{"id":40756,"date":"2022-09-08T11:26:09","date_gmt":"2022-09-08T11:26:09","guid":{"rendered":"https:\/\/www.clpu.es\/?post_type=publications&p=40756"},"modified":"2025-02-03T11:26:31","modified_gmt":"2025-02-03T11:26:31","slug":"liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations","status":"publish","type":"publications","link":"https:\/\/www.clpu.es\/en\/publications\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\/","title":{"rendered":"Liouville Theory for fully analytic studies of transverse beam dynamics in laser-plasma ion accelerations"},"content":{"rendered":"

The exact solution of the Liouville equation expressed in terms of exponential operators can describe the phase space evolution of particle beams in transport lines. In this paper, we generalize the solution of the above equation for the case of beam losses induced by apertures and for particle beams with large spreads in the momentum space. We discuss the applicability of such approach to ion beams produced by high-intensity lasers interacting with critical plasmas, based on the comparison between theoretical findings and measurements.<\/p>\n","protected":false},"author":1,"featured_media":0,"template":"","meta":{"_acf_changed":false,"inline_featured_image":false},"a_os":[36],"class_list":["post-40756","publications","type-publications","status-publish","hentry","a_os-36","entry"],"acf":[],"yoast_head":"\nLiouville Theory for fully analytic studies of transverse beam dynamics in laser-plasma ion accelerations - CLPU<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.clpu.es\/publications\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Liouville Theory for fully analytic studies of transverse beam dynamics in laser-plasma ion accelerations - CLPU\" \/>\n<meta property=\"og:description\" content=\"The exact solution of the Liouville equation expressed in terms of exponential operators can describe the phase space evolution of particle beams in transport lines. In this paper, we generalize the solution of the above equation for the case of beam losses induced by apertures and for particle beams with large spreads in the momentum… Continue reading Liouville Theory for fully analytic studies of transverse beam dynamics in laser-plasma ion accelerations\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.clpu.es\/publications\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\/\" \/>\n<meta property=\"og:site_name\" content=\"CLPU\" \/>\n<meta property=\"article:modified_time\" content=\"2025-02-03T11:26:31+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/www.clpu.es\\\/publications\\\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\\\/\",\"url\":\"https:\\\/\\\/www.clpu.es\\\/publications\\\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\\\/\",\"name\":\"Liouville Theory for fully analytic studies of transverse beam dynamics in laser-plasma ion accelerations - CLPU\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.clpu.es\\\/#website\"},\"datePublished\":\"2022-09-08T11:26:09+00:00\",\"dateModified\":\"2025-02-03T11:26:31+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/www.clpu.es\\\/publications\\\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/www.clpu.es\\\/publications\\\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/www.clpu.es\\\/publications\\\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Portada\",\"item\":\"https:\\\/\\\/www.clpu.es\\\/en\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Publications\",\"item\":\"https:\\\/\\\/www.clpu.es\\\/publications\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Liouville Theory for fully analytic studies of transverse beam dynamics in laser-plasma ion accelerations\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/www.clpu.es\\\/#website\",\"url\":\"https:\\\/\\\/www.clpu.es\\\/\",\"name\":\"CLPU\",\"description\":\"Centro de L\u00e1seres Pulsados\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/www.clpu.es\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Liouville Theory for fully analytic studies of transverse beam dynamics in laser-plasma ion accelerations - CLPU","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.clpu.es\/publications\/liouville-theory-for-fully-analytic-studies-of-transverse-beam-dynamics-in-laser-plasma-ion-accelerations\/","og_locale":"en_US","og_type":"article","og_title":"Liouville Theory for fully analytic studies of transverse beam dynamics in laser-plasma ion accelerations - CLPU","og_description":"The exact solution of the Liouville equation expressed in terms of exponential operators can describe the phase space evolution of particle beams in transport lines. 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