Collider" title="Large Hadron Collider">Large Hadron Collider</a>) at <a href="/wiki/CERN" title="CERN">CERN</a>. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=16" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Askaryan_radiation" title="Askaryan radiation">Askaryan radiation</a>, similar radiation produced by fast uncharged particles</li> <li><a href="/wiki/Colors_of_noise#Blue_noise" title="Colors of noise">Blue noise</a></li> <li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a>, radiation produced when charged particles are decelerated by other charged particles</li> <li><a href="/wiki/Faster-than-light" title="Faster-than-light">Faster-than-light</a>, about conjectural propagation of information or matter faster than the speed of light</li> <li><a href="/wiki/Frank%E2%80%93Tamm_formula" title="Frank–Tamm formula">Frank–Tamm formula</a>, giving the spectrum of Cherenkov radiation</li> <li><a href="/wiki/Light_echo" title="Light echo">Light echo</a></li> <li><a href="/wiki/List_of_light_sources" title="List of light sources">List of light sources</a></li> <li><a href="/wiki/Nonradiation_condition" title="Nonradiation condition">Non-radiation condition</a></li> <li><a href="/wiki/Radioluminescence" title="Radioluminescence">Radioluminescence</a></li> <li><a href="/wiki/Tachyon" title="Tachyon">Tachyon</a></li> <li><a href="/wiki/Transition_radiation" title="Transition radiation">Transition radiation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Citations">Citations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=17" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output 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New York: <a href="/wiki/Pergamon_Press" title="Pergamon Press">Pergamon Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-030275-1" title="Special:BookSources/978-0-08-030275-1"><bdi>978-0-08-030275-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Electrodynamics+of+Continuous+Media&rft.place=New+York&rft.pub=Pergamon+Press&rft.date=1984&rft.isbn=978-0-08-030275-1&rft.aulast=Landau&rft.aufirst=L.+D.&rft.au=Liftshitz%2C+E.+M.&rft.au=Pitaevskii%2C+L.+P.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felectrodynamicso0000land&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACherenkov+radiation" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJelley1958" class="citation book cs1">Jelley, J. V. (1958). <a rel="nofollow" class="external text" href="https://archive.org/details/cerenkovradiatio030980mbp"><i>Cerenkov Radiation and Its Applications</i></a>. London: <a href="/wiki/Pergamon_Press" title="Pergamon Press">Pergamon Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cerenkov+Radiation+and+Its+Applications&rft.place=London&rft.pub=Pergamon+Press&rft.date=1958&rft.aulast=Jelley&rft.aufirst=J.+V.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcerenkovradiatio030980mbp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACherenkov+radiation" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmithPurcell1953" class="citation journal cs1">Smith, S. J.; Purcell, E. M. (1953). "Visible Light from Localized Surface Charges Moving across a Grating". <i><a href="/wiki/Physical_Review" title="Physical Review">Physical Review</a></i>. <b>92</b> (4): 1069. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1953PhRv...92.1069S">1953PhRv...92.1069S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRev.92.1069">10.1103/PhysRev.92.1069</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review&rft.atitle=Visible+Light+from+Localized+Surface+Charges+Moving+across+a+Grating&rft.volume=92&rft.issue=4&rft.pages=1069&rft.date=1953&rft_id=info%3Adoi%2F10.1103%2FPhysRev.92.1069&rft_id=info%3Abibcode%2F1953PhRv...92.1069S&rft.aulast=Smith&rft.aufirst=S.+J.&rft.au=Purcell%2C+E.+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACherenkov+radiation" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cherenkov_radiation&action=edit&section=19" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Cherenkov_radiation" class="extiw" title="commons:Category:Cherenkov radiation">Cherenkov radiation</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=Sb9i-toCcwg"><span class="plainlinks">Nuclear Reactor start up</span></a> on <a href="/wiki/YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a></li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=CYcesh3uHb4"><span class="plainlinks">Nuclear Reactor starting up (alternate link)</span></a> on <a href="/wiki/YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRadović2002" class="citation journal cs1">Radović, Andrija (2002). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160304081226/http://www.journaloftheoretics.com/Articles/4-4/AR.pdf">"Cherenkov's Particles as Magnetons"</a> <span class="cs1-format">(PDF)</span>. <i>Journal of Theoretics</i>. <b>4</b> (4): 1–5. Archived from <a rel="nofollow" class="external text" href="http://www.journaloftheoretics.com/Articles/4-4/AR.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2016-03-04<span class="reference-accessdate">. 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style="padding:0 0.25em"> <ul><li><a href="/wiki/Acoustic_radiation_force" title="Acoustic radiation force">Acoustic radiation force</a></li> <li><a href="/wiki/Infrared" title="Infrared">Infrared</a></li> <li><a href="/wiki/Light" title="Light">Light</a></li> <li><a href="/wiki/Starlight" title="Starlight">Starlight</a></li> <li><a href="/wiki/Sunlight" title="Sunlight">Sunlight</a></li> <li><a href="/wiki/Microwave" title="Microwave">Microwave</a></li> <li><a href="/wiki/Radio_wave" title="Radio wave">Radio waves</a></li> <li><a href="/wiki/Ultraviolet" title="Ultraviolet">Ultraviolet</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Ionizing_radiation" title="Ionizing radiation">Ionizing radiation</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Radioactive_decay" title="Radioactive decay">Radioactive decay</a></li> <li><a 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<li><a href="/wiki/Radionuclide" title="Radionuclide">Radioactive materials</a></li> <li><a href="/wiki/X-ray" title="X-ray">X-ray</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Earth%27s_energy_budget" title="Earth's energy budget">Earth's energy budget</a></li> <li><a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li> <li><a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li> <li><a href="/wiki/Thermal_radiation" title="Thermal radiation">Thermal radiation</a></li> <li><a href="/wiki/Black-body_radiation" title="Black-body radiation">Black-body radiation</a></li> <li><a href="/wiki/Particle_radiation" title="Particle radiation">Particle radiation</a></li> <li><a href="/wiki/Gravitational_radiation" class="mw-redirect" title="Gravitational radiation">Gravitational radiation</a></li> <li><a href="/wiki/Cosmic_background_radiation" title="Cosmic background radiation">Cosmic background radiation</a></li> <li><a class="mw-selflink selflink">Cherenkov radiation</a></li> <li><a href="/wiki/Askaryan_radiation" title="Askaryan radiation">Askaryan radiation</a></li> <li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Unruh_radiation" class="mw-redirect" title="Unruh radiation">Unruh radiation</a></li> <li><a href="/wiki/Dark_radiation" title="Dark radiation">Dark radiation</a></li> <li><a href="/wiki/Radiation_exposure" title="Radiation exposure">Radiation exposure</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Radiation <br />and health</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Radiation syndrome <ul><li><a href="/wiki/Acute_radiation_syndrome" title="Acute radiation syndrome">acute</a></li> <li><a href="/wiki/Chronic_radiation_syndrome" title="Chronic radiation syndrome">chronic</a></li></ul></li> <li><a href="/wiki/Health_physics" title="Health physics">Health physics</a></li> <li><a href="/wiki/Dosimetry" title="Dosimetry">Dosimetry</a></li> <li><a href="/wiki/Electromagnetic_radiation_and_health" title="Electromagnetic radiation and health">Electromagnetic radiation and health</a></li> <li><a href="/wiki/Laser_safety" title="Laser safety">Laser safety</a></li> <li><a href="/wiki/Lasers_and_aviation_safety" title="Lasers and aviation safety">Lasers and aviation safety</a></li> <li><a href="/wiki/Medical_radiography" class="mw-redirect" title="Medical radiography">Medical radiography</a></li> <li><a href="/wiki/Radiation_protection" title="Radiation protection">Radiation protection</a></li> <li><a href="/wiki/Radiation_therapy" title="Radiation therapy">Radiation therapy</a></li> <li><a href="/wiki/Radiation_damage" title="Radiation damage">Radiation damage</a></li> <li><a href="/wiki/Radioactivity_in_the_life_sciences" title="Radioactivity in the life sciences">Radioactivity in the life sciences</a></li> <li><a href="/wiki/Radioactive_contamination" title="Radioactive contamination">Radioactive contamination</a></li> <li><a href="/wiki/Radiobiology" title="Radiobiology">Radiobiology</a></li> <li><a href="/wiki/Sievert" title="Sievert">Biological dose units and quantities</a></li> <li><a href="/wiki/Wireless_device_radiation_and_health" title="Wireless device radiation and health">Wireless device radiation and health</a></li> <li><a href="/wiki/Wireless_electronic_devices_and_health" class="mw-redirect" title="Wireless electronic devices and health">Wireless electronic devices and health</a></li> <li><a href="/wiki/Heat_transfer" title="Heat transfer">Radiation heat-transfer</a></li> <li><a href="/wiki/Linear_energy_transfer" title="Linear energy transfer">Linear energy transfer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Radiation incidents</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_civilian_radiation_accidents" title="List of civilian radiation accidents">List of civilian radiation accidents</a></li> <li><a href="/wiki/1996_San_Juan_de_Dios_radiotherapy_accident" title="1996 San Juan de Dios radiotherapy accident">1996 Costa Rica accident</a></li> <li><a href="/wiki/Goi%C3%A2nia_accident" title="Goiânia accident">1987 Goiânia accident</a></li> <li><a href="/wiki/1984_Moroccan_radiation_accident" title="1984 Moroccan radiation accident">1984 Moroccan accident</a></li> <li><a href="/wiki/1990_Clinic_of_Zaragoza_radiotherapy_accident" class="mw-redirect" title="1990 Clinic of Zaragoza radiotherapy accident">1990 Zaragoza accident</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related articles</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Half-life" title="Half-life">Half-life</a></li> <li><a href="/wiki/Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li> <li><a href="/wiki/Radioactive_source" title="Radioactive source">Radioactive source</a></li> <li><a href="/wiki/Radiation_hardening" title="Radiation hardening">Radiation hardening</a></li> <li><a href="/wiki/Havana_syndrome" title="Havana syndrome">Havana syndrome</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><div role="note" class="hatnote navigation-not-searchable selfref">See also the categories <a href="/wiki/Category:Radiation_effects" title="Category:Radiation effects">Radiation effects</a>, <a href="/wiki/Category:Radioactivity" title="Category:Radioactivity">Radioactivity</a>, <a href="/wiki/Category:Radiobiology" title="Category:Radiobiology">Radiobiology</a>, and <a href="/wiki/Category:Radiation_protection" title="Category:Radiation protection">Radiation protection</a></div></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" 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